rfc9935.original.xml   rfc9935.xml 
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<!ENTITY zwsp "&#8203;"> <!ENTITY zwsp "&#8203;">
<!ENTITY nbhy "&#8209;"> <!ENTITY nbhy "&#8209;">
<!ENTITY wj "&#8288;"> <!ENTITY wj "&#8288;">
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<front> <front>
<title abbrev="ML-KEM in Certificates">Internet X.509 Public Key Infrastruct ure - Algorithm Identifiers for the Module-Lattice-Based Key-Encapsulation Mecha nism (ML-KEM)</title> <title abbrev="ML-KEM in Certificates">Internet X.509 Public Key Infrastruct ure - Algorithm Identifiers for the Module-Lattice-Based Key-Encapsulation Mecha nism (ML-KEM)</title>
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-kyber-certificates <!-- [rfced] We note that this document does not seem to describe ML-KEM as an a
-11"/> lgorithm. Is this correct?
Original:
Internet X.509 Public Key Infrastructure - Algorithm Identifiers
for the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM)
Perhaps:
Conventions for Using ML-KEM Algorithms in the Internet X.509
Public Key Infrastructure
-->
<seriesInfo name="RFC" value="9935"/>
<author initials="S." surname="Turner" fullname="Sean Turner"> <author initials="S." surname="Turner" fullname="Sean Turner">
<organization>sn3rd</organization> <organization>sn3rd</organization>
<address> <address>
<email>sean@sn3rd.com</email> <email>sean@sn3rd.com</email>
</address> </address>
</author> </author>
<author initials="P." surname="Kampanakis" fullname="Panos Kampanakis"> <author initials="P." surname="Kampanakis" fullname="Panos Kampanakis">
<organization>AWS</organization> <organization>AWS</organization>
<address> <address>
<email>kpanos@amazon.com</email> <email>kpanos@amazon.com</email>
skipping to change at line 39 skipping to change at line 49
<address> <address>
<email>jakemas@amazon.com</email> <email>jakemas@amazon.com</email>
</address> </address>
</author> </author>
<author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan"> <author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan">
<organization>Cloudflare</organization> <organization>Cloudflare</organization>
<address> <address>
<email>bas@westerbaan.name</email> <email>bas@westerbaan.name</email>
</address> </address>
</author> </author>
<date year="2025" month="July" day="16"/> <date year="2026" month="February"/>
<area>SEC</area> <area>SEC</area>
<workgroup>LAMPS</workgroup> <workgroup>lamps</workgroup>
<keyword>ML-KEM Kyber KEM Certificate X.509 PKIX</keyword> <keyword>ML-KEM</keyword>
<abstract> <keyword>Kyber</keyword>
<?line 111?> <keyword>KEM</keyword>
<keyword>Certificate</keyword>
<keyword>X.509</keyword>
<keyword>PKIX</keyword>
<abstract>
<t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) is a <t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) is a
quantum-resistant key-encapsulation mechanism (KEM). This document quantum-resistant Key Encapsulation Mechanism (KEM). This document specifies the
specifies the conventions for using the ML-KEM in X.509 Public Key conventions for using the ML-KEM in X.509 Public Key Infrastructure. The conven
Infrastructure. The conventions for the subject public keys and tions for the subject public keys and
private keys are also specified.</t> private keys are also specified.</t>
</abstract> </abstract>
<note removeInRFC="true">
<name>About This Document</name>
<t>
The latest revision of this draft can be found at <eref target="https://
lamps-wg.github.io/kyber-certificates/#go.draft-ietf-lamps-kyber-certificates.ht
ml"/>.
Status information for this document may be found at <eref target="https
://datatracker.ietf.org/doc/draft-ietf-lamps-kyber-certificates/"/>.
</t>
<t>
Discussion of this document takes place on the
Limited Additional Mechanisms for PKIX and SMIME (lamps) Working Group m
ailing list (<eref target="mailto:spasm@ietf.org"/>),
which is archived at <eref target="https://mailarchive.ietf.org/arch/bro
wse/spasm/"/>.
Subscribe at <eref target="https://www.ietf.org/mailman/listinfo/spasm/"
/>.
</t>
<t>Source for this draft and an issue tracker can be found at
<eref target="https://github.com/lamps-wg/kyber-certificates"/>.</t>
</note>
</front> </front>
<middle> <middle>
<?line 119?>
<section anchor="introduction"> <section anchor="introduction">
<!-- [rfced] We have removed "the earlier" because it is redundant with "prior t
o". Please let us know if it is important to specify "earlier versions".
Original:
Prior to
standardization, the earlier versions of the mechanism were known as
Kyber.
Current:
Prior to
standardization, versions of the mechanism were known as Kyber.
-->
<name>Introduction</name> <name>Introduction</name>
<t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) standardi zed in <t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) standardi zed in
<xref target="FIPS203"/> is a quantum-resistant <xref target="FIPS203"/> is a quantum-resistant
key-encapsulation mechanism (KEM) standardized by the US National Institute Key Encapsulation Mechanism (KEM) standardized by the US National Institute
of Standards and Technology (NIST) PQC Project <xref target="NIST-PQC"/>. Prior of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) Project <xref
to target="NIST-PQC"/>. Prior to
standardization, the earlier versions of the mechanism were known as standardization, versions of the mechanism were known as
Kyber. ML-KEM and Kyber are not compatible. This document specifies the use Kyber. ML-KEM and Kyber are not compatible. This document specifies the use
of ML-KEM in Public Key Infrastructure X.509 (PKIX) certificates <xref target="R FC5280"/> of ML-KEM in Public Key Infrastructure using X.509 (PKIX) certificates <xref tar get="RFC5280"/>
at three security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024, using at three security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024, using
object identifiers assigned by NIST. The private key format is also object identifiers (OIDs) assigned by NIST. The private key format is also
specified.</t> specified.</t>
<section anchor="applicability-statement"> <section anchor="applicability-statement">
<name>Applicability Statement</name> <name>Applicability Statement</name>
<t>ML-KEM certificates are used in protocols where the public key is use d to <t>ML-KEM certificates are used in protocols where the public key is use d to
generate and encapsulate a shared secret used to derive a symmetric key used generate and encapsulate a shared secret used to derive a symmetric key used
to encrypt a payload; see <xref target="I-D.ietf-lamps-cms-kyber"/>. To be used in TLS, to encrypt a payload; see <xref target="RFC9936"/>. To be used in TLS,
ML-KEM certificates could only be used as end-entity identity certificates ML-KEM certificates could only be used as end-entity identity certificates
and would require significant updates to the protocol; see, for example, and would require significant updates to the protocol; for example, see
<xref target="I-D.celi-wiggers-tls-authkem"/>.</t> <xref target="I-D.celi-wiggers-tls-authkem"/>.</t>
</section> </section>
</section> </section>
<section anchor="conventions-and-definitions"> <section anchor="conventions-and-definitions">
<name>Conventions and Definitions</name> <name>Conventions and Definitions</name>
<t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14 <t>
>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECO "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>
MMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", ",
"<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be i "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
nterpreted as "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
only when, they be
appear in all capitals, as shown here.</t> interpreted as described in BCP&nbsp;14 <xref target="RFC2119"/> <xref
<?line -18?> target="RFC8174"/> when, and only when, they appear in all capitals, as
shown here.
</section> </t>
</section>
<section anchor="oids"> <section anchor="oids">
<name>Algorithm Identifiers</name> <name>Algorithm Identifiers</name>
<t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t> <t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t>
<artwork><![CDATA[ <artwork><![CDATA[
AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
SEQUENCE { SEQUENCE {
algorithm ALGORITHM-TYPE.&id({AlgorithmSet}), algorithm ALGORITHM-TYPE.&id({AlgorithmSet}),
parameters ALGORITHM-TYPE. parameters ALGORITHM-TYPE.
&Params({AlgorithmSet}{@algorithm}) OPTIONAL &Params({AlgorithmSet}{@algorithm}) OPTIONAL
} }]]></artwork>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The fields in <tt>AlgorithmIdentifier</tt> have the following meanings: </t> <t>The fields in <tt>AlgorithmIdentifier</tt> have the following meanings: </t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> identifies the cryptographic algorithm with an o <t><tt>algorithm</tt> identifies the cryptographic algorithm with an O
bject ID.</t>
identifier.</t>
</li> </li>
<li> <li>
<t><tt>parameters</tt>, which are optional, are the associated paramet ers for <t><tt>parameters</tt>, which are optional, are the associated paramet ers for
the algorithm identifier in the <tt>algorithm</tt> field.</t> the algorithm identifier in the <tt>algorithm</tt> field.</t>
</li> </li>
</ul> </ul>
<t>The <tt>AlgorithmIdentifier</tt> for an ML-KEM public key <bcp14>MUST</ bcp14> use one of the <t>The <tt>AlgorithmIdentifier</tt> for an ML-KEM public key <bcp14>MUST</ bcp14> use one of the
<tt>id-alg-ml-kem</tt> object identifiers (OID) from NIST <xref target="CSOR"/> listed below, based on the security <tt>id-alg-ml-kem</tt> OIDs from NIST <xref target="CSOR"/> listed below, based on the security
level. The <tt>parameters</tt> field of the <tt>AlgorithmIdentifier</tt> for the ML-KEM level. The <tt>parameters</tt> field of the <tt>AlgorithmIdentifier</tt> for the ML-KEM
public key <bcp14>MUST</bcp14> be absent.</t> public key <bcp14>MUST</bcp14> be absent.</t>
<artwork><![CDATA[ <artwork><![CDATA[
nistAlgorithms OBJECT IDENTIFIER ::= { joint-iso-ccitt(2) nistAlgorithms OBJECT IDENTIFIER ::= { joint-iso-ccitt(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) } nistAlgorithm(4) }
kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 } kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 }
id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 } id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 }
id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 } id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 }
id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3 } id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3 }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="pub-key"> <section anchor="pub-key">
<name>Subject Public Key Fields</name> <name>Subject Public Key Fields</name>
<t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he <t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he
<tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t> <tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t>
<artwork><![CDATA[ <artwork><![CDATA[
SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE { SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}}, algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
subjectPublicKey BIT STRING subjectPublicKey BIT STRING
} }]]></artwork>
]]></artwork>
<t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t> <t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> is the algorithm identifier and parameters for t he <t><tt>algorithm</tt> is the algorithm identifier and parameters for t he
public key (see above).</t> public key (see above).</t>
</li> </li>
<li> <li>
<t><tt>subjectPublicKey</tt> contains the byte stream of the public ke y.</t> <t><tt>subjectPublicKey</tt> contains the byte stream of the public ke y.</t>
</li> </li>
</ul> </ul>
<t>For each ML-KEM parameter set, see <xref target="tab-strengths"/>, <t>For each ML-KEM parameter set (see <xref target="tab-strengths"/>),
we define a <tt>PUBLIC-KEY</tt> ASN.1 type as follows.</t> we define a <tt>PUBLIC-KEY</tt> ASN.1 type as follows:</t>
<artwork><![CDATA[ <artwork><![CDATA[
pk-ml-kem-512 PUBLIC-KEY ::= { pk-ml-kem-512 PUBLIC-KEY ::= {
IDENTIFIER id-alg-ml-kem-512 IDENTIFIER id-alg-ml-kem-512
-- KEY no ASN.1 wrapping; 800 octets -- -- KEY no ASN.1 wrapping; 800 octets --
PARAMS ARE absent PARAMS ARE absent
CERT-KEY-USAGE { keyEncipherment } CERT-KEY-USAGE { keyEncipherment }
PRIVATE-KEY ML-KEM-512-PrivateKey -- defined in Section 6 PRIVATE-KEY ML-KEM-512-PrivateKey -- defined in Section 6
} }
pk-ml-kem-768 PUBLIC-KEY ::= { pk-ml-kem-768 PUBLIC-KEY ::= {
skipping to change at line 199 skipping to change at line 204
-- KEY no ASN.1 wrapping; 1568 octets -- -- KEY no ASN.1 wrapping; 1568 octets --
PARAMS ARE absent PARAMS ARE absent
CERT-KEY-USAGE { keyEncipherment } CERT-KEY-USAGE { keyEncipherment }
PRIVATE-KEY ML-KEM-1024-PrivateKey -- defined in Section 6 PRIVATE-KEY ML-KEM-1024-PrivateKey -- defined in Section 6
} }
ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800)) ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800))
ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184)) ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184))
ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568)) ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568))]]></artwork>
]]></artwork>
<t>When an ML-KEM public key appears outside of a <tt>SubjectPublicKeyInfo </tt> <t>When an ML-KEM public key appears outside of a <tt>SubjectPublicKeyInfo </tt>
type in an environment that uses ASN.1 encoding, it can be encoded type in an environment that uses ASN.1 encoding, it can be encoded
as an OCTET STRING by using the <tt>ML-KEM-512-PublicKey</tt>, as an OCTET STRING by using the <tt>ML-KEM-512-PublicKey</tt>,
<tt>ML-KEM-768-PublicKey</tt>, and <tt>ML-KEM-1024-PublicKey</tt> types correspo nding to <tt>ML-KEM-768-PublicKey</tt>, and <tt>ML-KEM-1024-PublicKey</tt> types correspo nding to
the correct key size.</t> the correct key size.</t>
<t><xref target="RFC5958"/> describes the Asymmetric Key Package's <tt>One AsymmetricKey</tt> <t><xref target="RFC5958"/> describes the Asymmetric Key Package's <tt>One AsymmetricKey</tt>
type for encoding asymmetric keypairs. When an ML-KEM private key or type for encoding asymmetric key pairs. When an ML-KEM private key or
keypair is encoded as a <tt>OneAsymmetricKey</tt>, it follows the description key pair is encoded as a <tt>OneAsymmetricKey</tt>, it follows the description
in <xref target="priv-key"/>.</t> in <xref target="priv-key"/>.</t>
<t>When the ML-KEM private key appears outside of an Asymmetric Key Packag e <t>When the ML-KEM private key appears outside of an Asymmetric Key Packag e
in an environment that uses ASN.1 encoding, it can be encoded using one in an environment that uses ASN.1 encoding, it can be encoded using one
of the <tt>ML-KEM-PrivateKey CHOICE</tt> formats defined in <xref target="priv-k ey"/>. The of the <tt>ML-KEM-PrivateKey CHOICE</tt> formats defined in <xref target="priv-k ey"/>. The
<tt>seed</tt> format is <bcp14>RECOMMENDED</bcp14> as it efficiently stores both the private and <tt>seed</tt> format is <bcp14>RECOMMENDED</bcp14>, as it efficiently stores bot h the private and
public key.</t> public key.</t>
<t><xref target="example-public"/> contains examples for ML-KEM public key s <t><xref target="example-public"/> contains examples for ML-KEM public key s
encoded using the textual encoding defined in <xref target="RFC7468"/>.</t> encoded using the textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="key-usage-bits"> <section anchor="key-usage-bits">
<name>Key Usage Bits</name> <name>Key Usage Bits</name>
<!-- [rfced] We have updated the parenthetical text for clarity. Please let us
know if corrections are needed.
