<?xml version='1.0'encoding='utf-8'?>encoding='UTF-8'?> <!DOCTYPE rfc [ <!ENTITY nbsp " "> <!ENTITY zwsp "​"> <!ENTITY nbhy "‑"> <!ENTITY wj "⁠"> ]><?xml-stylesheet type="text/xsl" href="rfc2629.xslt" ?> <!-- generated by https://github.com/cabo/kramdown-rfc version 1.7.19 (Ruby 2.6.10) --><rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft-ietf-lamps-kyber-certificates-11" number="9935" updates="" obsoletes="" xml:lang="en" category="std" consensus="true" submissionType="IETF" tocInclude="true" sortRefs="true" symRefs="true" version="3"><!-- xml2rfc v2v3 conversion 3.23.2 --><front> <title abbrev="ML-KEM in Certificates">Internet X.509 Public Key Infrastructure - Algorithm Identifiers for the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM)</title> <!-- [rfced] We note that this document does not seem to describe ML-KEM as an algorithm. 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 --> <seriesInfoname="Internet-Draft" value="draft-ietf-lamps-kyber-certificates-11"/>name="RFC" value="9935"/> <author initials="S." surname="Turner" fullname="Sean Turner"> <organization>sn3rd</organization> <address> <email>sean@sn3rd.com</email> </address> </author> <author initials="P." surname="Kampanakis" fullname="Panos Kampanakis"> <organization>AWS</organization> <address> <email>kpanos@amazon.com</email> </address> </author> <author initials="J." surname="Massimo" fullname="Jake Massimo"> <organization>AWS</organization> <address> <email>jakemas@amazon.com</email> </address> </author> <author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan"> <organization>Cloudflare</organization> <address> <email>bas@westerbaan.name</email> </address> </author> <dateyear="2025" month="July" day="16"/>year="2026" month="February"/> <area>SEC</area><workgroup>LAMPS</workgroup> <keyword>ML-KEM Kyber KEM Certificate X.509 PKIX</keyword><workgroup>lamps</workgroup> <keyword>ML-KEM</keyword> <keyword>Kyber</keyword> <keyword>KEM</keyword> <keyword>Certificate</keyword> <keyword>X.509</keyword> <keyword>PKIX</keyword> <abstract><?line 111?><t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) is a quantum-resistantkey-encapsulation mechanismKey Encapsulation Mechanism (KEM). This document specifies the conventions for using the ML-KEM in X.509 Public Key Infrastructure. The conventions for the subject public keys and private keys are also specified.</t> </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.html"/>. 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 mailing list (<eref target="mailto:spasm@ietf.org"/>), which is archived at <eref target="https://mailarchive.ietf.org/arch/browse/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> <middle><?line 119?><section anchor="introduction"> <!-- [rfced] We have removed "the earlier" because it is redundant with "prior to". 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> <t>The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) standardized in <xref target="FIPS203"/> is a quantum-resistantkey-encapsulation mechanismKey Encapsulation Mechanism (KEM) standardized by the US National Institute of Standards and Technology (NIST)PQCPost-Quantum Cryptography (PQC) Project <xref target="NIST-PQC"/>. Prior to standardization,the earlierversions of the mechanism were known as Kyber. ML-KEM and Kyber are not compatible. This document specifies the use of ML-KEM in Public Key Infrastructure using X.509 (PKIX) certificates <xref target="RFC5280"/> at three security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024, using object identifiers (OIDs) assigned by NIST. The private key format is also specified.</t> <section anchor="applicability-statement"> <name>Applicability Statement</name> <t>ML-KEM certificates are used in protocols where the public key is used to generate and encapsulate a shared secret used to derive a symmetric key used to encrypt a payload; see <xreftarget="I-D.ietf-lamps-cms-kyber"/>.target="RFC9936"/>. To be used in TLS, ML-KEM certificates could only be used as end-entity identity certificates and would require significant updates to the protocol;see,for example, see <xref target="I-D.celi-wiggers-tls-authkem"/>.</t> </section> </section> <section anchor="conventions-and-definitions"> <name>Conventions and Definitions</name><t>The<t> The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be interpreted as described inBCP 14BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and only when, they appear in all capitals, as shownhere.</t> <?line -18?>here. </t> </section> <section anchor="oids"> <name>Algorithm Identifiers</name> <t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC5912"/> as follows:</t> <artwork><![CDATA[ AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= SEQUENCE { algorithm ALGORITHM-TYPE.&id({AlgorithmSet}), parameters ALGORITHM-TYPE. &Params({AlgorithmSet}{@algorithm}) OPTIONAL} ]]></artwork>}]]></artwork> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t>The fields in <tt>AlgorithmIdentifier</tt> have the following meanings:</t> <ul spacing="normal"> <li> <t><tt>algorithm</tt> identifies the cryptographic algorithm with anobject identifier.</t>OID.</t> </li> <li> <t><tt>parameters</tt>, which are optional, are the associated parameters for the algorithm identifier in the <tt>algorithm</tt> field.</t> </li> </ul> <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)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 public key <bcp14>MUST</bcp14> be absent.</t> <artwork><![CDATA[ nistAlgorithms OBJECT IDENTIFIER ::= { joint-iso-ccitt(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithm(4) } kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 } id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 } id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 } id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3} ]]></artwork>}]]></artwork> </section> <section anchor="pub-key"> <name>Subject Public Key Fields</name> <t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has the <tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t> <artwork><![CDATA[ SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE { algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}}, subjectPublicKey BIT STRING} ]]></artwork>}]]></artwork> <t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning:</t> <ul spacing="normal"> <li> <t><tt>algorithm</tt> is the algorithm identifier and parameters for the public key (see above).</t> </li> <li> <t><tt>subjectPublicKey</tt> contains the byte stream of the public key.</t> </li> </ul> <t>For each ML-KEM parameterset, seeset (see <xreftarget="tab-strengths"/>,target="tab-strengths"/>), we define a <tt>PUBLIC-KEY</tt> ASN.1 type asfollows.