Original:
If the
keyUsage extension is present in certificates, then keyEncipherement
MUST be the only key usage set for certificates that indicate id-alg-
ml-kem-* in SubjectPublicKeyInfo, (with * either 512, 768, or 1024.)
Current:
... (with * being one of 512, 768, or 1024.)
-->
<t>The intended application for the key is indicated in the keyUsage certi ficate <t>The intended application for the key is indicated in the keyUsage certi ficate
extension; see <xref section="4.2.1.3" sectionFormat="of" target="RFC5280"/>. If the <tt>keyUsage</tt> extension is extension; see <xref section="4.2.1.3" sectionFormat="of" target="RFC5280"/>. If the <tt>keyUsage</tt> extension is
present in certificates, then <tt>keyEncipherement</tt> <bcp14>MUST</bcp14> be t he only key usage set present in certificates, then <tt>keyEncipherement</tt> <bcp14>MUST</bcp14> be t he only key usage set
for certificates that indicate <tt>id-alg-ml-kem-*</tt> in <tt>SubjectPublicKeyI nfo</tt>, for certificates that indicate <tt>id-alg-ml-kem-*</tt> in <tt>SubjectPublicKeyI nfo</tt>,
(with <tt>*</tt> either 512, 768, or 1024.)</t> (with <tt>*</tt> being one of 512, 768, or 1024.)</t>
</section> </section>
<section anchor="priv-key"> <section anchor="priv-key">
<name>Private Key Format</name> <name>Private Key Format</name>
<t><xref target="FIPS203"/> specifies two formats for an ML-KEM private ke y: a 64-octet <t><xref target="FIPS203"/> specifies two formats for an ML-KEM private ke y: a 64-octet
seed and an (expanded) private key, which is referred to as the seed and an (expanded) private key, which is referred to as the
decapsulation key. The expanded private key (and public key) decapsulation key. The expanded private key (and public key)
is computed from the seed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) is computed from the seed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16)
using the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em >. using the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em >.
If the expanded private key is generated without exporting the seed, If the expanded private key is generated without exporting the seed,
<tt>ML-KEM.KeyGen()</tt> (algorithm 19), which combines seed generation with <tt>ML-KEM.KeyGen()</tt> (algorithm 19) is used; it combines seed generation wit
<tt>ML-KEM.KeyGen_internal(d,z)</tt>, is used.</t> h
<t>A keypair is generated by sampling 64 octets uniformly at random <tt>ML-KEM.KeyGen_internal(d,z)</tt>.</t>
<t>A key pair is generated by sampling 64 octets uniformly at random
for the seed (private key) from a cryptographically secure for the seed (private key) from a cryptographically secure
pseudorandom number generator (CSPRNGs). The public key can then pseudorandom number generator (CSPRNG). The public key can then
be computed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> as described earlier.</t> be computed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> as described earlier.</t>
<t>"Asymmetric Key Packages" <xref target="RFC5958"/> describes how to enc ode a private <t>"Asymmetric Key Packages" <xref target="RFC5958"/> describes how to enc ode a private
key in a structure that both identifies which algorithm the private key key in a structure that both identifies which algorithm the private key
is for and allows for the public key and additional attributes about the is for and allows for the public key and additional attributes about the
key to be included as well. For illustration, the ASN.1 structure key to be included as well. For illustration, the ASN.1 structure
<tt>OneAsymmetricKey</tt> is replicated below.</t> <tt>OneAsymmetricKey</tt> is replicated below.</t>
<artwork><![CDATA[ <artwork><![CDATA[
OneAsymmetricKey ::= SEQUENCE { OneAsymmetricKey ::= SEQUENCE {
version Version, version Version,
privateKeyAlgorithm SEQUENCE { privateKeyAlgorithm SEQUENCE {
skipping to change at line 263 skipping to change at line 279
privateKey OCTET STRING (CONTAINING privateKey OCTET STRING (CONTAINING
PUBLIC-KEY.&PrivateKey({PublicKeySet} PUBLIC-KEY.&PrivateKey({PublicKeySet}
{@privateKeyAlgorithm.algorithm})), {@privateKeyAlgorithm.algorithm})),
attributes [0] Attributes OPTIONAL, attributes [0] Attributes OPTIONAL,
..., ...,
[[2: publicKey [1] BIT STRING (CONTAINING [[2: publicKey [1] BIT STRING (CONTAINING
PUBLIC-KEY.&Params({PublicKeySet} PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm}) {@privateKeyAlgorithm.algorithm})
OPTIONAL ]], OPTIONAL ]],
... ...
} }]]></artwork>
]]></artwork>
<t>For ML-KEM private keys, the privateKey field in <tt>OneAsymmetricKey</ tt> contains <t>For ML-KEM private keys, the privateKey field in <tt>OneAsymmetricKey</ tt> contains
one of the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> one of the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt>
format is a fixed 64-byte <tt>OCTET STRING</tt> (66 bytes total with the <tt>0x8 040</tt> format is a fixed 64-byte <tt>OCTET STRING</tt> (66 bytes total with the <tt>0x8 040</tt>
tag and length) for all security levels, while the <tt>expandedKey</tt> tag and length) for all security levels, while the <tt>expandedKey</tt>
and <tt>both</tt> formats vary in size by security level:</t> and <tt>both</tt> formats vary in size by security level:</t>
<artwork><![CDATA[ <artwork><![CDATA[
ML-KEM-512-PrivateKey ::= CHOICE { ML-KEM-512-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (64)), seed [0] OCTET STRING (SIZE (64)),
expandedKey OCTET STRING (SIZE (1632)), expandedKey OCTET STRING (SIZE (1632)),
both SEQUENCE { both SEQUENCE {
skipping to change at line 296 skipping to change at line 311
} }
} }
ML-KEM-1024-PrivateKey ::= CHOICE { ML-KEM-1024-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (64)), seed [0] OCTET STRING (SIZE (64)),
expandedKey OCTET STRING (SIZE (3168)), expandedKey OCTET STRING (SIZE (3168)),
both SEQUENCE { both SEQUENCE {
seed OCTET STRING (SIZE (64)), seed OCTET STRING (SIZE (64)),
expandedKey OCTET STRING (SIZE (3168)) expandedKey OCTET STRING (SIZE (3168))
} }
} }]]></artwork>
]]></artwork>
<t>The <tt>CHOICE</tt> allows three representations of the private key:</t > <t>The <tt>CHOICE</tt> allows three representations of the private key:</t >
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t>The <tt>seed</tt> format (tag [0]) contains just the 64-byte seed v alue <t>The <tt>seed</tt> format (tag [0]) contains just the 64-byte seed v alue
from which both the expanded private key and public key can be from which both the expanded private key and public key can be
derived using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using derived using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using
the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>.</t> the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>.</t>
</li> </li>
<li> <li>
<t>The <tt>expandedKey</tt> format contains the expanded private key <t>The <tt>expandedKey</tt> format contains the expanded private key
skipping to change at line 323 skipping to change at line 337
<t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing <t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing
for interoperability; some may want to use and retain the seed and for interoperability; some may want to use and retain the seed and
others may only support expanded private keys.</t> others may only support expanded private keys.</t>
</li> </li>
</ul> </ul>
<t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure <t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure
with the appropriate OID as defined in <xref target="oids"/>.</t> with the appropriate OID as defined in <xref target="oids"/>.</t>
<t>The publicKey field contains the byte stream of the public key. If <t>The publicKey field contains the byte stream of the public key. If
present, the <tt>publicKey</tt> field will hold the encoded public key as present, the <tt>publicKey</tt> field will hold the encoded public key as
defined in <xref target="pub-key"/>.</t> defined in <xref target="pub-key"/>.</t>
<!-- [rfced] Please review whether any of the notes in this document
should be in the <aside> element. It is defined as "a container for
content that is semantically less important or tangential to the
content that surrounds it" (https://authors.ietf.org/en/rfcxml-vocabulary#aside)
.
-->
<t>NOTE: While the private key can be stored in multiple formats, the seed -only <t>NOTE: While the private key can be stored in multiple formats, the seed -only
format is <bcp14>RECOMMENDED</bcp14> as it is the most compact representation. B oth the format is <bcp14>RECOMMENDED</bcp14>, as it is the most compact representation. Both the
expanded private key and the public key can be deterministically derived expanded private key and the public key can be deterministically derived
from the seed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using th e from the seed using <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using th e
first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>. Altern atively, first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>. Altern atively,
the public key can be extracted from the expanded private key. While the public key can be extracted from the expanded private key. While
the <tt>publicKey</tt> field and the <tt>publicKey</tt> field and
<tt>expandedKey</tt> format are technically redundant when using the seed-only f ormat, <tt>expandedKey</tt> format are technically redundant when using the seed-only f ormat,
they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during import operations.</t> they <bcp14>MAY</bcp14> be included to enable key pair consistency checks during import operations.</t>
<t>When parsing the private key, the ASN.1 tag explicitly indicates which <t>When parsing the private key, the ASN.1 tag explicitly indicates which
variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt> variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt>
(raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and (raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and
<tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any <tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any
other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t> other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t>
<t><xref target="example-private"/> contains examples for ML-KEM private k eys <t><xref target="example-private"/> contains examples for ML-KEM private k eys
encoded using the textual encoding defined in <xref target="RFC7468"/>.</t> encoded using the textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="implementation-considerations"> <section anchor="implementation-considerations">
<name>Implementation Considerations</name> <name>Implementation Considerations</name>
<t>Though section 7.1 of <xref target="FIPS203"/> mentions the potential t o save seed values for future expansion, Algorithm 19 does not make the seed val ues available to a caller for serialization. <t>Though Section 7.1 of <xref target="FIPS203"/> mentions the potential t o save seed values for future expansion, Algorithm 19 does not make the seed val ues available to a caller for serialization.
Similarly, the algorithm that expands seed values is not listed as one of the "m ain algorithms" and features "internal" in the name even though it is clear that it is allowed to be exposed externally for the purposes of expanding a key from a seed. Similarly, the algorithm that expands seed values is not listed as one of the "m ain algorithms" and features "internal" in the name even though it is clear that it is allowed to be exposed externally for the purposes of expanding a key from a seed.
Below are possible ways to extend the APIs defined in <xref target="FIPS203"/> t o support serialization of seed values as private keys.</t> Below are possible ways to extend the APIs defined in <xref target="FIPS203"/> t o support serialization of seed values as private keys.</t>
<t>To support serialization of seed values as private keys, let Algorithm <t>To support serialization of seed values as private keys, let Algorithm
19b denote the same procedure as Algorithm 19 in <xref target="FIPS203"/> except 19b denote the same procedure as Algorithm 19 in <xref target="FIPS203"/>, excep
it returns (ek, dk, d, z) on line 7. Additionally, Algorithm 16 should be promo t it returns (ek, dk, d, z) on line 7. Additionally, Algorithm 16 should be prom
ted to be a "main algorithm" for external use in expanding seed values.</t> oted to be a "main algorithm" for external use in expanding seed values.</t>
<t>Note also that unlike other private key compression methods in other al <t>Note also that unlike other private key compression methods in other al
gorithms, expanding a private key from a seed is a one-way function, meaning tha gorithms, expanding a private key from a seed is a one-way function, meaning tha
t once a full key is expanded from seed and the seed discarded, the seed cannot t once a full key is expanded from a seed and the seed discarded, the seed canno
be re-created even if the full expanded private key is available. For this reaso t be recreated even if the full expanded private key is available. For this reas
n it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the se on, it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the
ed, even when also exporting the expanded private key.</t> seed, even when also exporting the expanded private key.</t>
</section> </section>
<section anchor="private-key-consistency-testing"> <section anchor="private-key-consistency-testing">
<name>Private Key Consistency Testing</name> <name>Private Key Consistency Testing</name>
<!-- [rfced] Should "but" be "and", or perhaps "so"? It's not clear that the te
xt after "but" is in contrast to the earlier part of the sentence.
Original:
Recipients that do not perform this seed consistency check avoid
keygen and compare operations, but are unable to ensure that the seed
and expandedKey match.
Perhaps:
Recipients that do not perform this seed consistency check avoid
keygen and compare operations and are unable to ensure that the seed
and expandedKey match.
-->
<t>When receiving a private key that contains both the seed and the <t>When receiving a private key that contains both the seed and the
expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency chec k to expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency chec k to
ensure that the sender properly generated the private key. Recipients ensure that the sender properly generated the private key. Recipients
that do not perform this seed consistency check avoid keygen that do not perform this seed consistency check avoid keygen
and compare operations, but are unable to ensure that the <tt>seed</tt> and and compare operations, but they are unable to ensure that the <tt>seed</tt> and
<tt>expandedKey</tt> match.</t> <tt>expandedKey</tt> match.</t>
<t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</tt> are not consistent, <t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</tt> are not consistent,
the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t> the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t>
<t>When receiving a private key that contains an <tt>expandedKey</tt>, <t>When receiving a private key that contains an <tt>expandedKey</tt>,
<xref target="FIPS203"/> stipulates in section 7.3 that before use, <xref target="FIPS203"/> stipulates in Section 7.3 that before use,
a "hash check" <bcp14>MUST</bcp14> be performed. That section stipulates two oth er a "hash check" <bcp14>MUST</bcp14> be performed. That section stipulates two oth er
checks on the type and length of the <tt>expandedKey</tt> which are ensured checks on the type and length of the <tt>expandedKey</tt>, which are ensured
by this standard.</t> by this standard.</t>
<t>The seed consistency check consists of regenerating the expanded form f rom <t>The seed consistency check consists of regenerating the expanded form f rom
the seed via <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using the first the seed via <tt>ML-KEM.KeyGen_internal(d,z)</tt> (algorithm 16) using the first
32 octets as <em>d</em> and the remaining 32 octets as <em>z</em> and ensuring i t is 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em> and ensuring i t is
bytewise equal to the value presented in the private key.</t> bytewise equal to the value presented in the private key.</t>
<t><xref target="example-bad"/> includes some examples of inconsistent see ds and <t><xref target="example-bad"/> includes some examples of inconsistent see ds and
expanded private keys.</t> expanded private keys.</t>
</section> </section>
<section anchor="security-considerations"> <section anchor="security-considerations">
<name>Security Considerations</name> <name>Security Considerations</name>
<t>The Security Considerations section of <xref target="RFC5280"/> applies to this <t>The Security Considerations section of <xref target="RFC5280"/> applies to this
specification as well.</t> specification as well.</t>
<t>Protection of the private-key information, i.e., the seed, is vital to <t>Protection of the private key information, i.e., the seed, is vital to
public-key cryptography. Disclosure of the private-key material to another public key cryptography. Disclosure of the private key material to another
entity can lead to masquerades.</t> entity can lead to masquerades.</t>
<t>The generation of private keys relies on random numbers. The use of <t>The generation of private keys relies on random numbers. The use of
inadequate pseudo-random number generators (PRNGs) to generate these inadequate pseudorandom number generators (PRNGs) to generate these
values can result in little or no security. An attacker may find it values can result in little or no security. An attacker may find it
much easier to reproduce the PRNG environment that produced the keys, much easier to reproduce the PRNG environment that produced the keys,
searching the resulting small set of possibilities, rather than brute searching the resulting small set of possibilities, rather than brute
force searching the whole key space. The generation of quality force searching the whole key space. The generation of quality
random numbers is difficult. ML-KEM key generation has specific requirements aro und randomness generation random numbers is difficult. ML-KEM key generation has specific requirements aro und randomness generation
as described in section 3.3 of <xref target="FIPS203"/>.</t> as described in Section 3.3 of <xref target="FIPS203"/>.</t>
<t>Many protocols only rely on the IND-CCA security of a KEM. Some <t>Many protocols only rely on the IND-CCA security of a KEM. Some
(implicitly) require further binding properties, formalized (implicitly) require further binding properties, formalized
in <xref target="CDM23"/>. in <xref target="CDM23"/>.
The private key format influences these binding properties. The private key format influences these binding properties.
Per <xref target="KEMMY24"/>, ML-KEM is LEAK-BIND-K-PK-secure and Per <xref target="KEMMY24"/>, ML-KEM is LEAK-BIND-K-PK-secure and
LEAK-BIND-K-CT-secure when using the expanded private key format, LEAK-BIND-K-CT-secure when using the expanded private key format,
but not MAL-BIND-K-CT nor MAL-BIND-K-PK. but not MAL-BIND-K-CT nor MAL-BIND-K-PK secure.
Using the 64-byte seed format provides a step up in binding security, Using the 64-byte seed format provides a step up in binding security,
additionally providing MAL-BIND-K-CT security, but still not MAL-BIND-K-PK.</t> and additionally provides MAL-BIND-K-CT security (but still does not provide sec urity for MAL-BIND-K-PK).</t>
<t>For more detailed ML-KEM specific security considerations regarding thi s, <t>For more detailed ML-KEM specific security considerations regarding thi s,
randomness, misbinding properties, decapsulation failures, key reuse, and randomness, misbinding properties, decapsulation failures, key reuse, and
key checks, refer to <xref target="I-D.sfluhrer-cfrg-ml-kem-security-considerati ons"/>.</t> key checks, refer to <xref target="I-D.sfluhrer-cfrg-ml-kem-security-considerati ons"/>.</t>
</section> </section>
<section anchor="iana-considerations"> <section anchor="iana-considerations">
<name>IANA Considerations</name> <name>IANA Considerations</name>
<t>For the ASN.1 Module in <xref target="asn1"/>, IANA is requested to ass <t>For the ASN.1 module in <xref target="asn1"/>, IANA has assigned
ign an an OID for the module identifier (121) with a
object identifier (OID) for the module identifier (TBD) with a description of "id-mod-x509-ml-kem-2025" in the "SMI Security for PKIX Module Id
Description of "id-mod-x509-ml-kem-2025". The OID for the module entifier" registry (1.3.6.1.5.5.7.0).</t>
should be allocated in the "SMI Security for PKIX Module Identifier"
registry (1.3.6.1.5.5.7.0).</t>
</section> </section>
</middle> </middle>
<back> <back>
<displayreference target="I-D.sfluhrer-cfrg-ml-kem-security-considerations" to="
ML-KEM-SEC-CONS"/>
<displayreference target="I-D.celi-wiggers-tls-authkem" to="KEM-TLS"/>
<references anchor="sec-combined-references"> <references anchor="sec-combined-references">
<name>References</name> <name>References</name>
<references anchor="sec-normative-references"> <references anchor="sec-normative-references">
<name>Normative References</name> <name>Normative References</name>
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer-
security-objects-register/algorithm-registration"> <!-- [rfced] References
<front>
<title>Computer Security Objects Register</title> a) FYI: We updated the date of [CSOR] from 20 August 2024 to 13 June
<author> 2025 to match the one provided at the URL.
<organization>NIST</organization>
</author> Original:
<date year="2024" month="August" day="20"/> [CSOR] NIST, "Computer Security Objects Register", 20 August
</front> 2024, <https://csrc.nist.gov/projects/computer-security-
</reference> objects-register/algorithm-registration>.
Current:
[CSOR] NIST, "Computer Security Objects Register (CSOR)", 13 June
2025, <https://csrc.nist.gov/projects/computer-security-
objects-register/algorithm-registration>.
b) FYI: We've updated the date for [NIST-PQC] from 20 December 2016 to 28 July
2025 to match the date provided at the URL.
Original:
[NIST-PQC] National Institute of Standards and Technology (NIST),
"Post-Quantum Cryptography Project", 20 December 2016,
<https://csrc.nist.gov/projects/post-quantum-
cryptography>.
Current:
[NIST-PQC] NIST, "Post-Quantum Cryptography (PQC)", 28 July 2025,
<https://csrc.nist.gov/projects/post-quantum-
cryptography>.
-->
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer
-security-objects-register/algorithm-registration">
<front>
<title>Computer Security Objects Register (CSOR)</title>
<author>
<organization>NIST</organization>
</author>
<date year="2025" month="June" day="13"/>
</front>
</reference>
<reference anchor="X680" target="https://www.itu.int/rec/T-REC-X.680"> <reference anchor="X680" target="https://www.itu.int/rec/T-REC-X.680">
<front> <front>
<title>Information technology - Abstract Syntax Notation One (ASN.1) : Specification of basic notation</title> <title>Information technology - Abstract Syntax Notation One (ASN.1) : Specification of basic notation</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ITU-T Recommendation" value="X.680"/>
<seriesInfo name="ISO/IEC" value="8824-1:2021"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/>
</reference> </reference>
<reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690"> <reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690">
<front> <front>
<title>Information technology - Abstract Syntax Notation One (ASN.1) : ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical E ncoding Rules (CER) and Distinguished Encoding Rules (DER)</title> <title>Information technology - ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ITU-T Recommendation" value="X.690"/>
<seriesInfo name="ISO/IEC" value="8825-1:2021"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/>
</reference> </reference>
<reference anchor="FIPS203">
<front> <reference anchor="FIPS203" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.
<title>Module-lattice-based key-encapsulation mechanism standard</ti FIPS.203.pdf">
tle> <front>
<author> <title>Module-Lattice-Based Key-Encapsulation Mechanism Standard</title>
<organization/> <author>
</author> <organization abbrev="NIST">National Institute of Standards and Technology
<date month="August" year="2024"/> </organization>
</front> </author>
<seriesInfo name="DOI" value="10.6028/nist.fips.203"/> <date month="August" year="2024"/>
<refcontent>National Institute of Standards and Technology (U.S.)</ref </front>
content> <seriesInfo name="NIST FIPS" value="203"/>
</reference> <seriesInfo name="DOI" value="10.6028/NIST.FIPS.203"/>
<reference anchor="RFC5280"> </reference>
<front>
<title>Internet X.509 Public Key Infrastructure Certificate and Cert <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
ificate Revocation List (CRL) Profile</title> 280.xml"/>
<author fullname="D. Cooper" initials="D." surname="Cooper"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2
<author fullname="S. Santesson" initials="S." surname="Santesson"/> 119.xml"/>
<author fullname="S. Farrell" initials="S." surname="Farrell"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8
<author fullname="S. Boeyen" initials="S." surname="Boeyen"/> 174.xml"/>
<author fullname="R. Housley" initials="R." surname="Housley"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
<author fullname="W. Polk" initials="W." surname="Polk"/> 912.xml"/>
<date month="May" year="2008"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
<abstract> 958.xml"/>
<t>This memo profiles the X.509 v3 certificate and X.509 v2 certif <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9
icate revocation list (CRL) for use in the Internet. An overview of this approac 629.xml"/>
h and model is provided as an introduction. The X.509 v3 certificate format is d
escribed in detail, with additional information regarding the format and semanti
cs of Internet name forms. Standard certificate extensions are described and two
Internet-specific extensions are defined. A set of required certificate extensi
ons is specified. The X.509 v2 CRL format is described in detail along with stan
dard and Internet-specific extensions. An algorithm for X.509 certification path
validation is described. An ASN.1 module and examples are provided in the appen
dices. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5280"/>
<seriesInfo name="DOI" value="10.17487/RFC5280"/>
</reference>
<reference anchor="RFC2119">
<front>
<title>Key words for use in RFCs to Indicate Requirement Levels</tit
le>
<author fullname="S. Bradner" initials="S." surname="Bradner"/>
<date month="March" year="1997"/>
<abstract>
<t>In many standards track documents several words are used to sig
nify the requirements in the specification. These words are often capitalized. T
his document defines these words as they should be interpreted in IETF documents
. This document specifies an Internet Best Current Practices for the Internet Co
mmunity, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author fullname="B. Leiba" initials="B." surname="Leiba"/>
<date month="May" year="2017"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying that
only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
<reference anchor="RFC5912">
<front>
<title>New ASN.1 Modules for the Public Key Infrastructure Using X.5
09 (PKIX)</title>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<date month="June" year="2010"/>
<abstract>
<t>The Public Key Infrastructure using X.509 (PKIX) certificate fo
rmat, and many associated formats, are expressed using ASN.1. The current ASN.1
modules conform to the 1988 version of ASN.1. This document updates those ASN.1
modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire c
hanges to any of the formats; this is simply a change to the syntax. This docume
nt is not an Internet Standards Track specification; it is published for informa
tional purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5912"/>
<seriesInfo name="DOI" value="10.17487/RFC5912"/>
</reference>
<reference anchor="RFC5958">
<front>
<title>Asymmetric Key Packages</title>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="August" year="2010"/>
<abstract>
<t>This document defines the syntax for private-key information an
d a content type for it. Private-key information includes a private key for a sp
ecified public-key algorithm and a set of attributes. The Cryptographic Message
Syntax (CMS), as defined in RFC 5652, can be used to digitally sign, digest, aut
henticate, or encrypt the asymmetric key format content type. This document obso
letes RFC 5208. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5958"/>
<seriesInfo name="DOI" value="10.17487/RFC5958"/>
</reference>
<reference anchor="RFC9629">
<front>
<title>Using Key Encapsulation Mechanism (KEM) Algorithms in the Cry
ptographic Message Syntax (CMS)</title>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<author fullname="J. Gray" initials="J." surname="Gray"/>
<author fullname="T. Okubo" initials="T." surname="Okubo"/>
<date month="August" year="2024"/>
<abstract>
<t>The Cryptographic Message Syntax (CMS) supports key transport a
nd key agreement algorithms. In recent years, cryptographers have been specifyin
g Key Encapsulation Mechanism (KEM) algorithms, including quantum-secure KEM alg
orithms. This document defines conventions for the use of KEM algorithms by the
originator and recipients to encrypt and decrypt CMS content. This document upda
tes RFC 5652.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="9629"/>
<seriesInfo name="DOI" value="10.17487/RFC9629"/>
</reference>
</references> </references>
<references anchor="sec-informative-references"> <references anchor="sec-informative-references">
<name>Informative References</name> <name>Informative References</name>
<reference anchor="CDM23" target="https://eprint.iacr.org/2023/1933.pdf" > <reference anchor="CDM23" target="https://eprint.iacr.org/2023/1933.pdf" >
<front> <front>
<title>Keeping Up with the KEMs: Stronger Security Notions for KEMs and automated analysis of KEM-based protocols</title> <title>Keeping Up with the KEMs: Stronger Security Notions for KEMs and automated analysis of KEM-based protocols</title>
<author initials="C." surname="Cremers" fullname="Cas Cremers"> <author initials="C." surname="Cremers" fullname="Cas Cremers">
<organization>CISPA Helmholtz Center for Information Security</org anization> <organization>CISPA Helmholtz Center for Information Security</org anization>
</author> </author>
<author initials="A." surname="Dax" fullname="Alexander Dax"> <author initials="A." surname="Dax" fullname="Alexander Dax">
<organization>CISPA Helmholtz Center for Information Security</org anization> <organization>CISPA Helmholtz Center for Information Security</org anization>
</author> </author>
<author initials="N." surname="Medinger" fullname="Niklas Medinger"> <author initials="N." surname="Medinger" fullname="Niklas Medinger">
<organization>CISPA Helmholtz Center for Information Security</org anization> <organization>CISPA Helmholtz Center for Information Security</org anization>
</author> </author>
<date year="2023"/> <date year="2023"/>
</front> </front>
<refcontent>Cryptology ePrint Archive, Paper 2023/1933</refcontent>
</reference> </reference>
<reference anchor="KEMMY24" target="https://eprint.iacr.org/2024/523.pdf "> <reference anchor="KEMMY24" target="https://eprint.iacr.org/2024/523.pdf ">
<front> <front>
<title>Unbindable Kemmy Schmidt: ML-KEM is neither MAL-BIND-K-CT nor MAL-BIND-K-PK</title> <title>Unbindable Kemmy Schmidt: ML-KEM is neither MAL-BIND-K-CT nor MAL-BIND-K-PK</title>
<author initials="S." surname="Schmieg" fullname="Sophie Schmieg"> <author initials="S." surname="Schmieg" fullname="Sophie Schmieg">
<organization/> <organization/>
</author> </author>
<date year="2024"/> <date year="2024"/>
</front> </front>
<refcontent>Cryptology ePrint Archive, Paper 2024/523</refcontent>
</reference> </reference>
<reference anchor="NIST-PQC" target="https://csrc.nist.gov/projects/post -quantum-cryptography"> <reference anchor="NIST-PQC" target="https://csrc.nist.gov/projects/post -quantum-cryptography">
<front> <front>
<title>Post-Quantum Cryptography Project</title> <title>Post-Quantum Cryptography (PQC)</title>
<author> <author>
<organization>National Institute of Standards and Technology (NIST )</organization> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date year="2016" month="December" day="20"/> <date year="2025" month="July" day="28"/>
</front> </front>
</reference> </reference>
<reference anchor="I-D.ietf-lamps-cms-kyber">
<front>
<title>Use of ML-KEM in the Cryptographic Message Syntax (CMS)</titl
e>
<author fullname="PRAT Julien" initials="J." surname="Prat">
<organization>CryptoNext Security</organization>
</author>
<author fullname="Mike Ounsworth" initials="M." surname="Ounsworth">
<organization>Entrust Limited</organization>
</author>
<author fullname="Daniel Van Geest" initials="D." surname="Van Geest
">
<organization>CryptoNext Security</organization>
</author>
<date day="1" month="July" year="2025"/>
<abstract>
<t> Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) is
a
quantum-resistant key-encapsulation mechanism (KEM). Three parameter
sets for the ML-KEM algorithm are specified by NIST in FIPS 203. In
order of increasing security strength (and decreasing performance),
these parameter sets are ML-KEM-512, ML-KEM-768, and ML-KEM-1024.
This document specifies the conventions for using ML-KEM with the
Cryptographic Message Syntax (CMS) using the KEMRecipientInfo
structure.