</t>follows:</t> <artwork><![CDATA[ pk-ml-kem-512 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-512 -- KEY no ASN.1 wrapping; 800 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-512-PrivateKey -- defined in Section 6 } pk-ml-kem-768 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-768 -- KEY no ASN.1 wrapping; 1184 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-768-PrivateKey -- defined in Section 6 } pk-ml-kem-1024 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-1024 -- KEY no ASN.1 wrapping; 1568 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-1024-PrivateKey -- defined in Section 6 } ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800)) ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184)) ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE(1568)) ]]></artwork>(1568))]]></artwork> <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 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 corresponding to the correct key size.</t> <t><xref target="RFC5958"/> describes the Asymmetric Key Package's <tt>OneAsymmetricKey</tt> type for encoding asymmetrickeypairs.key pairs. When an ML-KEM private key orkeypairkey pair is encoded as a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-key"/>.</t> <t>When the ML-KEM private key appears outside of an Asymmetric Key Package 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-key"/>. The <tt>seed</tt> format is<bcp14>RECOMMENDED</bcp14><bcp14>RECOMMENDED</bcp14>, as it efficiently stores both the private and public key.</t> <t><xref target="example-public"/> contains examples for ML-KEM public keys encoded using the textual encoding defined in <xref target="RFC7468"/>.</t> </section> <section anchor="key-usage-bits"> <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 certificate 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 the only key usage set for certificates that indicate <tt>id-alg-ml-kem-*</tt> in <tt>SubjectPublicKeyInfo</tt>, (with <tt>*</tt>eitherbeing one of 512, 768, or 1024.)</t> </section> <section anchor="priv-key"> <name>Private Key Format</name> <t><xref target="FIPS203"/> specifies two formats for an ML-KEM private key: a 64-octet seed and an (expanded) private key, which is referred to as the 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) 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, <tt>ML-KEM.KeyGen()</tt> (algorithm19), which19) is used; it combines seed generation with<tt>ML-KEM.KeyGen_internal(d,z)</tt>, is used.</t><tt>ML-KEM.KeyGen_internal(d,z)</tt>.</t> <t>Akeypairkey pair is generated by sampling 64 octets uniformly at random for the seed (private key) from a cryptographically secure pseudorandom number generator(CSPRNGs).(CSPRNG). The public key can then 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 encode a private 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 key to be included as well. For illustration, the ASN.1 structure <tt>OneAsymmetricKey</tt> is replicated below.</t> <artwork><![CDATA[ OneAsymmetricKey ::= SEQUENCE { version Version, privateKeyAlgorithm SEQUENCE { algorithm PUBLIC-KEY.&id({PublicKeySet}), parameters PUBLIC-KEY.&Params({PublicKeySet} {@privateKeyAlgorithm.algorithm}) OPTIONAL} privateKey OCTET STRING (CONTAINING PUBLIC-KEY.&PrivateKey({PublicKeySet} {@privateKeyAlgorithm.algorithm})), attributes [0] Attributes OPTIONAL, ..., [[2: publicKey [1] BIT STRING (CONTAINING PUBLIC-KEY.&Params({PublicKeySet} {@privateKeyAlgorithm.algorithm}) OPTIONAL ]], ...} ]]></artwork>}]]></artwork> <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> format is a fixed 64-byte <tt>OCTET STRING</tt> (66 bytes total with the <tt>0x8040</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> <artwork><![CDATA[ ML-KEM-512-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (1632)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (1632)) } } ML-KEM-768-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (2400)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (2400)) } } ML-KEM-1024-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (3168)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (3168)) }} ]]></artwork>}]]></artwork> <t>The <tt>CHOICE</tt> allows three representations of the private key:</t> <ul spacing="normal"> <li> <t>The <tt>seed</tt> format (tag [0]) contains just the 64-byte seed value 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 the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>.</t> </li> <li> <t>The <tt>expandedKey</tt> format contains the expanded private key that was derived from the seed. If the seed is not exported, both the expanded private key and public key can be derived using <tt>ML-KEM.KeyGen()</tt> (algorithm 16).</t> </li> <li> <t>The <tt>both</tt> format contains both the seed and expanded private key, allowing for interoperability; some may want to use and retain the seed and others may only support expanded private keys.</t> </li> </ul> <t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier</tt> structure with the appropriate OID as defined in <xref target="oids"/>.</t> <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 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 format is<bcp14>RECOMMENDED</bcp14><bcp14>RECOMMENDED</bcp14>, as it is the most compact representation. Both the 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 the first 32 octets as <em>d</em> and the remaining 32 octets as <em>z</em>. Alternatively, the public key can be extracted from the expanded private key. While the <tt>publicKey</tt> field and <tt>expandedKey</tt> format are technically redundant when using the seed-only format, they <bcp14>MAY</bcp14> be included to enablekeypairkey pair consistency checks during import operations.</t> <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-specific 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 <tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, rather than any other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t> <t><xref target="example-private"/> contains examples for ML-KEM private keys encoded using the textual encoding defined in <xref target="RFC7468"/>.</t> </section> <section anchor="implementation-considerations"> <name>Implementation Considerations</name> <t>ThoughsectionSection 7.1 of <xref target="FIPS203"/> mentions the potential to save seed values for future expansion, Algorithm 19 does not make the seed values available to a caller for serialization. Similarly, the algorithm that expands seed values is not listed as one of the "main 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"/> to support serialization of seed values as private keys.