</t> <!-- [I-D.ietf-lamps-cms-kyber]
</abstract> companion doc RFC 9936
</front> -->
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-cms-kyber-11
"/>
</reference>
<reference anchor="I-D.celi-wiggers-tls-authkem">
<front>
<title>KEM-based Authentication for TLS 1.3</title>
<author fullname="Thom Wiggers" initials="T." surname="Wiggers">
<organization>PQShield</organization>
</author>
<author fullname="Sofia Celi" initials="S." surname="Celi">
<organization>Brave Software</organization>
</author>
<author fullname="Peter Schwabe" initials="P." surname="Schwabe">
<organization>Radboud University and MPI-SP</organization>
</author>
<author fullname="Douglas Stebila" initials="D." surname="Stebila">
<organization>University of Waterloo</organization>
</author>
<author fullname="Nick Sullivan" initials="N." surname="Sullivan">
</author>
<date day="22" month="April" year="2025"/>
<abstract>
<t> This document gives a construction for a Key Encapsulation M
echanism
(KEM)-based authentication mechanism in TLS 1.3. This proposal
authenticates peers via a key exchange protocol, using their long-
term (KEM) public keys.
</t> <reference anchor="RFC9936" target="https://www.rfc-editor.org/info/rfc9936">
</abstract> <front>
</front> <title>Use of ML-KEM in the Cryptographic Message Syntax (CMS)</title>
<seriesInfo name="Internet-Draft" value="draft-celi-wiggers-tls-authke <author initials='J' surname='Prat' fullname='Julien Prat'>
m-05"/> <organization/>
</reference> </author>
<reference anchor="RFC7468"> <author initials='M' surname='Ounsworth' fullname='Mike Ounsworth'>
<front> <organization/>
<title>Textual Encodings of PKIX, PKCS, and CMS Structures</title> </author>
<author fullname="S. Josefsson" initials="S." surname="Josefsson"/> <author initials='D' surname='Van Geest' fullname='Daniel Van Geest'>
<author fullname="S. Leonard" initials="S." surname="Leonard"/> <organization/>
<date month="April" year="2015"/> </author>
<abstract> <date month='February' year='2026'/>
<t>This document describes and discusses the textual encodings of </front>
the Public-Key Infrastructure X.509 (PKIX), Public-Key Cryptography Standards (P <seriesInfo name="RFC" value="9936"/>
KCS), and Cryptographic Message Syntax (CMS). The textual encodings are well-kno <seriesInfo name="DOI" value="10.17487/RFC9936"/>
wn, are implemented by several applications and libraries, and are widely deploy </reference>
ed. This document articulates the de facto rules by which existing implementatio
ns operate and defines them so that future implementations can interoperate.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="7468"/>
<seriesInfo name="DOI" value="10.17487/RFC7468"/>
</reference>
<reference anchor="I-D.sfluhrer-cfrg-ml-kem-security-considerations">
<front>
<title>ML-KEM Security Considerations</title>
<author fullname="Scott Fluhrer" initials="S." surname="Fluhrer">
<organization>Cisco Systems</organization>
</author>
<author fullname="Quynh Dang" initials="Q." surname="Dang">
<organization>National Institute of Standards and Technology</orga
nization>
</author>
<author fullname="John Preuß Mattsson" initials="J. P." surname="Mat
tsson">
<organization>Ericsson</organization>
</author>
<author fullname="Kevin Milner" initials="K." surname="Milner">
<organization>Quantinuum</organization>
</author>
<author fullname="Daniel Shiu" initials="D." surname="Shiu">
<organization>Arqit Quantum Inc</organization>
</author>
<date day="15" month="May" year="2025"/>
<abstract>
<t> NIST standardized ML-KEM as FIPS 203 in August 2024. This d
ocument
discusses how to use ML-KEM and how to use it within protocols - that
is, what problem it solves, and what you need to do to use it
securely.
</t> <!-- [I-D.celi-wiggers-tls-authkem]
</abstract> draft-celi-wiggers-tls-authkem-06
</front> IESG State: I-D Exists as of 11-4-2025
<seriesInfo name="Internet-Draft" value="draft-sfluhrer-cfrg-ml-kem-se -->
curity-considerations-03"/>
</reference>
<reference anchor="I-D.ietf-lamps-dilithium-certificates">
<front>
<title>Internet X.509 Public Key Infrastructure - Algorithm Identifi
ers for the Module-Lattice-Based Digital Signature Algorithm (ML-DSA)</title>
<author fullname="Jake Massimo" initials="J." surname="Massimo">
<organization>AWS</organization>
</author>
<author fullname="Panos Kampanakis" initials="P." surname="Kampanaki
s">
<organization>AWS</organization>
</author>
<author fullname="Sean Turner" initials="S." surname="Turner">
<organization>sn3rd</organization>
</author>
<author fullname="Bas Westerbaan" initials="B." surname="Westerbaan"
>
<organization>Cloudflare</organization>
</author>
<date day="26" month="June" year="2025"/>
<abstract>
<t> Digital signatures are used within X.509 certificates, Certi
ficate
Revocation Lists (CRLs), and to sign messages. This document
specifies the conventions for using FIPS 204, the Module-Lattice-
Based Digital Signature Algorithm (ML-DSA) in Internet X.509
certificates and certificate revocation lists. The conventions for
the associated signatures, subject public keys, and private key are
also described.
</t> <xi:include href="https://bib.ietf.org/public/rfc/bibxml3/reference.I-D.
</abstract> celi-wiggers-tls-authkem.xml"/>
</front> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-dilithium-ce 468.xml"/>
rtificates-12"/> <!-- [I-D.sfluhrer-cfrg-ml-kem-security-considerations]
</reference> draft-sfluhrer-cfrg-ml-kem-security-considerations-03
IESG State: I-D Exists as of 11-17-2025
-->
<xi:include href="https://bib.ietf.org/public/rfc/bibxml3/reference.I-D.
sfluhrer-cfrg-ml-kem-security-considerations.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9881.xml"
/>
</references> </references>
</references> </references>
<?line 493?> <?line 493?>
<section anchor="asn1"> <section anchor="asn1">
<name>ASN.1 Module</name> <name>ASN.1 Module</name>
<t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-KEM. Note that <t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-KEM. Note that
as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see
<xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> and <xref target="RFC9629"/>.</t> <xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> and <xref target="RFC9629"/>.</t>
<sourcecode markers="true"><![CDATA[ <sourcecode markers="true" type="asn.1"><![CDATA[
X509-ML-KEM-2025 X509-ML-KEM-2025
{ iso(1) identified-organization(3) dod(6) { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-x509-ml-kem-2025(TBD) } id-mod-x509-ml-kem-2025(121) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL; EXPORTS ALL;
IMPORTS IMPORTS
PUBLIC-KEY PUBLIC-KEY
FROM AlgorithmInformation-2009 -- [RFC 5912] FROM AlgorithmInformation-2009 -- [RFC 5912]
{ iso(1) identified-organization(3) dod(6) internet(1) { iso(1) identified-organization(3) dod(6) internet(1)
skipping to change at line 824 skipping to change at line 725
expandedKey OCTET STRING (SIZE (3168)) expandedKey OCTET STRING (SIZE (3168))
} }
} }
ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800)) ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800))
ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184)) ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184))
ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568)) ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568))
END END]]></sourcecode>
]]></sourcecode>
</section> </section>
<section anchor="arnold"> <section anchor="arnold">
<name>Parameter Set Security and Sizes</name> <name>Parameter Set Security and Sizes</name>
<t>Instead of defining the strength of a quantum algorithm in a traditiona l <t>Instead of defining the strength of a quantum algorithm in a traditiona l
manner using the imprecise notion of bits of security, NIST has manner using the imprecise notion of bits of security, NIST has
defined security levels by picking a reference scheme, which defined security levels by picking a reference scheme, which
NIST expects to offer notable levels of resistance to both quantum and is expected to offer notable levels of resistance to both quantum and
classical attack. To wit, a KEM algorithm that achieves NIST PQC classical attacks. To wit, a KEM algorithm that achieves NIST PQC
security must require computational resources to break IND-CCA security must require computational resources to break IND-CCA
security comparable or greater than that required for key search security comparable or greater than that required for key search
on AES-128, AES-192, and AES-256 for Levels 1, 3, and 5, respectively. on AES-128, AES-192, and AES-256 for Levels 1, 3, and 5, respectively.
Levels 2 and 4 use collision search for SHA-256 and SHA-384 as reference.</t> Levels 2 and 4 use collision search for SHA-256 and SHA-384 as reference.</t>
<table anchor="tab-strengths"> <table anchor="tab-strengths">
<name>Mapping between NIST Security Level, ML-KEM parameter set, and siz es in bytes</name> <name>Mapping Between NIST Security Level, ML-KEM Parameter Sets, and Si zes in Bytes</name>
<thead> <thead>
<tr> <tr>
<th align="left">Level</th> <th align="left">Level</th>
<th align="left">Parameter Set</th> <th align="left">Parameter Set</th>
<th align="left">Encap. Key</th> <th align="left">Encap. Key</th>
<th align="left">Decap. Key</th> <th align="left">Decap. Key</th>
<th align="left">Ciphertext</th> <th align="left">Ciphertext</th>
<th align="left">Secret</th> <th align="left">Secret</th>
</tr> </tr>
</thead> </thead>
skipping to change at line 901 skipping to change at line 801
<section anchor="ml-kem-512-private-key-examples"> <section anchor="ml-kem-512-private-key-examples">
<name>ML-KEM-512 Private Key Examples</name> <name>ML-KEM-512 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format"> <section anchor="seed-format">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MFQCAQAwCwYJYIZIAWUDBAQBBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MFQCAQAwCwYJYIZIAWUDBAQBBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8= GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343 5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
5363738393a3b3c3d3e3f` } 5363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format"> <section anchor="expanded-format">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz
bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
skipping to change at line 956 skipping to change at line 854
tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2 uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `70554fd436344f2785b1b3b1bac184b6679003336c26 OCTET_STRING { `70554fd436344f2785b1b3b1bac184b6679003336c26
f15a7de878c4825c6be03f3c4a480f75b7486aad31d3a00518623fd207ab528d f15a7de878c4825c6be03f3c4a480f75b7486aad31d3a00518623fd207ab528d
d62721495835ae0062c367b74a71baf10aad0e8a2902076be31348beb15ccc09 d62721495835ae0062c367b74a71baf10aad0e8a2902076be31348beb15ccc09
skipping to change at line 1018 skipping to change at line 916
903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf0211 903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf0211
7f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cdb 7f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cdb
33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baab 33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baab
71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec372 71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec372
25c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b32 25c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b32
4334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81c 4334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81c
3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2feada 3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2feada
de150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f303132333435 de150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f303132333435
363738393a3b3c3d3e3f` } 363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format"> <section anchor="both-format">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF
GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1 GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1
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skipping to change at line 1062 skipping to change at line 959
dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa
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JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN
Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG
dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0 dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0
VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9 VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
Pj8= Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334 15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
skipping to change at line 1129 skipping to change at line 1026
117f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26c 117f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26c
db33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61ba db33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61ba
ab71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec3 ab71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec3
7225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b 7225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b
324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b8 324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b8
1c3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2fea 1c3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2fea
dade150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f3031323334 dade150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f3031323334