</t> <t>To support serialization of seed values as private keys, let Algorithm 19b denote the same procedure as Algorithm 19 in <xreftarget="FIPS203"/>target="FIPS203"/>, except it returns (ek, dk, d, z) on line 7. Additionally, Algorithm 16 should be promoted 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 algorithms, expanding a private key from a seed is a one-way function, meaning that once a full key is expanded from a seed and the seed discarded, the seed cannot bere-createdrecreated even if the full expanded private key is available. For thisreasonreason, it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the seed, even when also exporting the expanded private key.</t> </section> <section anchor="private-key-consistency-testing"> <name>Private Key Consistency Testing</name> <!-- [rfced] Should "but" be "and", or perhaps "so"? It's not clear that the text 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 expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency check to ensure that the sender properly generated the private key. Recipients that do not perform this seed consistency check avoid keygen and compare operations, but they are unable to ensure that the <tt>seed</tt> and <tt>expandedKey</tt> match.</t> <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> <t>When receiving a private key that contains an <tt>expandedKey</tt>, <xref target="FIPS203"/> stipulates insectionSection 7.3 that before use, a "hash check" <bcp14>MUST</bcp14> be performed. That section stipulates two other checks on the type and length of the<tt>expandedKey</tt><tt>expandedKey</tt>, which are ensured by this standard.</t> <t>The seed consistency check consists of regenerating the expanded form from 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 it is bytewise equal to the value presented in the private key.</t> <t><xref target="example-bad"/> includes some examples of inconsistent seeds and expanded private keys.</t> </section> <section anchor="security-considerations"> <name>Security Considerations</name> <t>The Security Considerations section of <xref target="RFC5280"/> applies to this specification as well.</t> <t>Protection of theprivate-keyprivate key information, i.e., the seed, is vital topublic-keypublic key cryptography. Disclosure of theprivate-keyprivate key material to another entity can lead to masquerades.</t> <t>The generation of private keys relies on random numbers. The use of inadequatepseudo-randompseudorandom number generators (PRNGs) to generate these values can result in little or no security. An attacker may find it much easier to reproduce the PRNG environment that produced the keys, searching the resulting small set of possibilities, rather than brute force searching the whole key space. The generation of quality random numbers is difficult. ML-KEM key generation has specific requirements around randomness generation as described insectionSection 3.3 of <xref target="FIPS203"/>.</t> <t>Many protocols only rely on the IND-CCA security of a KEM. Some (implicitly) require further binding properties, formalized in <xref target="CDM23"/>. The private key format influences these binding properties. 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, but not MAL-BIND-K-CT norMAL-BIND-K-PK.MAL-BIND-K-PK secure. Using the 64-byte seed format provides a step up in binding security, and additionallyprovidingprovides MAL-BIND-K-CTsecurity, butsecurity (but still does notMAL-BIND-K-PK.</t>provide security for MAL-BIND-K-PK).</t> <t>For more detailed ML-KEM specific security considerations regarding this, randomness, misbinding properties, decapsulation failures, key reuse, and key checks, refer to <xref target="I-D.sfluhrer-cfrg-ml-kem-security-considerations"/>.</t> </section> <section anchor="iana-considerations"> <name>IANA Considerations</name> <t>For the ASN.1Modulemodule in <xref target="asn1"/>, IANAis requested to assignhas assigned anobject identifier (OID)OID for the module identifier(TBD)(121) with aDescriptiondescription of"id-mod-x509-ml-kem-2025". The OID for the module should be allocated"id-mod-x509-ml-kem-2025" in the "SMI Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).</t> </section> </middle> <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"> <name>References</name> <references anchor="sec-normative-references"> <name>Normative References</name> <!-- [rfced] References a) FYI: We updated the date of [CSOR] from 20 August 2024 to 13 June 2025 to match the one provided at the URL. Original: [CSOR] NIST, "Computer Security Objects Register", 20 August 2024, <https://csrc.nist.gov/projects/computer-security- 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 ObjectsRegister</title>Register (CSOR)</title> <author> <organization>NIST</organization> </author> <dateyear="2024" month="August" day="20"/>year="2025" month="June" day="13"/> </front> </reference> <reference anchor="X680" target="https://www.itu.int/rec/T-REC-X.680"> <front> <title>Information technology - Abstract Syntax Notation One (ASN.1): Specification of basic notation</title> <author> <organization>ITU-T</organization> </author> <date year="2021" month="February"/> </front> <seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/> </reference> <reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690"> <front> <title>Information technology -Abstract Syntax Notation One (ASN.1):ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title> <author> <organization>ITU-T</organization> </author> <date year="2021" month="February"/> </front> <seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/> </reference> <referenceanchor="FIPS203">anchor="FIPS203" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.203.pdf"> <front><title>Module-lattice-based key-encapsulation mechanism standard</title><title>Module-Lattice-Based Key-Encapsulation Mechanism Standard</title> <author><organization/> </author> <date month="August" year="2024"/> </front> <seriesInfo name="DOI" value="10.6028/nist.fips.203"/> <refcontent>National<organization abbrev="NIST">National Institute of Standards andTechnology (U.S.)