35363738393a3b3c3d3e3f` } 35363738393a3b3c3d3e3f` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-kem-768-private-key-examples"> <section anchor="ml-kem-768-private-key-examples">
<name>ML-KEM-768 Private Key Examples</name> <name>ML-KEM-768 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-1"> <section anchor="seed-format-1">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MFQCAQAwCwYJYIZIAWUDBAQCBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MFQCAQAwCwYJYIZIAWUDBAQCBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8= GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343 5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
5363738393a3b3c3d3e3f` } 5363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-1"> <section anchor="expanded-format-1">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIJeAIBADALBglghkgBZQMEBAIEgglkBIIJYCfSp38zdW9hII7xE6voJZWHPUq8 MIIJeAIBADALBglghkgBZQMEBAIEgglkBIIJYCfSp38zdW9hII7xE6voJZWHPUq8
cw5bXWeVKb9qTOtjg0JyMahhL0FVBRWsulLkjq2LlCgzu+aGXRPRSnnSxcPgfwoF cw5bXWeVKb9qTOtjg0JyMahhL0FVBRWsulLkjq2LlCgzu+aGXRPRSnnSxcPgfwoF
bY3nqt/KugWMSTyAs3yrjFYnU7s7prbsgpf4heqnVA1TABWoRAblWxNmtXfiNs5Y bY3nqt/KugWMSTyAs3yrjFYnU7s7prbsgpf4heqnVA1TABWoRAblWxNmtXfiNs5Y
om2KHrWkTVQjI8IWfZv0pH+YVpnKBbrkO43sYX8COAo4kK/UuMfsft4mVToCXzzl om2KHrWkTVQjI8IWfZv0pH+YVpnKBbrkO43sYX8COAo4kK/UuMfsft4mVToCXzzl
vF16YhMDBCNcsa1INrVmtbhjvZvbRaKESnBHtsjTg+RIUl4EC03IorSMbDfJbWLU vF16YhMDBCNcsa1INrVmtbhjvZvbRaKESnBHtsjTg+RIUl4EC03IorSMbDfJbWLU
skipping to change at line 1214 skipping to change at line 1109
wN2Uv+shQZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4 wN2Uv+shQZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4
Jw1Ybhv4MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9c Jw1Ybhv4MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9c
t4TlU/QbkY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67 t4TlU/QbkY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67
QI5JqeP4edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPB QI5JqeP4edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPB
u3lyvsWjBuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhK u3lyvsWjBuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhK
SClrmN1DIrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7 SClrmN1DIrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7
y05qBc9FAhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCx y05qBc9FAhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCx
JKhVjfcrvje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD JKhVjfcrvje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD
4ssy2ovDQvpN6gV4ok4W2Pj5ODqVt3BQ9Nn9L1cz7sHWPvPCPr+ZGBc2aacgISIj 4ssy2ovDQvpN6gV4ok4W2Pj5ODqVt3BQ9Nn9L1cz7sHWPvPCPr+ZGBc2aacgISIj
JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc730e OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc730e
5b5d679529bf6a4ceb6383427231a8612f41550515acba52e48ead8b942833bb 5b5d679529bf6a4ceb6383427231a8612f41550515acba52e48ead8b942833bb
e6865d13d14a79d2c5c3e07f0a056d8de7aadfcaba058c493c80b37cab8c5627 e6865d13d14a79d2c5c3e07f0a056d8de7aadfcaba058c493c80b37cab8c5627
skipping to change at line 1300 skipping to change at line 1195
72bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc6607 72bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc6607
77ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba4 77ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba4
4a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4e 4a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4e
6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b9 6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b9
9aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c6 9aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c6
33fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2cb 33fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2cb
32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d63e 32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d63e
f3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f303132333435 f3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f303132333435
363738393a3b3c3d3e3f` } 363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-1"> <section anchor="both-format-1">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIJvgIBADALBglghkgBZQMEBAIEggmqMIIJpgRAAAECAwQFBgcICQoLDA0ODxAR MIIJvgIBADALBglghkgBZQMEBAIEggmqMIIJpgRAAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
CWAn0qd/M3VvYSCO8ROr6CWVhz1KvHMOW11nlSm/akzrY4NCcjGoYS9BVQUVrLpS CWAn0qd/M3VvYSCO8ROr6CWVhz1KvHMOW11nlSm/akzrY4NCcjGoYS9BVQUVrLpS
5I6ti5QoM7vmhl0T0Up50sXD4H8KBW2N56rfyroFjEk8gLN8q4xWJ1O7O6a27IKX 5I6ti5QoM7vmhl0T0Up50sXD4H8KBW2N56rfyroFjEk8gLN8q4xWJ1O7O6a27IKX
+IXqp1QNUwAVqEQG5VsTZrV34jbOWKJtih61pE1UIyPCFn2b9KR/mFaZygW65DuN +IXqp1QNUwAVqEQG5VsTZrV34jbOWKJtih61pE1UIyPCFn2b9KR/mFaZygW65DuN
skipping to change at line 1360 skipping to change at line 1254
8iWFlYenMHcEmsvP1E0PAlQ44V0VOCcNWG4b+DGSqUWc9jwOly+FKXZ5gx7PEhUJ 8iWFlYenMHcEmsvP1E0PAlQ44V0VOCcNWG4b+DGSqUWc9jwOly+FKXZ5gx7PEhUJ
hRy4NA9vEHsPoaDv0bNqgYm8CFxPXLeE5VP0G5GPgDl84ZVveFvuN3ypqovmmYra hRy4NA9vEHsPoaDv0bNqgYm8CFxPXLeE5VP0G5GPgDl84ZVveFvuN3ypqovmmYra
MMJrfD2Ma1UlTMliA7IMQq7grE4eu0COSanj+HnQqweF63AlQl0TBaIpnAFeEg0W MMJrfD2Ma1UlTMliA7IMQq7grE4eu0COSanj+HnQqweF63AlQl0TBaIpnAFeEg0W
Ow4ZSUzlclPQJG0YJ0XLgZerdDizwbt5cr7Fowbro1Z4VcAUaZ/vZa5Ux3Cg2FwY Ow4ZSUzlclPQJG0YJ0XLgZerdDizwbt5cr7Fowbro1Z4VcAUaZ/vZa5Ux3Cg2FwY
QAz2Qq7cZgd3uksThQK9WngS9iH4Skgpa5jdQyK28VgouKjw4AqLpEpTw6ixQ1cb QAz2Qq7cZgd3uksThQK9WngS9iH4Skgpa5jdQyK28VgouKjw4AqLpEpTw6ixQ1cb
B0Cr1Wfa8c3px5wgS21eJZ0XZqMbu8tOagXPRQIXazAcHC9BJHdQFXvOyF6AmzCk B0Cr1Wfa8c3px5wgS21eJZ0XZqMbu8tOagXPRQIXazAcHC9BJHdQFXvOyF6AmzCk
1g13R83Q9bmaqMgmmHUXeTqqgICgsSSoVY33K743t19O27a+ghbWxjP7KyKA4lET 1g13R83Q9bmaqMgmmHUXeTqqgICgsSSoVY33K743t19O27a+ghbWxjP7KyKA4lET
2GleQ0gcPus5frGSUFIptnogHqiTw+LLMtqLw0L6TeoFeKJOFtj4+Tg6lbdwUPTZ 2GleQ0gcPus5frGSUFIptnogHqiTw+LLMtqLw0L6TeoFeKJOFtj4+Tg6lbdwUPTZ
/S9XM+7B1j7zwj6/mRgXNmmnICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9 /S9XM+7B1j7zwj6/mRgXNmmnICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
Pj8= Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334 15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
skipping to change at line 1451 skipping to change at line 1345
0777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8b 0777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8b
a44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb a44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb
4e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5 4e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5
b99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6 b99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6
c633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2 c633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2
cb32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d6 cb32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d6
3ef3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f3031323334 3ef3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f3031323334
35363738393a3b3c3d3e3f` } 35363738393a3b3c3d3e3f` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-kem-1024-private-key-examples"> <section anchor="ml-kem-1024-private-key-examples">
<name>ML-KEM-1024 Private Key Examples</name> <name>ML-KEM-1024 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-2"> <section anchor="seed-format-2">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MFQCAQAwCwYJYIZIAWUDBAQDBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MFQCAQAwCwYJYIZIAWUDBAQDBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8= GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343 5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
5363738393a3b3c3d3e3f` } 5363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-2"> <section anchor="expanded-format-2">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIMeAIBADALBglghkgBZQMEBAMEggxkBIIMYPd7f2sVxz/izFRrZ/t3TKGbQs1G MIIMeAIBADALBglghkgBZQMEBAMEggxkBIIMYPd7f2sVxz/izFRrZ/t3TKGbQs1G
Pqn7uYTKR3p3tscQh8vwUavkc2qQcsbocMgxHFWWP1AKPHsbjypYVY9JxiUntsWU Pqn7uYTKR3p3tscQh8vwUavkc2qQcsbocMgxHFWWP1AKPHsbjypYVY9JxiUntsWU
teess7z1lyc6V0NRfRUSCL1Kph51umewvVlKmUkZYnrAqATUieFxM2vDOfRmZwbl teess7z1lyc6V0NRfRUSCL1Kph51umewvVlKmUkZYnrAqATUieFxM2vDOfRmZwbl
E0QSs2aCPVAxjIvyYasSCiigT+wBzBXytxkSzuVKqO7YVGlLa6iGtet2YebVaqwh E0QSs2aCPVAxjIvyYasSCiigT+wBzBXytxkSzuVKqO7YVGlLa6iGtet2YebVaqwh
PMHYFNWSs5VVT650R200NxFjEpv4ZFJyUGBswhpTdGsgmXB3u6FVczsopOf6B3Y5 PMHYFNWSs5VVT650R200NxFjEpv4ZFJyUGBswhpTdGsgmXB3u6FVczsopOf6B3Y5
skipping to change at line 1552 skipping to change at line 1444
MELGSsZ5e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4Pxxs MELGSsZ5e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4Pxxs
B8y4j0EijEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0 B8y4j0EijEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0
YKdICXJmM4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZC YKdICXJmM4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZC
OclCHcMRm/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2 OclCHcMRm/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2
nhYSrO6yi5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iF nhYSrO6yi5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iF
cUkQiIsjEMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+np cUkQiIsjEMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+np
e6pSPXpEMWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0 e6pSPXpEMWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0
RvgYkYLSv16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB RvgYkYLSv16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB
7VjcYod2uYOILhF1YTSeXBMafhFqBGOGHX0YZjxWJ8OMcUfdqt/Uis16RTUgISIj 7VjcYod2uYOILhF1YTSeXBMafhFqBGOGHX0YZjxWJ8OMcUfdqt/Uis16RTUgISIj
JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `f77b7f6b15c73fe2cc546b67fb774ca19b42cd463ea9 OCTET_STRING { `f77b7f6b15c73fe2cc546b67fb774ca19b42cd463ea9
fbb984ca477a77b6c71087cbf051abe4736a9072c6e870c8311c55963f500a3c fbb984ca477a77b6c71087cbf051abe4736a9072c6e870c8311c55963f500a3c
7b1b8f2a58558f49c62527b6c594b5e7acb3bcf597273a5743517d151208bd4a 7b1b8f2a58558f49c62527b6c594b5e7acb3bcf597273a5743517d151208bd4a
skipping to change at line 1662 skipping to change at line 1554
12aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb9884 12aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb9884
f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b90 f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b90
03e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97baa 03e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97baa
523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba60f 523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba60f
81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8a1 81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8a1
3e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed58 3e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed58
dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c71 dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c71
47ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f303132333435 47ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f303132333435
363738393a3b3c3d3e3f` } 363738393a3b3c3d3e3f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-2"> <section anchor="both-format-2">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIMvgIBADALBglghkgBZQMEBAMEggyqMIIMpgRAAAECAwQFBgcICQoLDA0ODxAR MIIMvgIBADALBglghkgBZQMEBAMEggyqMIIMpgRAAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
DGD3e39rFcc/4sxUa2f7d0yhm0LNRj6p+7mEykd6d7bHEIfL8FGr5HNqkHLG6HDI DGD3e39rFcc/4sxUa2f7d0yhm0LNRj6p+7mEykd6d7bHEIfL8FGr5HNqkHLG6HDI
MRxVlj9QCjx7G48qWFWPScYlJ7bFlLXnrLO89ZcnOldDUX0VEgi9SqYedbpnsL1Z MRxVlj9QCjx7G48qWFWPScYlJ7bFlLXnrLO89ZcnOldDUX0VEgi9SqYedbpnsL1Z
SplJGWJ6wKgE1InhcTNrwzn0ZmcG5RNEErNmgj1QMYyL8mGrEgoooE/sAcwV8rcZ SplJGWJ6wKgE1InhcTNrwzn0ZmcG5RNEErNmgj1QMYyL8mGrEgoooE/sAcwV8rcZ
skipping to change at line 1738 skipping to change at line 1629
LLNQ8CmrU34oc0f9MHWsEJBqeD8cbAfMuI9BIoxL4cZA95C1w6XV08p5JJXXS8Rh LLNQ8CmrU34oc0f9MHWsEJBqeD8cbAfMuI9BIoxL4cZA95C1w6XV08p5JJXXS8Rh
ViZYwHrGACdrkkq1vJvh8ElMt2+C9GCnSAlyZjOB4WmZYGHXmYWexU1PXKXEEcAd ViZYwHrGACdrkkq1vJvh8ElMt2+C9GCnSAlyZjOB4WmZYGHXmYWexU1PXKXEEcAd
sVl7Fll3Zp3hOpKKNK+6wlj+qMR2QjnJQh3DEZv1tHaZIGl4MnscU0XvdGp5g4Qf sVl7Fll3Zp3hOpKKNK+6wlj+qMR2QjnJQh3DEZv1tHaZIGl4MnscU0XvdGp5g4Qf
BW4lNBAKsk1OmrvQsXxqlb1MPA5A9p4WEqzusouZCGyVEW5yBCc4kzkL9GuJmzYo BW4lNBAKsk1OmrvQsXxqlb1MPA5A9p4WEqzusouZCGyVEW5yBCc4kzkL9GuJmzYo
aw6/GUe7mIT3Mson2oKxm13AzH+IhXFJEIiLIxDE+TGdQQs05kM7kAPiF2u5lSV0 aw6/GUe7mIT3Mson2oKxm13AzH+IhXFJEIiLIxDE+TGdQQs05kM7kAPiF2u5lSV0
VhBuiVIWO4ulklMMxaoK60OtOY/p6XuqUj16RDFnfD068HGeR124XKla9Qib6r6w VhBuiVIWO4ulklMMxaoK60OtOY/p6XuqUj16RDFnfD068HGeR124XKla9Qib6r6w
Wy+qtIlrpg+ByIRypXtGqCiCagzftEb4GJGC0r9erE7BzF3q9ZnIoT5II1QG0X/9 Wy+qtIlrpg+ByIRypXtGqCiCagzftEb4GJGC0r9erE7BzF3q9ZnIoT5II1QG0X/9
3INEtsZphKhoqpL6AiJ6CGlQ6wyHAe1Y3GKHdrmDiC4RdWE0nlwTGn4RagRjhh19 3INEtsZphKhoqpL6AiJ6CGlQ6wyHAe1Y3GKHdrmDiC4RdWE0nlwTGn4RagRjhh19
GGY8VifDjHFH3arf1IrNekU1ICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9 GGY8VifDjHFH3arf1IrNekU1ICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
Pj8= Pj8=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334 15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
skipping to change at line 1853 skipping to change at line 1744
84f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b 84f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b
9003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97b 9003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97b