</refcontent> </reference> <reference anchor="RFC5280"> <front> <title>Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile</title> <author fullname="D. Cooper" initials="D." surname="Cooper"/> <author fullname="S. Santesson" initials="S." surname="Santesson"/> <author fullname="S. Farrell" initials="S." surname="Farrell"/> <author fullname="S. Boeyen" initials="S." surname="Boeyen"/> <author fullname="R. Housley" initials="R." surname="Housley"/> <author fullname="W. Polk" initials="W." surname="Polk"/> <date month="May" year="2008"/> <abstract> <t>This memo profiles the X.509 v3 certificate and X.509 v2 certificate revocation list (CRL) for use in the Internet. An overview of this approach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regarding the format and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples are provided in the appendices. [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</title> <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 signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, 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</title> <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 protocol 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.509 (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 format, 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 changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational 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 and a content type for it. Private-key information includes a private key for a specified 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, authenticate, or encrypt the asymmetric key format content type. This document obsoletes 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 Cryptographic 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"/>Technology</organization> </author> <date month="August" year="2024"/><abstract> <t>The Cryptographic Message Syntax (CMS) supports key transport and key agreement algorithms. In recent years, cryptographers have been specifying Key Encapsulation Mechanism (KEM) algorithms, including quantum-secure KEM algorithms. This document defines conventions for the use of KEM algorithms by the originator and recipients to encrypt and decrypt CMS content. This document updates RFC 5652.</t> </abstract></front> <seriesInfoname="RFC" value="9629"/>name="NIST FIPS" value="203"/> <seriesInfo name="DOI"value="10.17487/RFC9629"/>value="10.6028/NIST.FIPS.203"/> </reference> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5280.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2119.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8174.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5912.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5958.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9629.xml"/> </references> <references anchor="sec-informative-references"> <name>Informative References</name> <reference anchor="CDM23" target="https://eprint.iacr.org/2023/1933.pdf"> <front> <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"> <organization>CISPA Helmholtz Center for Information Security</organization> </author> <author initials="A." surname="Dax" fullname="Alexander Dax"> <organization>CISPA Helmholtz Center for Information Security</organization> </author> <author initials="N." surname="Medinger" fullname="Niklas Medinger"> <organization>CISPA Helmholtz Center for Information Security</organization> </author> <date year="2023"/> </front> <refcontent>Cryptology ePrint Archive, Paper 2023/1933</refcontent> </reference> <reference anchor="KEMMY24" target="https://eprint.iacr.org/2024/523.pdf"> <front> <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"> <organization/> </author> <date year="2024"/> </front> <refcontent>Cryptology ePrint Archive, Paper 2024/523</refcontent> </reference> <reference anchor="NIST-PQC" target="https://csrc.nist.gov/projects/post-quantum-cryptography"> <front> <title>Post-Quantum CryptographyProject</title>(PQC)</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology (NIST)</organization>Technology</organization> </author> <dateyear="2016" month="December" day="20"/>year="2025" month="July" day="28"/> </front> </reference> <!-- [I-D.ietf-lamps-cms-kyber] companion doc RFC 9936 --> <referenceanchor="I-D.ietf-lamps-cms-kyber">anchor="RFC9936" target="https://www.rfc-editor.org/info/rfc9936"> <front> <title>Use of ML-KEM in the Cryptographic Message Syntax (CMS)</title> <authorfullname="PRAT Julien" initials="J." surname="Prat"> <organization>CryptoNext Security</organization>initials='J' surname='Prat' fullname='Julien Prat'> <organization/> </author> <authorfullname="Mike Ounsworth" initials="M." surname="Ounsworth"> <organization>Entrust Limited</organization>initials='M' surname='Ounsworth' fullname='Mike Ounsworth'> <organization/> </author> <authorfullname="Danielinitials='D' surname='Van Geest' fullname='Daniel VanGeest" 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> </abstract> </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">Geest'> <organization/> </author> <dateday="22" month="April" year="2025"/> <abstract> <t> This document gives a construction for a Key Encapsulation Mechanism (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> </abstract> </front> <seriesInfo name="Internet-Draft" value="draft-celi-wiggers-tls-authkem-05"/> </reference> <reference anchor="RFC7468"> <front> <title>Textual Encodings of PKIX, PKCS, and CMS Structures</title> <author fullname="S. Josefsson" initials="S." surname="Josefsson"/> <author fullname="S. Leonard" initials="S." surname="Leonard"/> <date month="April" year="2015"/> <abstract> <t>This document describes and discusses the textual encodings of the Public-Key Infrastructure X.509 (PKIX), Public-Key Cryptography Standards (PKCS), and Cryptographic Message Syntax (CMS). The textual encodings are well-known, are implemented by several applications and libraries, and are widely deployed. This document articulates the de facto rules by which existing implementations operate and defines them so that future implementations can interoperate.</t> </abstract>month='February' year='2026'/> </front> <seriesInfo name="RFC"value="7468"/>value="9936"/> <seriesInfo name="DOI"value="10.17487/RFC7468"/>value="10.17487/RFC9936"/> </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<!-- [I-D.celi-wiggers-tls-authkem] draft-celi-wiggers-tls-authkem-06 IESG State: I-D Exists as ofStandards and Technology</organization> </author> <author fullname="John Preuß Mattsson" initials="J. P." surname="Mattsson"> <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-KEM11-4-2025 --> <xi:include href="https://bib.ietf.org/public/rfc/bibxml3/reference.I-D.celi-wiggers-tls-authkem.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7468.xml"/> <!-- [I-D.sfluhrer-cfrg-ml-kem-security-considerations] draft-sfluhrer-cfrg-ml-kem-security-considerations-03 IESG State: I-D Exists asFIPS 203 in August 2024. This document 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> </abstract> </front> <seriesInfo name="Internet-Draft" value="draft-sfluhrer-cfrg-ml-kem-security-considerations-03"/> </reference> <reference anchor="I-D.ietf-lamps-dilithium-certificates"> <front> <title>Internet X.509 Public Key Infrastructure - Algorithm Identifiers 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="Kampanakis"> <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, Certificate 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> </abstract> </front> <seriesInfo name="Internet-Draft" value="draft-ietf-lamps-dilithium-certificates-12"/> </reference>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> <?line 493?> <section anchor="asn1"> <name>ASN.1 Module</name> <t>This appendix includes the ASN.1 module <xref target="X680"/> for the ML-KEM. Note that as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rules; see <xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> and <xref target="RFC9629"/>.</t> <sourcecodemarkers="true"><![CDATA[markers="true" type="asn.1"><![CDATA[ X509-ML-KEM-2025 { iso(1) identified-organization(3) dod(6) 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 EXPORTS ALL; IMPORTS PUBLIC-KEY FROM AlgorithmInformation-2009 -- [RFC 5912] { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-algorithmInformation-02(58) } KEM-ALGORITHM FROM KEMAlgorithmInformation-2023 -- [RFC 9629] { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-kemAlgorithmInformation-2023(109) }; -- -- ML-KEM Identifiers -- nistAlgorithms OBJECT IDENTIFIER ::= { joint-iso-ccitt(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithm(4) } kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 } id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 } id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 } id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3 } -- -- Public Key Algorithms -- PublicKeys PUBLIC-KEY ::= { -- This expands PublicKeys from [RFC 5912] pk-ml-kem-512 | pk-ml-kem-768 | pk-ml-kem-1024, ... } -- -- ML-KEM Public Keys -- pk-ml-kem-512 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-512 -- KEY no ASN.1 wrapping; 800 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-512-PrivateKey } ML-KEM-512-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (1632)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (1632)) } } pk-ml-kem-768 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-768 -- KEY no ASN.1 wrapping; 1184 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-768-PrivateKey } ML-KEM-768-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (2400)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (2400)) } } pk-ml-kem-1024 PUBLIC-KEY ::= { IDENTIFIER id-alg-ml-kem-1024 -- KEY no ASN.1 wrapping; 1568 octets -- PARAMS ARE absent CERT-KEY-USAGE { keyEncipherment } PRIVATE-KEY ML-KEM-1024-PrivateKey } ML-KEM-1024-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (3168)), both SEQUENCE { seed OCTET STRING (SIZE (64)), expandedKey OCTET STRING (SIZE (3168)) } } ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800)) ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184)) ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568))END ]]></sourcecode>END]]></sourcecode> </section> <section anchor="arnold"> <name>Parameter Set Security and Sizes</name> <t>Instead of defining the strength of a quantum algorithm in a traditional manner using the imprecise notion of bits of security, NIST has defined security levels by picking a reference scheme, whichNIST expectsis expected to offer notable levels of resistance to both quantum and classicalattack.attacks. To wit, a KEM algorithm that achieves NIST PQC security must require computational resources to break IND-CCA 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. Levels 2 and 4 use collision search for SHA-256 and SHA-384 as reference.</t> <table anchor="tab-strengths"> <name>MappingbetweenBetween NIST Security Level, ML-KEMparameter set,Parameter Sets, andsizesSizes inbytes</name>Bytes</name> <thead> <tr> <th align="left">Level</th> <th align="left">Parameter Set</th> <th align="left">Encap. Key</th> <th align="left">Decap. Key</th> <th align="left">Ciphertext</th> <th align="left">Secret</th> </tr> </thead> <tbody> <tr> <td align="left">1</td> <td align="left">ML-KEM-512</td> <td align="left">800</td> <td align="left">1632</td> <td align="left">768</td> <td align="left">32</td> </tr> <tr> <td align="left">3</td> <td align="left">ML-KEM-768</td> <td align="left">1184</td> <td align="left">2400</td> <td align="left">1088</td> <td align="left">32</td> </tr> <tr> <td align="left">5</td> <td align="left">ML-KEM-1024</td> <td align="left">1568</td> <td align="left">3168</td> <td align="left">1568</td> <td align="left">32</td> </tr> </tbody> </table> </section> <section anchor="examples"> <name>Examples</name> <t>This appendix contains examples of ML-KEM public keys, private keys, certificates, and inconsistent seed and expanded private keys.</t> <section anchor="example-private"> <name>Example Private Keys</name> <t>The following examples show ML-KEM private keys in different formats, all derived from the same seed <tt>000102...1e1f</tt>. For each security level, we show the seed-only format (using a context-specific <tt>[0]</tt> primitive tag with an implicit encoding of <tt>OCTET STRING</tt>), the expanded format, and both formats together.</t> <t>NOTE: All examples use the same seed value, showing how the same seed produces different expanded private keys for each security level.</t> <section anchor="ml-kem-512-private-key-examples"> <name>ML-KEM-512 Private Key Examples</name> <t>Each of the examples includes the textual encoding <xref target="RFC7468"/> followed by the so-called "pretty print"; the private keys are the same.