aa523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba6 aa523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba6
0f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8 0f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8
a13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed a13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed
58dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c 58dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c
7147ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f3031323334 7147ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f3031323334
35363738393a3b3c3d3e3f` } 35363738393a3b3c3d3e3f` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
</section> </section>
<section anchor="example-public"> <section anchor="example-public">
<name>Example Public Keys</name> <name>Example Public Keys</name>
<t>The following is the ML-KEM-512 public key corresponding to the priva te <t>The following is the ML-KEM-512 public key corresponding to the priva te
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIDMjALBglghkgBZQMEBAEDggMhADmVgV5ZfRBDVc8pqlMzyTJRhp1bzb5IcST2 MIIDMjALBglghkgBZQMEBAEDggMhADmVgV5ZfRBDVc8pqlMzyTJRhp1bzb5IcST2
Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHmvG+QsOSb Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHmvG+QsOSb
aTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbWf/mqvJdQ aTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbWf/mqvJdQ
Pyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lAk0Frg7gS Pyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lAk0Frg7gS
Tmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8XSCVcuD8 Tmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8XSCVcuD8
dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoEZM5BqLtE dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoEZM5BqLtE
wtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRrevpsRZMl wtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRrevpsRZMl
JqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5JPSQpaxU JqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5JPSQpaxU
lfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6tnVUAAUH lfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6tnVUAAUH
gVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10zgGocjicy gVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10zgGocjicy
r5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyekb7U7oR3l r5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyekb7U7oR3l
y0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oXthQzzRr4 y0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oXthQzzRr4
D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPMFgCQPmUp D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPMFgCQPmUp
NWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGmgx1bVMC3 NWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGmgx1bVMC3
kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9huqtxp6PT kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9huqtxp6PT
UZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2NoPwS/eg UZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2NoPwS/eg
nMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3guBw7xZoG nMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3guBw7xZoG
WhttY7Js WhttY7Js
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
} }
BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5bcdb BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5bcdb
e487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c62 e487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c62
efa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016ddf efa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016ddf
c1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67ff c1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67ff
9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491a 9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491a
skipping to change at line 1916 skipping to change at line 1807
53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e30 53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e30
fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980b fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980b
1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc160 1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc160
0903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf021 0903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf021
17f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cd 17f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cd
b33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baa b33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baa
b71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec37 b71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec37
225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b3 225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b3
24334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81 24334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81
c3bc59a065a1b6d63b26c` } c3bc59a065a1b6d63b26c` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-KEM-768 public key corresponding to the priva te <t>The following is the ML-KEM-768 public key corresponding to the priva te
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIEsjALBglghkgBZQMEBAIDggShACmKoQ1CPI3aBp0CvFnmzfA6CWuLPaTKubgM MIIEsjALBglghkgBZQMEBAIDggShACmKoQ1CPI3aBp0CvFnmzfA6CWuLPaTKubgM
pKFJB2cszvHsT68jSgvFt+nUc/KzEzs7JqHRdctnp4BZGWmcAvdlMbmcX4kYBwS7 pKFJB2cszvHsT68jSgvFt+nUc/KzEzs7JqHRdctnp4BZGWmcAvdlMbmcX4kYBwS7
TKRTXFuJcmecZgoHxeUUuHAJyGLrj1FXaV77P8QKne9rgcHMAqJJrk8JStDZvTSF TKRTXFuJcmecZgoHxeUUuHAJyGLrj1FXaV77P8QKne9rgcHMAqJJrk8JStDZvTSF
wcHGgIBSCnyMYyAyzuc4FU5cUXbAfaVgJHdqQw/nbqz2ZaP3uDIQIhW8gvEJOcg1 wcHGgIBSCnyMYyAyzuc4FU5cUXbAfaVgJHdqQw/nbqz2ZaP3uDIQIhW8gvEJOcg1
VwQzao+sHYHkuwSFql18dNa1m75cXpcqDYusQRtVtdVVfNaAoaj3G064a8SMmgUJ VwQzao+sHYHkuwSFql18dNa1m75cXpcqDYusQRtVtdVVfNaAoaj3G064a8SMmgUJ
cxpUvZ1ykLJ5Y+Q3Lcmxmc/crAsBrNKKYjlREuTENkjWIsSMgjTQFEDozDdskn8j cxpUvZ1ykLJ5Y+Q3Lcmxmc/crAsBrNKKYjlREuTENkjWIsSMgjTQFEDozDdskn8j
pa/JrAR0xmInTkJFJchVLs47P+JlFt6QG8fVFb3olVjmJslcgLkzQvgBAATznmxs pa/JrAR0xmInTkJFJchVLs47P+JlFt6QG8fVFb3olVjmJslcgLkzQvgBAATznmxs
lIccXjRMqzlmyDX5qWpZr9McQChrOLHBp4RwurlHUYk0RTzoZzapGfH1ptUQqG9U lIccXjRMqzlmyDX5qWpZr9McQChrOLHBp4RwurlHUYk0RTzoZzapGfH1ptUQqG9U
skipping to change at line 1950 skipping to change at line 1840
skqgebH0GbphdbRCr7EZCdSla3CgM1soc5IYqnyTSOLDwvPrPRWkHmQXwN2Uv+sh skqgebH0GbphdbRCr7EZCdSla3CgM1soc5IYqnyTSOLDwvPrPRWkHmQXwN2Uv+sh
QZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4Jw1Ybhv4 QZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4Jw1Ybhv4
MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9ct4TlU/Qb MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9ct4TlU/Qb
kY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67QI5JqeP4 kY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67QI5JqeP4
edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPBu3lyvsWj edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPBu3lyvsWj
BuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhKSClrmN1D BuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhKSClrmN1D
IrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7y05qBc9F IrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7y05qBc9F
AhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCxJKhVjfcr AhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCxJKhVjfcr
vje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD4ssy2ovD vje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD4ssy2ovD
QvpN6gV4 QvpN6gV4
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
} }
BIT_STRING { `00` `298aa10d423c8dda069d02bc59e6cdf03a096b8b3da BIT_STRING { `00` `298aa10d423c8dda069d02bc59e6cdf03a096b8b3da
4cab9b80ca4a14907672ccef1ec4faf234a0bc5b7e9d473f2b3133b3b26a1d17 4cab9b80ca4a14907672ccef1ec4faf234a0bc5b7e9d473f2b3133b3b26a1d17
5cb67a7805919699c02f76531b99c5f89180704bb4ca4535c5b8972679c660a0 5cb67a7805919699c02f76531b99c5f89180704bb4ca4535c5b8972679c660a0
7c5e514b87009c862eb8f5157695efb3fc40a9def6b81c1cc02a249ae4f094ad 7c5e514b87009c862eb8f5157695efb3fc40a9def6b81c1cc02a249ae4f094ad
0d9bd3485c1c1c68080520a7c8c632032cee738154e5c5176c07da56024776a4 0d9bd3485c1c1c68080520a7c8c632032cee738154e5c5176c07da56024776a4
skipping to change at line 1995 skipping to change at line 1885
4e553f41b918f80397ce1956f785bee377ca9aa8be6998ada30c26b7c3d8c6b5 4e553f41b918f80397ce1956f785bee377ca9aa8be6998ada30c26b7c3d8c6b5
5254cc96203b20c42aee0ac4e1ebb408e49a9e3f879d0ab0785eb7025425d130 5254cc96203b20c42aee0ac4e1ebb408e49a9e3f879d0ab0785eb7025425d130
5a2299c015e120d163b0e19494ce57253d0246d182745cb8197ab7438b3c1bb7 5a2299c015e120d163b0e19494ce57253d0246d182745cb8197ab7438b3c1bb7
972bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc660 972bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc660
777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba 777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba
44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4 44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4
e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b
99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c 99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c
633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2c 633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2c
b32da8bc342fa4dea0578` } b32da8bc342fa4dea0578` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-KEM-1024 public key corresponding to the priv ate <t>The following is the ML-KEM-1024 public key corresponding to the priv ate
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIGMjALBglghkgBZQMEBAMDggYhAEuUwpRQERGRgjs1FMmsHqPZglzLhjk6LfsE MIIGMjALBglghkgBZQMEBAMDggYhAEuUwpRQERGRgjs1FMmsHqPZglzLhjk6LfsE
ZU+iGS03v60cSXxlAu7lyoCnO/zguvWlSohYWkATl6PSMvQmp6+wgrwhpEMXCQ6q ZU+iGS03v60cSXxlAu7lyoCnO/zguvWlSohYWkATl6PSMvQmp6+wgrwhpEMXCQ6q
x1ksLqiKZTxEkeoZOTEzX1LpiaPEzFbZxVNzLVfEcPtBq3WbZdLQREU4L82cTjRK x1ksLqiKZTxEkeoZOTEzX1LpiaPEzFbZxVNzLVfEcPtBq3WbZdLQREU4L82cTjRK
ESj6nhHgQ1jhku0BSyMjKn7isi4jcX9EER7jNXU5nDdkbamBPsmyEq/pTl3FwjMK ESj6nhHgQ1jhku0BSyMjKn7isi4jcX9EER7jNXU5nDdkbamBPsmyEq/pTl3FwjMK
cpTMH0I0ptP7tPFoWriJLASssXzRwXDXsGEbanF2x5TMjGf1X8kjwq0gMQDzZZkY cpTMH0I0ptP7tPFoWriJLASssXzRwXDXsGEbanF2x5TMjGf1X8kjwq0gMQDzZZkY
skipping to change at line 2036 skipping to change at line 1925
VEdCTRcCIEgRH/vTfhxnD2TxS4p7MrlMGkm0XdL8OM1SidkQrWNgLPXhMELGSsZ5 VEdCTRcCIEgRH/vTfhxnD2TxS4p7MrlMGkm0XdL8OM1SidkQrWNgLPXhMELGSsZ5
e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4PxxsB8y4j0Ei e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4PxxsB8y4j0Ei
jEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0YKdICXJm jEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0YKdICXJm
M4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZCOclCHcMR M4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZCOclCHcMR
m/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2nhYSrO6y m/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2nhYSrO6y
i5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iFcUkQiIsj i5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iFcUkQiIsj
EMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+npe6pSPXpE EMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+npe6pSPXpE
MWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0RvgYkYLS MWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0RvgYkYLS
v16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB7VjcYod2 v16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB7VjcYod2
uYOILhF1 uYOILhF1
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
} }
BIT_STRING { `00` `4b94c29450111191823b3514c9ac1ea3d9825ccb863 BIT_STRING { `00` `4b94c29450111191823b3514c9ac1ea3d9825ccb863
93a2dfb04654fa2192d37bfad1c497c6502eee5ca80a73bfce0baf5a54a88585 93a2dfb04654fa2192d37bfad1c497c6502eee5ca80a73bfce0baf5a54a88585
a401397a3d232f426a7afb082bc21a44317090eaac7592c2ea88a653c4491ea1 a401397a3d232f426a7afb082bc21a44317090eaac7592c2ea88a653c4491ea1
93931335f52e989a3c4cc56d9c553732d57c470fb41ab759b65d2d04445382fc 93931335f52e989a3c4cc56d9c553732d57c470fb41ab759b65d2d04445382fc
d9c4e344a1128fa9e11e04358e192ed014b23232a7ee2b22e23717f44111ee33 d9c4e344a1128fa9e11e04358e192ed014b23232a7ee2b22e23717f44111ee33
skipping to change at line 2093 skipping to change at line 1982
7480972663381e169996061d799859ec54d4f5ca5c411c01db1597b165977669 7480972663381e169996061d799859ec54d4f5ca5c411c01db1597b165977669
de13a928a34afbac258fea8c4764239c9421dc3119bf5b47699206978327b1c5 de13a928a34afbac258fea8c4764239c9421dc3119bf5b47699206978327b1c5
345ef746a7983841f056e2534100ab24d4e9abbd0b17c6a95bd4c3c0e40f69e1 345ef746a7983841f056e2534100ab24d4e9abbd0b17c6a95bd4c3c0e40f69e1
612aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb988 612aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb988
4f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b9 4f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b9
003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97ba 003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97ba
a523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba60 a523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba60
f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8a f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8a
13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed5 13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed5
8dc628776b983882e1175` } 8dc628776b983882e1175` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-certificate"> <section anchor="example-certificate">