</t> <section anchor="seed-format"> <name>Seed Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MFQCAQAwCwYJYIZIAWUDBAQBBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } } OCTET_STRING { [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343 5363738393a3b3c3d3e3f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x 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`000102030405060708090a0b0c0d0e0f1011121314 15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334 35363738393a3b3c3d3e3f` } OCTET_STRING { `70554fd436344f2785b1b3b1bac184b6679003336c 26f15a7de878c4825c6be03f3c4a480f75b7486aad31d3a00518623fd207ab52 8dd62721495835ae0062c367b74a71baf10aad0e8a2902076be31348beb15ccc 0957cdebb4aff226756bbc601b6568ab784acbaeb34702f0f86a26202118b22b 23f83558776c79c14dba983379c803e0dcc3160a11757030e69c6919798d81eb 698a9a4483a99e5a5cb2c31c9a661799f3cc89c790706ea041629045d42a83ae d88860e394c69187e2105d28cc14ec393592d67dd00aa43fe8b4eae441400286 6b5c713c6a8d7d16cf78b819d6f12e9e5a74233908f0b15e3c4ba8329c5cdda5 5c84928e3aa8063e5aa9676403f91735b11010c7f593091364dc86445bc80484 0a9a21724212469f8a7b0ce0ac698eb86cad39a7f4824d9a5163aac21ee6808b 053c8a3facb0b6744b5262bbcb26a43f664c8732b64cfc7acf099605f41c7960 60976ac433833fe00343fb1828300a424741116e4b45bb276ea81129a0db4c6e 60bce611101e8c625474925e0222679308a3e7708d1972a7b423eb232851c36d 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f9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491 ab3872765d320d0b71920fa213c94093416b83b8124e69f65e62cb5000dcc37a a9a0fff73970c4772f357d24189ca6f5305568c0e2376a3762a68c605e563c5d 209572e0fc7532ca294729535567b5fc413c5e8792d2464536cc808f98add746 64f141566f9016a90a541829a98a0464ce41a8bb44c2d4fa3c2c209460728ef1 4a1a7c4c9b98d12203b4cc3529160a9ab2d7838f7ff6b53ae05aa31a7d646b7a fa6c45932526a3c3755619be994c211c2a31c05b3447836cb2150be1829dae6b 04c5535cff546e392ba797411720f924f490a5ac5495f21356d550b782a64c16 88b6b655bcc7842197a434c2f6563b5b7f09a78bcc488232783561d16f4cbab6 755400050781570c66604b817ad1252294736e8b01861a4b5a74519b8b6fe514 89a5072392e587626c713776575d33806a1c8e2732af97c2680f51666331c4eb 8bbc0431c4f96832daf1b3c45528fba153f6c78b1c198702947ccd337727a46f b53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e3 0fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980 b1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc16 00903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf02 117f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26c db33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61ba ab71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec3 7225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b 324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b8 1c3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2fea dade150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f3031323334 35363738393a3b3c3d3e3f` } } }} ]]></artwork>}]]></artwork> </section> </section> <section anchor="ml-kem-768-private-key-examples"> <name>ML-KEM-768 Private Key Examples</name> <t>Each of the examples includes the textual encoding <xref target="RFC7468"/> followed by the so-called "pretty print"; the private keys are the same.</t> <section anchor="seed-format-1"> <name>Seed Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MFQCAQAwCwYJYIZIAWUDBAQCBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } } OCTET_STRING { [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343 5363738393a3b3c3d3e3f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format-1"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIJeAIBADALBglghkgBZQMEBAIEgglkBIIJYCfSp38zdW9hII7xE6voJZWHPUq8 cw5bXWeVKb9qTOtjg0JyMahhL0FVBRWsulLkjq2LlCgzu+aGXRPRSnnSxcPgfwoF bY3nqt/KugWMSTyAs3yrjFYnU7s7prbsgpf4heqnVA1TABWoRAblWxNmtXfiNs5Y om2KHrWkTVQjI8IWfZv0pH+YVpnKBbrkO43sYX8COAo4kK/UuMfsft4mVToCXzzl vF16YhMDBCNcsa1INrVmtbhjvZvbRaKESnBHtsjTg+RIUl4EC03IorSMbDfJbWLU Pz/YjiiBxAogXJ4kj2UrWSeBp3n4aIDyoUe2eGPzkcwaWpCMAJXgchIpHi74o265 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]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } } OCTET_STRING { OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc730e 5b5d679529bf6a4ceb6383427231a8612f41550515acba52e48ead8b942833bb e6865d13d14a79d2c5c3e07f0a056d8de7aadfcaba058c493c80b37cab8c5627 53bb3ba6b6ec8297f885eaa7540d530015a84406e55b1366b577e236ce58a26d 8a1eb5a44d542323c2167d9bf4a47f985699ca05bae43b8dec617f02380a3890 afd4b8c7ec7ede26553a025f3ce5bc5d7a62130304235cb1ad4836b566b5b863 bd9bdb45a2844a7047b6c8d383e448525e040b4dc8a2b48c6c37c96d62d43f3f d88e2881c40a205c9e248f652b592781a779f86880f2a147b67863f391cc1a5a 908c0095e07212291e2ef8a36eb9a9c0c6073225b34703a4af049382c47573da 68fde9245ad444e31b1fbdb521f1f61f37bc0cef292067e670d28a1ffd904f6f 1190a996918a13037a6cabf3c373bf8296cd37ab33ba7746809cc3f8ade1b363 9bd57bfcc69650aaaf1de198fc4c0463299e52c461780cc428fc5d04a5c51850 cba6c2a5274340675793dda09be44c29e6395c65f85d2a0a7c6df411e6911b1f 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32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d63e f3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f303132333435 363738393a3b3c3d3e3f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="both-format-1"> <name>Both Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIJvgIBADALBglghkgBZQMEBAIEggmqMIIJpgRAAAECAwQFBgcICQoLDA0ODxAR EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC CWAn0qd/M3VvYSCO8ROr6CWVhz1KvHMOW11nlSm/akzrY4NCcjGoYS9BVQUVrLpS 5I6ti5QoM7vmhl0T0Up50sXD4H8KBW2N56rfyroFjEk8gLN8q4xWJ1O7O6a27IKX +IXqp1QNUwAVqEQG5VsTZrV34jbOWKJtih61pE1UIyPCFn2b9KR/mFaZygW65DuN 7GF/AjgKOJCv1LjH7H7eJlU6Al885bxdemITAwQjXLGtSDa1ZrW4Y72b20WihEpw R7bI04PkSFJeBAtNyKK0jGw3yW1i1D8/2I4ogcQKIFyeJI9lK1kngad5+GiA8qFH tnhj85HMGlqQjACV4HISKR4u+KNuuanAxgcyJbNHA6SvBJOCxHVz2mj96SRa1ETj Gx+9tSHx9h83vAzvKSBn5nDSih/9kE9vEZCplpGKEwN6bKvzw3O/gpbNN6szundG gJzD+K3hs2Ob1Xv8xpZQqq8d4Zj8TARjKZ5SxGF4DMQo/F0EpcUYUMumwqUnQ0Bn 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`000102030405060708090a0b0c0d0e0f1011121314 15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334 35363738393a3b3c3d3e3f` } OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc73 0e5b5d679529bf6a4ceb6383427231a8612f41550515acba52e48ead8b942833 bbe6865d13d14a79d2c5c3e07f0a056d8de7aadfcaba058c493c80b37cab8c56 2753bb3ba6b6ec8297f885eaa7540d530015a84406e55b1366b577e236ce58a2 6d8a1eb5a44d542323c2167d9bf4a47f985699ca05bae43b8dec617f02380a38 90afd4b8c7ec7ede26553a025f3ce5bc5d7a62130304235cb1ad4836b566b5b8 63bd9bdb45a2844a7047b6c8d383e448525e040b4dc8a2b48c6c37c96d62d43f 3fd88e2881c40a205c9e248f652b592781a779f86880f2a147b67863f391cc1a 5a908c0095e07212291e2ef8a36eb9a9c0c6073225b34703a4af049382c47573 da68fde9245ad444e31b1fbdb521f1f61f37bc0cef292067e670d28a1ffd904f 6f1190a996918a13037a6cabf3c373bf8296cd37ab33ba7746809cc3f8ade1b3 639bd57bfcc69650aaaf1de198fc4c0463299e52c461780cc428fc5d04a5c518 50cba6c2a5274340675793dda09be44c29e6395c65f85d2a0a7c6df411e6911b 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5363738393a3b3c3d3e3f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format-2"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIMeAIBADALBglghkgBZQMEBAMEggxkBIIMYPd7f2sVxz/izFRrZ/t3TKGbQs1G Pqn7uYTKR3p3tscQh8vwUavkc2qQcsbocMgxHFWWP1AKPHsbjypYVY9JxiUntsWU teess7z1lyc6V0NRfRUSCL1Kph51umewvVlKmUkZYnrAqATUieFxM2vDOfRmZwbl E0QSs2aCPVAxjIvyYasSCiigT+wBzBXytxkSzuVKqO7YVGlLa6iGtet2YebVaqwh PMHYFNWSs5VVT650R200NxFjEpv4ZFJyUGBswhpTdGsgmXB3u6FVczsopOf6B3Y5 lSR2PrSBzqoRNmw0dKBGhfQMPwiwQk9Av/lJoKyScEw7oMbrNvH1tiHYvytjJ761 fNP6y5QYb+P8mrChQ0uykdLJu3ByMFfiJUBZZW9WWRmjLPdFed6JaBzSxak1pStK qi0ky11cniBynsVJLsNpYe+4ooy8AKwwNSMpXz2ANqvBYDMHznDXhIo1ZXpWh91Y