<name>Example Certificates</name> <name>Example Certificates</name>
<aside> <t>The following is the ML-KEM-512 certificate corresponding to the
<t>RFC EDITOR: Please replace the following reference to
<xref target="I-D.ietf-lamps-dilithium-certificates"/> with a reference to the
published RFC.</t>
</aside>
<t>The following is the ML-KEM-512 certificate that corresponding to the
public key in the previous section signed with the ML-DSA-44 private key public key in the previous section signed with the ML-DSA-44 private key
from <xref target="I-D.ietf-lamps-dilithium-certificates"/>. The textual encodin g <xref target="RFC7468"/> from <xref target="RFC9881"/>. The textual encoding <xref target="RFC7468"/>
is followed by the so-called "pretty print"; the certificates are the same.</t> is followed by the so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIINpDCCBBqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMR MIINpDCCBBqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMR
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggMyMAsGCWCGSAFlAwQEAQOCAyEAOZWBXll9EENVzymqUzPJMlGG TEFNUFMgV0cwggMyMAsGCWCGSAFlAwQEAQOCAyEAOZWBXll9EENVzymqUzPJMlGG
nVvNvkhxJPYCuLambBbEdhZIrXZc9dgAa1FekFp/CsB2sMYu+jKBU+fKVwFpnxMF nVvNvkhxJPYCuLambBbEdhZIrXZc9dgAa1FekFp/CsB2sMYu+jKBU+fKVwFpnxMF
8ea8b5Cw5JtpNRK2zpkqi4AW3fwaZix+P5YZy9hp3Xca8wiWzNWRisbLd0ZsXneZ 8ea8b5Cw5JtpNRK2zpkqi4AW3fwaZix+P5YZy9hp3Xca8wiWzNWRisbLd0ZsXneZ
ltZ/+aq8l1A/LHt+LQANhkUPsYB8pMq9pGWCWjHHiaG3pJGrOHJ2XTINC3GSD6IT ltZ/+aq8l1A/LHt+LQANhkUPsYB8pMq9pGWCWjHHiaG3pJGrOHJ2XTINC3GSD6IT
yUCTQWuDuBJOafZeYstQANzDeqmg//c5cMR3LzV9JBicpvUwVWjA4jdqN2KmjGBe yUCTQWuDuBJOafZeYstQANzDeqmg//c5cMR3LzV9JBicpvUwVWjA4jdqN2KmjGBe
skipping to change at line 2181 skipping to change at line 2067
p598lYloyvlS1VYhwmLrpFmz0BB9OEepvdq0ZX11XM532I6WIF4lAUh0YEx1FInO p598lYloyvlS1VYhwmLrpFmz0BB9OEepvdq0ZX11XM532I6WIF4lAUh0YEx1FInO
XJ74LC2uMxa92W6nceJAjiraJKhi4VnURhPa7MUt/2oA5WY8zzmVGn94UlPsEmPj XJ74LC2uMxa92W6nceJAjiraJKhi4VnURhPa7MUt/2oA5WY8zzmVGn94UlPsEmPj
/nl7vXBVLb9Nojt9AkIO637bT+1wszCvOH8nelnzNDsCBi9B8+mdgzizEN08UKSk /nl7vXBVLb9Nojt9AkIO637bT+1wszCvOH8nelnzNDsCBi9B8+mdgzizEN08UKSk
dCaNbCB86LVeo+umyY5abmgr2NOI7XaSTqWMs7ezemR5AkIUka35LgVIKvZw2WEz dCaNbCB86LVeo+umyY5abmgr2NOI7XaSTqWMs7ezemR5AkIUka35LgVIKvZw2WEz
G3KxZImSviV+XMsakqGTdXof7k1usEcmbJ/EJLi9ecaxMZKuLjT9sFtNo8uvE/m1 G3KxZImSviV+XMsakqGTdXof7k1usEcmbJ/EJLi9ecaxMZKuLjT9sFtNo8uvE/m1
1pf4bGnGXgBERGpZsqnm+JNxDDTbD1WntdPpyeF8/6iXd/eNiHboV830Olj0dXJ4 1pf4bGnGXgBERGpZsqnm+JNxDDTbD1WntdPpyeF8/6iXd/eNiHboV830Olj0dXJ4
YbTrQBcWbfUeZ8+8gGJ0bgshMtPCrOdYVMAfWfcu7DyFi0tQdtS1pmo5Co+OwLxe YbTrQBcWbfUeZ8+8gGJ0bgshMtPCrOdYVMAfWfcu7DyFi0tQdtS1pmo5Co+OwLxe
IyKgwlIYOghCE3r6SBCrx0+sTP0sixV5Refu2JIBkjoywPavmK3+109l1F0BkzST IyKgwlIYOghCE3r6SBCrx0+sTP0sixV5Refu2JIBkjoywPavmK3+109l1F0BkzST
fQ1pAwENGx0oLVFdZHB1f4CSlZaiq8Te7AtOfX6Qtba4w8bP1+j2FSVCWGt4goSv fQ1pAwENGx0oLVFdZHB1f4CSlZaiq8Te7AtOfX6Qtba4w8bP1+j2FSVCWGt4goSv
s7TAwcrR1drv9BRiaH2qytnr8PcAAAAAAAAAAAAAAAAAAAAAFSM2QA== s7TAwcrR1drv9BRiaH2qytnr8PcAAAAAAAAAAAAAAAAAAAAAFSM2QA==
]]></artwork> -----END CERTIFICATE-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
skipping to change at line 2370 skipping to change at line 2256
3eba6c98e5a6e682bd8d388ed76924ea58cb3b7b37a647902421491adf92e054 3eba6c98e5a6e682bd8d388ed76924ea58cb3b7b37a647902421491adf92e054
82af670d961331b72b1648992be257e5ccb1a92a193757a1fee4d6eb047266c9 82af670d961331b72b1648992be257e5ccb1a92a193757a1fee4d6eb047266c9
fc424b8bd79c6b13192ae2e34fdb05b4da3cbaf13f9b5d697f86c69c65e00444 fc424b8bd79c6b13192ae2e34fdb05b4da3cbaf13f9b5d697f86c69c65e00444
46a59b2a9e6f893710c34db0f55a7b5d3e9c9e17cffa89777f78d8876e857cdf 46a59b2a9e6f893710c34db0f55a7b5d3e9c9e17cffa89777f78d8876e857cdf
43a58f475727861b4eb4017166df51e67cfbc8062746e0b2132d3c2ace75854c 43a58f475727861b4eb4017166df51e67cfbc8062746e0b2132d3c2ace75854c
01f59f72eec3c858b4b5076d4b5a66a390a8f8ec0bc5e2322a0c252183a08421 01f59f72eec3c858b4b5076d4b5a66a390a8f8ec0bc5e2322a0c252183a08421
37afa4810abc74fac4cfd2c8b157945e7eed89201923a32c0f6af98adfed74f6 37afa4810abc74fac4cfd2c8b157945e7eed89201923a32c0f6af98adfed74f6
5d45d019334937d0d6903010d1b1d282d515d6470757f80929596a2abc4deec0 5d45d019334937d0d6903010d1b1d282d515d6470757f80929596a2abc4deec0
b4e7d7e90b5b6b8c3c6cfd7e8f6152542586b788284afb3b4c0c1cad1d5daeff b4e7d7e90b5b6b8c3c6cfd7e8f6152542586b788284afb3b4c0c1cad1d5daeff
41462687daacad9ebf0f70000000000000000000000000000000015233640` } 41462687daacad9ebf0f70000000000000000000000000000000015233640` }
} }]]></artwork>
]]></artwork>
<aside> <t>The following is the ML-KEM-768 certificate corresponding to the
<t>RFC EDITOR: Please replace the following reference to
<xref target="I-D.ietf-lamps-dilithium-certificates"/> with a reference to the
published RFC.</t>
</aside>
<t>The following is the ML-KEM-768 certificate that corresponding to the
public key in the previous section signed with the ML-DSA-65 private key public key in the previous section signed with the ML-DSA-65 private key
from <xref target="I-D.ietf-lamps-dilithium-certificates"/>. The textual encodin g <xref target="RFC7468"/> from <xref target="RFC9881"/>. The textual encoding <xref target="RFC7468"/>
is followed by the so-called "pretty print"; the certificates are the same.</t> is followed by the so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIISnTCCBZqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMS MIISnTCCBZqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMS
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggSyMAsGCWCGSAFlAwQEAgOCBKEAKYqhDUI8jdoGnQK8WebN8DoJ TEFNUFMgV0cwggSyMAsGCWCGSAFlAwQEAgOCBKEAKYqhDUI8jdoGnQK8WebN8DoJ
a4s9pMq5uAykoUkHZyzO8exPryNKC8W36dRz8rMTOzsmodF1y2engFkZaZwC92Ux a4s9pMq5uAykoUkHZyzO8exPryNKC8W36dRz8rMTOzsmodF1y2engFkZaZwC92Ux
uZxfiRgHBLtMpFNcW4lyZ5xmCgfF5RS4cAnIYuuPUVdpXvs/xAqd72uBwcwCokmu uZxfiRgHBLtMpFNcW4lyZ5xmCgfF5RS4cAnIYuuPUVdpXvs/xAqd72uBwcwCokmu
TwlK0Nm9NIXBwcaAgFIKfIxjIDLO5zgVTlxRdsB9pWAkd2pDD+durPZlo/e4MhAi TwlK0Nm9NIXBwcaAgFIKfIxjIDLO5zgVTlxRdsB9pWAkd2pDD+durPZlo/e4MhAi
FbyC8Qk5yDVXBDNqj6wdgeS7BIWqXXx01rWbvlxelyoNi6xBG1W11VV81oChqPcb FbyC8Qk5yDVXBDNqj6wdgeS7BIWqXXx01rWbvlxelyoNi6xBG1W11VV81oChqPcb
skipping to change at line 2482 skipping to change at line 2365
0qHWt1xSO0G6FPK4zTyEY/84z+ecXFvxxynXLYYCm5kEhK06PYiVY5OKOaBe9vma 0qHWt1xSO0G6FPK4zTyEY/84z+ecXFvxxynXLYYCm5kEhK06PYiVY5OKOaBe9vma
qS66MzHNpfjNblJfG9O/HeiJLJ3vV7/F3U/kfxs3PStrMgoXMRt1KBrmIBB3F1xE qS66MzHNpfjNblJfG9O/HeiJLJ3vV7/F3U/kfxs3PStrMgoXMRt1KBrmIBB3F1xE
5WCaEONmuYSmJMZPbdkB+7rEsbC4v1cnyE0800BAGNYpVyPyTYbfPBthNEmYsBIV 5WCaEONmuYSmJMZPbdkB+7rEsbC4v1cnyE0800BAGNYpVyPyTYbfPBthNEmYsBIV
KSYuVQ1259Ju69UE22dqnXnorsCZCXWEpmcmRO8/Gvb0Y7OYFWltDeGLFJRbJ4av KSYuVQ1259Ju69UE22dqnXnorsCZCXWEpmcmRO8/Gvb0Y7OYFWltDeGLFJRbJ4av
5dtNm2ZH53uLPi3aYsZU9cyfxh7AcbKSfQlRSVKCj6o0BQ3ZvmBPPOvcsUbUU5oo 5dtNm2ZH53uLPi3aYsZU9cyfxh7AcbKSfQlRSVKCj6o0BQ3ZvmBPPOvcsUbUU5oo
FgCPOse60fvnKhEEO9zEnuU3RObcQPkDQRmMQ3OhibiGzOEOaU6PCEVJ3P+N+lJm FgCPOse60fvnKhEEO9zEnuU3RObcQPkDQRmMQ3OhibiGzOEOaU6PCEVJ3P+N+lJm
/0M2lNaYgaks0kmKoYdEmpLdmdGSCCB6HJ+nIIlwodrM0wK9SZUqkd+kFoGvGf7+ /0M2lNaYgaks0kmKoYdEmpLdmdGSCCB6HJ+nIIlwodrM0wK9SZUqkd+kFoGvGf7+
XkFvmlJbGn4UCaaHOUaDZsFBMiAcMAAcPv9FIM+A9NIjbC2imd0TJf+tLf6tLA6P XkFvmlJbGn4UCaaHOUaDZsFBMiAcMAAcPv9FIM+A9NIjbC2imd0TJf+tLf6tLA6P
gFHtzTF9yuL8FSI+bbLr9go0PG2SnqPM4RQha4s2OoOvtNkQI2Smvu0AAAAAAAAA gFHtzTF9yuL8FSI+bbLr9go0PG2SnqPM4RQha4s2OoOvtNkQI2Smvu0AAAAAAAAA
AAAAAAAAAAAAAAAFDBUZHyU= AAAAAAAAAAAAAAAFDBUZHyU=
]]></artwork> -----END CERTIFICATE-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
skipping to change at line 2711 skipping to change at line 2594
1344998b0121529262e550d76e7d26eebd504db676a9d79e8aec099097584a66 1344998b0121529262e550d76e7d26eebd504db676a9d79e8aec099097584a66
72644ef3f1af6f463b39815696d0de18b14945b2786afe5db4d9b6647e77b8b3 72644ef3f1af6f463b39815696d0de18b14945b2786afe5db4d9b6647e77b8b3
e2dda62c654f5cc9fc61ec071b2927d09514952828faa34050dd9be604f3cebd e2dda62c654f5cc9fc61ec071b2927d09514952828faa34050dd9be604f3cebd
cb146d4539a2816008f3ac7bad1fbe72a11043bdcc49ee53744e6dc40f903411 cb146d4539a2816008f3ac7bad1fbe72a11043bdcc49ee53744e6dc40f903411
98c4373a189b886cce10e694e8f084549dcff8dfa5266ff433694d69881a92cd 98c4373a189b886cce10e694e8f084549dcff8dfa5266ff433694d69881a92cd
2498aa187449a92dd99d19208207a1c9fa7208970a1daccd302bd49952a91dfa 2498aa187449a92dd99d19208207a1c9fa7208970a1daccd302bd49952a91dfa
41681af19fefe5e416f9a525b1a7e1409a68739468366c14132201c30001c3ef 41681af19fefe5e416f9a525b1a7e1409a68739468366c14132201c30001c3ef
f4520cf80f4d2236c2da299dd1325ffad2dfead2c0e8f8051edcd317dcae2fc1 f4520cf80f4d2236c2da299dd1325ffad2dfead2c0e8f8051edcd317dcae2fc1
5223e6db2ebf60a343c6d929ea3cce114216b8b363a83afb4d9102364a6beed0 5223e6db2ebf60a343c6d929ea3cce114216b8b363a83afb4d9102364a6beed0
00000000000000000000000000000000000050c15191f25` } 00000000000000000000000000000000000050c15191f25` }
} }]]></artwork>
]]></artwork> <t>The following is the ML-KEM-1024 certificate corresponding to the
<aside>
<t>RFC EDITOR: Please replace the following reference to
<xref target="I-D.ietf-lamps-dilithium-certificates"/> with a reference to the
published RFC.</t>
</aside>
<t>The following is the ML-KEM-1024 certificate that corresponding to th
e
public key in the previous section signed with the ML-DSA-87 private key public key in the previous section signed with the ML-DSA-87 private key
from <xref target="I-D.ietf-lamps-dilithium-certificates"/>. The textual encodin g <xref target="RFC7468"/> from <xref target="RFC9881"/>. The textual encoding <xref target="RFC7468"/>
is followed by the so-called "pretty print"; the certificates are the same.</t> is followed by the so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIZQzCCBxqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMT MIIZQzCCBxqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMT
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggYyMAsGCWCGSAFlAwQEAwOCBiEAS5TClFAREZGCOzUUyaweo9mC TEFNUFMgV0cwggYyMAsGCWCGSAFlAwQEAwOCBiEAS5TClFAREZGCOzUUyaweo9mC
XMuGOTot+wRlT6IZLTe/rRxJfGUC7uXKgKc7/OC69aVKiFhaQBOXo9Iy9Canr7CC XMuGOTot+wRlT6IZLTe/rRxJfGUC7uXKgKc7/OC69aVKiFhaQBOXo9Iy9Canr7CC
vCGkQxcJDqrHWSwuqIplPESR6hk5MTNfUumJo8TMVtnFU3MtV8Rw+0GrdZtl0tBE vCGkQxcJDqrHWSwuqIplPESR6hk5MTNfUumJo8TMVtnFU3MtV8Rw+0GrdZtl0tBE
RTgvzZxONEoRKPqeEeBDWOGS7QFLIyMqfuKyLiNxf0QRHuM1dTmcN2RtqYE+ybIS RTgvzZxONEoRKPqeEeBDWOGS7QFLIyMqfuKyLiNxf0QRHuM1dTmcN2RtqYE+ybIS
r+lOXcXCMwpylMwfQjSm0/u08WhauIksBKyxfNHBcNewYRtqcXbHlMyMZ/VfySPC r+lOXcXCMwpylMwfQjSm0/u08WhauIksBKyxfNHBcNewYRtqcXbHlMyMZ/VfySPC
skipping to change at line 2858 skipping to change at line 2737
jE6JffIAEtZan8bJyuD9lNJgr4raeyt2rqRLmpoY1Emk5HSioIjsgUTu92FeMp/b jE6JffIAEtZan8bJyuD9lNJgr4raeyt2rqRLmpoY1Emk5HSioIjsgUTu92FeMp/b
YWP6Fc/rXHoYl5xR5kUW4BtiB+592H/XdJzPHJQx2kjzS4gh1NH5s0yENMOWYTar YWP6Fc/rXHoYl5xR5kUW4BtiB+592H/XdJzPHJQx2kjzS4gh1NH5s0yENMOWYTar
0HJecZth4BF3SNDzElWcOvGWnMQj/fpkHgAq+aqXa2UCd4P/FaEXVUOuxy+vnHwe 0HJecZth4BF3SNDzElWcOvGWnMQj/fpkHgAq+aqXa2UCd4P/FaEXVUOuxy+vnHwe
qqigp/mWD19+DiTyv7WEe+o/AomHctLyigGFlR2zs3yLXSwNnDJ6YANpgMlEspwS qqigp/mWD19+DiTyv7WEe+o/AomHctLyigGFlR2zs3yLXSwNnDJ6YANpgMlEspwS
3ToM7PbcVC9vDfjKhGdAhvdVT1lr7IU0fYeMVppE6HkoKS6tbsokb9qtbvtvWCfz 3ToM7PbcVC9vDfjKhGdAhvdVT1lr7IU0fYeMVppE6HkoKS6tbsokb9qtbvtvWCfz
I6342qm7BW6/SiZEx/Sl/DzF8qA3eLHM0xFR2kvHsn+5AB5ucy2ZOJF2W9XuwYSU I6342qm7BW6/SiZEx/Sl/DzF8qA3eLHM0xFR2kvHsn+5AB5ucy2ZOJF2W9XuwYSU
BPoRrmdIWKQYC8/MD5PtZMqUoEGvHl6jFpfbO6+RP6NakpA+q4Tl4xuDNyeKqOdD BPoRrmdIWKQYC8/MD5PtZMqUoEGvHl6jFpfbO6+RP6NakpA+q4Tl4xuDNyeKqOdD
9+XdE3acWR/r+JseircGaBDDkpjBElcYgZuLfqKrx1+G5i6t6gWopcNtLmVcuAWv 9+XdE3acWR/r+JseircGaBDDkpjBElcYgZuLfqKrx1+G5i6t6gWopcNtLmVcuAWv
HVT854OIkNIUoqfnESODrczb3C5kjJ230df4V156qMbJBwwcJFtzf5ObyO3ycnd/ HVT854OIkNIUoqfnESODrczb3C5kjJ230df4V156qMbJBwwcJFtzf5ObyO3ycnd/
kNggIp4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQIDxcdKS4x kNggIp4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQIDxcdKS4x
]]></artwork> -----END CERTIFICATE-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
skipping to change at line 3140 skipping to change at line 3019
e24f2bfb5847bea3f02898772d2f28a0185951db3b37c8b5d2c0d9c327a60036 e24f2bfb5847bea3f02898772d2f28a0185951db3b37c8b5d2c0d9c327a60036
980c944b29c12dd3a0cecf6dc542f6f0df8ca84674086f7554f596bec85347d8 980c944b29c12dd3a0cecf6dc542f6f0df8ca84674086f7554f596bec85347d8
78c569a44e87928292ead6eca246fdaad6efb6f5827f323adf8daa9bb056ebf4 78c569a44e87928292ead6eca246fdaad6efb6f5827f323adf8daa9bb056ebf4
a2644c7f4a5fc3cc5f2a03778b1ccd31151da4bc7b27fb9001e6e732d9938917 a2644c7f4a5fc3cc5f2a03778b1ccd31151da4bc7b27fb9001e6e732d9938917
65bd5eec1849404fa11ae674858a4180bcfcc0f93ed64ca94a041af1e5ea3169 65bd5eec1849404fa11ae674858a4180bcfcc0f93ed64ca94a041af1e5ea3169
7db3baf913fa35a92903eab84e5e31b8337278aa8e743f7e5dd13769c591febf 7db3baf913fa35a92903eab84e5e31b8337278aa8e743f7e5dd13769c591febf
89b1e8ab7066810c39298c1125718819b8b7ea2abc75f86e62eadea05a8a5c36 89b1e8ab7066810c39298c1125718819b8b7ea2abc75f86e62eadea05a8a5c36
d2e655cb805af1d54fce7838890d214a2a7e7112383adccdbdc2e648c9db7d1d d2e655cb805af1d54fce7838890d214a2a7e7112383adccdbdc2e648c9db7d1d
7f8575e7aa8c6c9070c1c245b737f939bc8edf272777f90d820229e000000000 7f8575e7aa8c6c9070c1c245b737f939bc8edf272777f90d820229e000000000
000000000000000000000000000000000000000000004080f171d292e31` } 000000000000000000000000000000000000000000004080f171d292e31` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-bad"> <section anchor="example-bad">
<name>Examples of Bad Private Keys</name> <name>Examples of Bad Private Keys</name>
<!-- [rfced] Please confirm that the WARNING should be tagged as an <aside>, whi
ch is defined as "a container for
content that is semantically less important or tangential to the
content that surrounds it" (https://authors.ietf.org/en/rfcxml-vocabulary#aside)
.