mSfqY3MWJquybsTkMbjrazsLweglc+5zsaAhGDGDUoEIri6srduVtGSguYRpwxnM J7+gG8MQVKaMBVArFmK4ef6YoXEcNCb2Q2ywIUzqN5rDp+X7YBhKN8HaHtphxsOc HdToR4RYEfKjWKQ3MVKFNtSjKRsEFYwsPcZBYkiCZ4vHgF9YqdlMcQRWeEaiBE5l rs4qIlNytgJHmaVHfWAjdQSqXArFe8cKNVjAjE3mh+8TArT8tVlEE9IsuVm8Mb5C 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53c612450c45c9e603bc16666e596b3471e103b6f15447424d17022048111ffb d37e1c670f64f14b8a7b32b94c1a49b45dd2fc38cd5289d910ad63602cf5e130 42c64ac6797b89fb551ad08e05a92d200cccb7e712ef23c9312cb350f029ab53 7e287347fd3075ac10906a783f1c6c07ccb88f41228c4be1c640f790b5c3a5d5 d3ca792495d74bc461562658c07ac600276b924ab5bc9be1f0494cb76f82f460 a7480972663381e169996061d799859ec54d4f5ca5c411c01db1597b16597766 9de13a928a34afbac258fea8c4764239c9421dc3119bf5b47699206978327b1c 5345ef746a7983841f056e2534100ab24d4e9abbd0b17c6a95bd4c3c0e40f69e 1612aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb98 84f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b 9003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97b aa523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba6 0f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8 a13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed 58dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c 7147ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f3031323334 35363738393a3b3c3d3e3f` } } }} ]]></artwork>}]]></artwork> </section> </section> </section> <section anchor="example-public"> <name>Example Public Keys</name> <t>The following is the ML-KEM-512 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIDMjALBglghkgBZQMEBAEDggMhADmVgV5ZfRBDVc8pqlMzyTJRhp1bzb5IcST2 Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHmvG+QsOSb aTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbWf/mqvJdQ Pyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lAk0Frg7gS Tmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8XSCVcuD8 dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoEZM5BqLtE wtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRrevpsRZMl JqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5JPSQpaxU lfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6tnVUAAUH gVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10zgGocjicy r5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyekb7U7oR3l y0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oXthQzzRr4 D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPMFgCQPmUp NWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGmgx1bVMC3 kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9huqtxp6PT UZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2NoPwS/eg nMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3guBw7xZoG WhttY7Js -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } } BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5bcdb e487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c62 efa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016ddf c1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67ff 9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491a b3872765d320d0b71920fa213c94093416b83b8124e69f65e62cb5000dcc37aa 9a0fff73970c4772f357d24189ca6f5305568c0e2376a3762a68c605e563c5d2 09572e0fc7532ca294729535567b5fc413c5e8792d2464536cc808f98add7466 4f141566f9016a90a541829a98a0464ce41a8bb44c2d4fa3c2c209460728ef14 a1a7c4c9b98d12203b4cc3529160a9ab2d7838f7ff6b53ae05aa31a7d646b7af a6c45932526a3c3755619be994c211c2a31c05b3447836cb2150be1829dae6b0 4c5535cff546e392ba797411720f924f490a5ac5495f21356d550b782a64c168 8b6b655bcc7842197a434c2f6563b5b7f09a78bcc488232783561d16f4cbab67 55400050781570c66604b817ad1252294736e8b01861a4b5a74519b8b6fe5148 9a5072392e587626c713776575d33806a1c8e2732af97c2680f51666331c4eb8 bbc0431c4f96832daf1b3c45528fba153f6c78b1c198702947ccd337727a46fb 53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e30 fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980b 1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc160 0903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf021 17f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cd b33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baa b71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec37 225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b3 24334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81 c3bc59a065a1b6d63b26c` }} ]]></artwork>}]]></artwork> <t>The following is the ML-KEM-768 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIEsjALBglghkgBZQMEBAIDggShACmKoQ1CPI3aBp0CvFnmzfA6CWuLPaTKubgM pKFJB2cszvHsT68jSgvFt+nUc/KzEzs7JqHRdctnp4BZGWmcAvdlMbmcX4kYBwS7 TKRTXFuJcmecZgoHxeUUuHAJyGLrj1FXaV77P8QKne9rgcHMAqJJrk8JStDZvTSF wcHGgIBSCnyMYyAyzuc4FU5cUXbAfaVgJHdqQw/nbqz2ZaP3uDIQIhW8gvEJOcg1 VwQzao+sHYHkuwSFql18dNa1m75cXpcqDYusQRtVtdVVfNaAoaj3G064a8SMmgUJ cxpUvZ1ykLJ5Y+Q3Lcmxmc/crAsBrNKKYjlREuTENkjWIsSMgjTQFEDozDdskn8j pa/JrAR0xmInTkJFJchVLs47P+JlFt6QG8fVFb3olVjmJslcgLkzQvgBAATznmxs lIccXjRMqzlmyDX5qWpZr9McQChrOLHBp4RwurlHUYk0RTzoZzapGfH1ptUQqG9U VPw5gMtcdlvSvV97NrFBDWY1yM60fE3aDXaijqyTnHHDAkgEhmxxYmZYRCFjwsIh F+UKzvzmN4qYVlIwKk7wws4Mxxa3eW4ray43d9+hrD2iWaMbWptTD4y2OKgaYqww GEmrr5WnMBvaMAaJCb/bfmfbzLs4pVUaJbGjoPaFdIrVdT2IgPABbGJ0hhZjhMVX H+I2WQA2TQODEeLYdds2ZoaTK17GAkMKNp6Hpu9cM4eGZXglvUwFes65I+sJNeaQ XmO0ztf4CFenc91ksVDSZhLqmsEgUtsgF78YQ8y0sygbaQ3HKK36hcACgbjjwJKH M1+Fa0/CiS9povV5Ia2gGRTECYhmLVd2lmKnhjUbm2ZJPat5WU2YbeIQDWW6D/Tq WLgVONJKRDWiWPrCVASqf0H2WLE4UGXhWNy2ARVzJyD0BFmqrBXkBpU6kKxSmX0c zQcAYO/GXbnmUzVEZ/rVbscTyG51QMQjrPJmn1L6b0rGiI2HHvPoR8ApqKr7uS4X skqgebH0GbphdbRCr7EZCdSla3CgM1soc5IYqnyTSOLDwvPrPRWkHmQXwN2Uv+sh QZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4Jw1Ybhv4 MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9ct4TlU/Qb kY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67QI5JqeP4 edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPBu3lyvsWj BuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhKSClrmN1D IrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7y05qBc9F AhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCxJKhVjfcr vje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD4ssy2ovD QvpN6gV4 -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 } } BIT_STRING { `00` `298aa10d423c8dda069d02bc59e6cdf03a096b8b3da 4cab9b80ca4a14907672ccef1ec4faf234a0bc5b7e9d473f2b3133b3b26a1d17 5cb67a7805919699c02f76531b99c5f89180704bb4ca4535c5b8972679c660a0 7c5e514b87009c862eb8f5157695efb3fc40a9def6b81c1cc02a249ae4f094ad 0d9bd3485c1c1c68080520a7c8c632032cee738154e5c5176c07da56024776a4 30fe76eacf665a3f7b832102215bc82f10939c8355704336a8fac1d81e4bb048 5aa5d7c74d6b59bbe5c5e972a0d8bac411b55b5d5557cd680a1a8f71b4eb86bc 48c9a0509731a54bd9d7290b27963e4372dc9b199cfdcac0b01acd28a6239511 