Original:
C.4. Examples of Bad Private Keys
| WARNING: These private keys are purposely bad do not use them
| in production systems.
-->
<aside> <aside>
<t>WARNING: These private keys are purposely bad do not use them in <t>WARNING: These private keys are purposely bad. Do not use them in
production systems.</t> production systems.</t>
</aside> </aside>
<t>The following examples demonstrate inconsistent seed and <t>The following examples demonstrate inconsistent seed and
expanded private keys.</t> expanded private keys.</t>
<section anchor="ml-kem-inconsistent-seed-and-expanded-private-keys"> <section anchor="ml-kem-inconsistent-seed-and-expanded-private-keys">
<name>ML-KEM Inconsistent Seed and Expanded Private Keys</name> <name>ML-KEM Inconsistent Seed and Expanded Private Keys</name>
<t>Four <tt>ML-KEM-512-PrivateKey</tt> examples of inconsistent seed a nd <t>Four <tt>ML-KEM-512-PrivateKey</tt> examples of inconsistent seed a nd
expanded private keys follow:</t> expanded private keys are shown as follows:</t>
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1"><li>
<t>The first <tt>ML-KEM-512-PrivateKey</tt> example includes the <t>The first <tt>ML-KEM-512-PrivateKey</tt> example includes the
<tt>both CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are <tt>both CHOICE</tt>, i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are
included. The <tt>seed</tt> and <tt>expanded</tt> values can be checked included. The <tt>seed</tt> and <tt>expanded</tt> values can be checked
for inconsistencies.</t> for inconsistencies.</t>
</li> </li>
<li> <li>
<t>The second <tt>ML-KEM-512-PrivateKey</tt> example includes only <t>The second <tt>ML-KEM-512-PrivateKey</tt> example includes only
<tt>expandedKey</tt>. The expanded private key has a mutated <tt>s_0</tt> <tt>expandedKey</tt>. The expanded private key has a mutated <tt>s_0</tt>
and a valid public key hash, but a pairwise consistency and a valid public key hash, but a pairwise consistency
check would find that the public key fails to match private.</t> check would find that the public key fails to match private.</t>
</li> </li>
<li> <li>
<t>The third <tt>ML-KEM-512-PrivateKey</tt> example includes only <t>The third <tt>ML-KEM-512-PrivateKey</tt> example includes only
<tt>expandedKey</tt>. The expanded private key has a mutated H(ek); both <tt>expandedKey</tt>. The expanded private key has a mutated H(ek); both
a public key digest check and a pairwise consistency check should fail.</t> a public key digest check and a pairwise consistency check should fail.</t>
</li> </li>
<li> <li>
<t>The fourth <tt>ML-KEM-512-PrivateKey</tt> example includes the <t>The fourth <tt>ML-KEM-512-PrivateKey</tt> example includes the
<tt>both CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are <tt>both CHOICE</tt>, i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are
included. There is mismatch of the seed and expanded private included. There is mismatch of the seed and expanded private
key in only the <tt>z</tt> implicit rejection secret; here the private key in only the <tt>z</tt> implicit rejection secret; here, the private
and public vectors match and the pairwise consistency check passes, and public vectors match and the pairwise consistency check passes,
but z is different.</t> but z is different.</t>
</li> </li>
</ol> </ol>
<t>The following is the first example:</t> <t>The following is the first example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8hIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/QASC EhMUFRYXGBkaGxwdHh8hIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/QASC
BmDvsn6JOEO1+bZhFYaTegU33BzhWY5u8TDVVBiwaUFnGLk3E4KY1lkkOQvUIErq BmDvsn6JOEO1+bZhFYaTegU33BzhWY5u8TDVVBiwaUFnGLk3E4KY1lkkOQvUIErq
skipping to change at line 3221 skipping to change at line 3110
wYcd92UvxsLZZMaOBGUG4y1oUnmy1hoKORa2y8xCVs7saBUDaanfGivRaoTByGal wYcd92UvxsLZZMaOBGUG4y1oUnmy1hoKORa2y8xCVs7saBUDaanfGivRaoTByGal
EG4ugDqhfI6RG7A2CCKkfLsdNDGBuRLqYg6RZXN0ai679nnZYsJTV0m/YV8iioKU EG4ugDqhfI6RG7A2CCKkfLsdNDGBuRLqYg6RZXN0ai679nnZYsJTV0m/YV8iioKU
mFhvgx4sK44rMAIKgmC+7LxHvHGra45wtjgwpg8NYH/vcbxvYwk/IyaOmQKGiGIA mFhvgx4sK44rMAIKgmC+7LxHvHGra45wtjgwpg8NYH/vcbxvYwk/IyaOmQKGiGIA
zLqF+4OEVlMQlUOxeh3spjJtm4rV2kUshji24i9h4ROPZ8DVZq4lqTfxJcsaVnJQ zLqF+4OEVlMQlUOxeh3spjJtm4rV2kUshji24i9h4ROPZ8DVZq4lqTfxJcsaVnJQ
4HhdomaWKnJ6lEpgMreOQlyYxp2GOAJf52GdIyKsAV9y2bfWMmuHhAniYarDxz0N 4HhdomaWKnJ6lEpgMreOQlyYxp2GOAJf52GdIyKsAV9y2bfWMmuHhAniYarDxz0N
+6JY0Q67VTT7AVHVx1aeVh3Vg6qVi7XX447eQoMy230pwnAMSI4fARfjZwA/5mev +6JY0Q67VTT7AVHVx1aeVh3Vg6qVi7XX447eQoMy230pwnAMSI4fARfjZwA/5mev
42xo+n6QWhj1BC8iEafPhBz/F5BtGVQwjMSii111xw/9+lygBlJOSR+8Gbu45oQ/ 42xo+n6QWhj1BC8iEafPhBz/F5BtGVQwjMSii111xw/9+lygBlJOSR+8Gbu45oQ/
uRoNz67mpuEldXK2fWtiQmYsoAnY0qhOArxWajY+/0pEdTMpOV105HVzD50LQ05m uRoNz67mpuEldXK2fWtiQmYsoAnY0qhOArxWajY+/0pEdTMpOV105HVzD50LQ05m
hHpZnF6s80FNh4KdUx3AVX9XISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+ hHpZnF6s80FNh4KdUx3AVX9XISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+
P0A= P0A=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the second example:</t> <t>The following is the second example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHFVT9Q2NE8nhbGzsbrBhLZnkAMz MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHFVT9Q2NE8nhbGzsbrBhLZnkAMz
bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX
NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA
iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK
skipping to change at line 3261 skipping to change at line 3151
tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2 uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the third example:</t> <t>The following is the third example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz
bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX
NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA
iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK
skipping to change at line 3301 skipping to change at line 3192
tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2 uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
uBw7xZoGWhttY7Jsg/EB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj uBw7xZoGWhttY7Jsg/EB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the fourth example:</t> <t>The following is the fourth example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF
GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1 GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1
a7xgG2Voq3hKy66zRwLw+GomICEYsisj+DVYd2x5wU26mDN5yAPg3MMWChF1cDDm a7xgG2Voq3hKy66zRwLw+GomICEYsisj+DVYd2x5wU26mDN5yAPg3MMWChF1cDDm
nGkZeY2B62mKmkSDqZ5aXLLDHJpmF5nzzInHkHBuoEFikEXUKoOu2Ihg45TGkYfi nGkZeY2B62mKmkSDqZ5aXLLDHJpmF5nzzInHkHBuoEFikEXUKoOu2Ihg45TGkYfi
EF0ozBTsOTWS1n3QCqQ/6LTq5EFAAoZrXHE8ao19Fs94uBnW8S6eWnQjOQjwsV48 EF0ozBTsOTWS1n3QCqQ/6LTq5EFAAoZrXHE8ao19Fs94uBnW8S6eWnQjOQjwsV48
S6gynFzdpVyEko46qAY+WqlnZAP5FzWxEBDH9ZMJE2TchkRbyASECpohckISRp+K S6gynFzdpVyEko46qAY+WqlnZAP5FzWxEBDH9ZMJE2TchkRbyASECpohckISRp+K
skipping to change at line 3343 skipping to change at line 3235
dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa
8bPEVSj7oVP2x4scGYcClHzNM3cnpG+1O6Ed5ctBkTRoWVFstq1yQA888gmyNq7z 8bPEVSj7oVP2x4scGYcClHzNM3cnpG+1O6Ed5ctBkTRoWVFstq1yQA888gmyNq7z
WlgKyH6z4w+v1mlzyop90mda9B96F7YUM80a+A93CIafZlSISXmAsawQoM3LY2oA WlgKyH6z4w+v1mlzyop90mda9B96F7YUM80a+A93CIafZlSISXmAsawQoM3LY2oA
7YaBs15CkSTKgDUHJbhfg6Xqw6SjzBYAkD5lKTVgubM25a8NUp2sGgSBGTAst6m8 7YaBs15CkSTKgDUHJbhfg6Xqw6SjzBYAkD5lKTVgubM25a8NUp2sGgSBGTAst6m8
wRC5SFG/AhF/GZ3EhahSt0c/CbgxpoMdW1TAt5DSJc9ruS2UYqJs2zPdpRI8eq8O wRC5SFG/AhF/GZ3EhahSt0c/CbgxpoMdW1TAt5DSJc9ruS2UYqJs2zPdpRI8eq8O
JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN
Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG
dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0 dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0
VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9 VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
Pj4= Pj4=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
</section> </section>
</section> </section>
</section> </section>
<section numbered="false" anchor="acknowledgments"> <section numbered="false" anchor="acknowledgments">
<name>Acknowledgments</name> <name>Acknowledgments</name>
<t>The authors wish to thank the following people for their contributions <t>The authors wish to thank the following people for their
to this document: Corey Bonnell, Deirdre Connolly, Viktor Dukhovni, Alicja Kario contributions to this document: <contact fullname="Corey Bonnell"/>,
, Russ <contact fullname="Deirdre Connolly"/>, <contact fullname="Viktor
Housley, Mike Ounsworth, Daniel Van Geest, Thom Wiggers, and Carl Wallace.</t> Dukhovni"/>, <contact fullname="Alicja Kario"/>, <contact fullname="Russ
<t>In addition, we would like to thank those who contributed to the privat Housley"/>, <contact fullname="Mike Ounsworth"/>, <contact
e fullname="Daniel Van Geest"/>, <contact fullname="Thom Wiggers"/>, and
key format discussion: Tony Arcieri, Bob Beck, Dmitry Belyavskiy, David <contact fullname="Carl Wallace"/>.</t>
Benjamin, Daniel Bernstein, Uri Blumenthal, Theo Buehler, Stephen Farrell, <t>In addition, we would like to thank those who contributed to the
Jean-Pierre Fiset, Scott Fluhrer, Alex Gaynor, John Gray, Peter Gutmann, private key format discussion: <contact fullname="Tony Arcieri"/>,
David Hook, Tim Hudson, Paul Kehrer, John Kemp, Watson Ladd, Adam Langley, <contact fullname="Bob Beck"/>, <contact fullname="Dmitry Belyavskiy"/>,
John Mattsson, Damien Miller, Robert Relyea, Michael Richardson, <contact fullname="David Benjamin"/>, <contact fullname="Daniel
Markku-Juhani O. Saarinen, Rich Salz, Roland Shoemaker, Sophie Schmieg, Bernstein"/>, <contact fullname="Uri Blumenthal"/>, <contact
Simo Sorce, Michael St. Johns, Falko Strenzke, Filippo Valsorda, and fullname="Theo Buehler"/>, <contact fullname="Stephen Farrell"/>,
Wei-Jun Wang.</t> <contact fullname="Jean-Pierre Fiset"/>, <contact fullname="Scott
Fluhrer"/>, <contact fullname="Alex Gaynor"/>, <contact fullname="John
Gray"/>, <contact fullname="Peter Gutmann"/>, <contact fullname="David
Hook"/>, <contact fullname="Tim Hudson"/>, <contact fullname="Paul
Kehrer"/>, <contact fullname="John Kemp"/>, <contact fullname="Watson
Ladd"/>, <contact fullname="Adam Langley"/>, <contact fullname="John
Mattsson"/>, <contact fullname="Damien Miller"/>, <contact
fullname="Robert Relyea"/>, <contact fullname="Michael Richardson"/>,
<contact fullname="Markku-Juhani O. Saarinen"/>, <contact fullname="Rich
Salz"/>, <contact fullname="Roland Shoemaker"/>, <contact
fullname="Sophie Schmieg"/>, <contact fullname="Simo Sorce"/>, <contact
fullname="Michael St. Johns"/>, <contact fullname="Falko Strenzke"/>,
<contact fullname="Filippo Valsorda"/>, and <contact fullname="Wei-Jun
Wang"/>.</t>
</section> </section>
</back> </back>
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<!-- [rfced] We have added expansions for abbreviations throughout the
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In addition, please consider whether "tradition" should be updated for
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<https://web.archive.org/web/20250214092458/https://www.nist.gov/nist-research-l
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indicates that this term is potentially biased, it is also ambiguous.
"Tradition" is a subjective term, as it is not the same for everyone. Possible
substitutions for "traditional" (used in past RFCs) include "commonly used",
"typical", "long-established", "conventional", and "time-honored". -->
</rfc> </rfc>
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