2e4c43648d622c48c8234d01440e8cc376c927f23a5afc9ac0474c662274e424 525c8552ece3b3fe26516de901bc7d515bde89558e626c95c80b93342f801000 4f39e6c6c94871c5e344cab3966c835f9a96a59afd31c40286b38b1c1a78470b ab947518934453ce86736a919f1f5a6d510a86f5454fc3980cb5c765bd2bd5f7 b36b1410d6635c8ceb47c4dda0d76a28eac939c71c3024804866c71626658442 163c2c22117e50acefce6378a985652302a4ef0c2ce0cc716b7796e2b6b2e377 7dfa1ac3da259a31b5a9b530f8cb638a81a62ac301849abaf95a7301bda30068 909bfdb7e67dbccbb38a5551a25b1a3a0f685748ad5753d8880f0016c6274861 66384c5571fe2365900364d038311e2d875db366686932b5ec602430a369e87a 6ef5c338786657825bd4c057aceb923eb0935e6905e63b4ced7f80857a773dd6 4b150d26612ea9ac12052db2017bf1843ccb4b3281b690dc728adfa85c00281b 8e3c09287335f856b4fc2892f69a2f57921ada01914c40988662d57769662a78 6351b9b66493dab79594d986de2100d65ba0ff4ea58b81538d24a4435a258fac 25404aa7f41f658b1385065e158dcb60115732720f40459aaac15e406953a90a c52997d1ccd070060efc65db9e653354467fad56ec713c86e7540c423acf2669 f52fa6f4ac6888d871ef3e847c029a8aafbb92e17b24aa079b1f419ba6175b44 2afb11909d4a56b70a0335b28739218aa7c9348e2c3c2f3eb3d15a41e6417c0d d94bfeb21419b311a7bb13a180bbe833218a9a6b17447cc85f225859587a7307 7049acbcfd44d0f025438e15d1538270d586e1bf83192a9459cf63c0e972f852 97679831ecf121509851cb8340f6f107b0fa1a0efd1b36a8189bc085c4f5cb78 4e553f41b918f80397ce1956f785bee377ca9aa8be6998ada30c26b7c3d8c6b5 5254cc96203b20c42aee0ac4e1ebb408e49a9e3f879d0ab0785eb7025425d130 5a2299c015e120d163b0e19494ce57253d0246d182745cb8197ab7438b3c1bb7 972bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc660 777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba 44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4 e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b 99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c 633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2c b32da8bc342fa4dea0578` }} ]]></artwork>}]]></artwork> <t>The following is the ML-KEM-1024 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIGMjALBglghkgBZQMEBAMDggYhAEuUwpRQERGRgjs1FMmsHqPZglzLhjk6LfsE ZU+iGS03v60cSXxlAu7lyoCnO/zguvWlSohYWkATl6PSMvQmp6+wgrwhpEMXCQ6q x1ksLqiKZTxEkeoZOTEzX1LpiaPEzFbZxVNzLVfEcPtBq3WbZdLQREU4L82cTjRK ESj6nhHgQ1jhku0BSyMjKn7isi4jcX9EER7jNXU5nDdkbamBPsmyEq/pTl3FwjMK cpTMH0I0ptP7tPFoWriJLASssXzRwXDXsGEbanF2x5TMjGf1X8kjwq0gMQDzZZkY gsMCQ9d4E4Q7XsfJZAMiY3BgkuzwDHUWvmTkWYykImwGm7XmfkF1zyKGyN1cSIps WGHzG6oL0CaUcOi1Ud07zTjIbBL5zbF2x33ItsAqcB9HiQLIVT9pTA2CcntMSlws EEEhKqEnSAi4IRGzd+x1IU6bGXj3YATUE52YYT9LjpjSCve1NAc6UJqVm3p1ZPm0 DKIYv2GCkyCoUCAXlU0yjXrGx2nsKXAHVuewaFs0DV4RgFlQSkmppQoQGY6xCleE Z460J9e0uruVUpM7BiiXlz4TGOrwoOrDdYSmVAGxcD4EKszYN1MUg/JBytzRwdN4 EZ5pRCnbGZrIkeTFNDdXCFuzrng2ZzUMRFjZdnLoYegLHSZ5UQ6jpvI2DHekaULH oGpVTSKAgMhLR67xTbF2IMsWwGqzChvkzacIK+n4fpwhHEaRY0mluo6qUgHHKUo8 CIW1O2V0UhCIJexkbJCgRhIyTufQMa/lNDEyy+9ntu+xpewoCbdzU4znez2LBOsL PCJWAR5McWwZqLoHUr9xSSEXZJ8GFcMpD8KaRv3kvVLbkobWAziCRCWcFaesK2QK YMwDN2pYQaP7ikc1aPqbGiZyFfNMAWl7Dw5icXXXIQW3cHwpueYUvcM6b2yBipU3 C0J4gte0dnlqnsbrmTJ0zZsjkagrpF4zk9Lprpchyp1sG5iLWCdxP5CmWF3pQzUo wCsDzhC7X3IBOND7tMMMEma5GOUpJd/hezf5XSK8pU9HWRmshZCYwPDQisWHXvKb Vv0UHm7xX3AKC2bzlZXFiBdzc8RmmyG8Bx5MOqXwtKMbYljzXaJKw80px/IJJBDF B4NVsTj7U6a5rm4LnAgkPnuqRcRzduuMfxPUz1Gqc2+jFUDJJB83DaVEv5+cKNml fi8qfKlaTktGbmQas7zHat8ROdVnpvErUvOmXn7AquJryqjFWDOwTlmZjryaGTD7 ttIjPFPSwfi5UY48Lec6Gd7ms4Clsylxz2ThKf1sH6bnXUojRQHpZt06VAr1yPTz SmtKJT7ihJJWbV5nxvVYVfywUG+wbBVnRNmgOjGib6lMrRTxV7fzA9B6acdzdo/L TQecCQWXA6DDqU3kuZ6jovFlg9D5Fwo5UNsHtPC8MIApJ/n3lhtiWYkmNqlQKicF MDY3eZ3TRNpFHBz3v2eEDOsweauMa4wZJ/ZAU8YSRQxFyeYDvBZmbllrNHHhA7bx VEdCTRcCIEgRH/vTfhxnD2TxS4p7MrlMGkm0XdL8OM1SidkQrWNgLPXhMELGSsZ5 e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4PxxsB8y4j0Ei jEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0YKdICXJm M4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZCOclCHcMR m/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2nhYSrO6y i5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iFcUkQiIsj EMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+npe6pSPXpE MWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0RvgYkYLS v16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB7VjcYod2 uYOILhF1 -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 } } BIT_STRING { `00` `4b94c29450111191823b3514c9ac1ea3d9825ccb863 93a2dfb04654fa2192d37bfad1c497c6502eee5ca80a73bfce0baf5a54a88585 a401397a3d232f426a7afb082bc21a44317090eaac7592c2ea88a653c4491ea1 93931335f52e989a3c4cc56d9c553732d57c470fb41ab759b65d2d04445382fc d9c4e344a1128fa9e11e04358e192ed014b23232a7ee2b22e23717f44111ee33 575399c37646da9813ec9b212afe94e5dc5c2330a7294cc1f4234a6d3fbb4f16 85ab8892c04acb17cd1c170d7b0611b6a7176c794cc8c67f55fc923c2ad20310 0f365991882c30243d77813843b5ec7c964032263706092ecf00c7516be64e45 98ca4226c069bb5e67e4175cf2286c8dd5c488a6c5861f31baa0bd0269470e8b 551dd3bcd38c86c12f9cdb176c77dc8b6c02a701f478902c8553f694c0d82727 b4c4a5c2c1041212aa1274808b82111b377ec75214e9b1978f76004d4139d986 13f4b8e98d20af7b534073a509a959b7a7564f9b40ca218bf61829320a850201 7954d328d7ac6c769ec29700756e7b0685b340d5e118059504a49a9a50a10198 eb10a5784678eb427d7b4babb9552933b062897973e1318eaf0a0eac37584a65 401b1703e042accd837531483f241cadcd1c1d378119e694429db199ac891e4c 5343757085bb3ae783667350c4458d97672e861e80b1d2679510ea3a6f2360c7 7a46942c7a06a554d228080c84b47aef14db17620cb16c06ab30a1be4cda7082 be9f87e9c211c46916349a5ba8eaa5201c7294a3c0885b53b657452108825ec6 46c90a04612324ee7d031afe5343132cbef67b6efb1a5ec2809b773538ce77b3 d8b04eb0b3c2256011e4c716c19a8ba0752bf71492117649f0615c3290fc29a4 6fde4bd52db9286d603388244259c15a7ac2b640a60cc03376a5841a3fb8a473 568fa9b1a267215f34c01697b0f0e627175d72105b7707c29b9e614bdc33a6f6 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target="I-D.ietf-lamps-dilithium-certificates"/> with a reference to the published RFC.</t> </aside><t>The following is the ML-KEM-512 certificatethatcorresponding to the public key in the previous section signed with the ML-DSA-44 private key from <xreftarget="I-D.ietf-lamps-dilithium-certificates"/>.target="RFC9881"/>. The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIINpDCCBBqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMR MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggMyMAsGCWCGSAFlAwQEAQOCAyEAOZWBXll9EENVzymqUzPJMlGG nVvNvkhxJPYCuLambBbEdhZIrXZc9dgAa1FekFp/CsB2sMYu+jKBU+fKVwFpnxMF 8ea8b5Cw5JtpNRK2zpkqi4AW3fwaZix+P5YZy9hp3Xca8wiWzNWRisbLd0ZsXneZ ltZ/+aq8l1A/LHt+LQANhkUPsYB8pMq9pGWCWjHHiaG3pJGrOHJ2XTINC3GSD6IT yUCTQWuDuBJOafZeYstQANzDeqmg//c5cMR3LzV9JBicpvUwVWjA4jdqN2KmjGBe VjxdIJVy4Px1MsopRylTVWe1/EE8XoeS0kZFNsyAj5it10Zk8UFWb5AWqQpUGCmp igRkzkGou0TC1Po8LCCUYHKO8UoafEybmNEiA7TMNSkWCpqy14OPf/a1OuBaoxp9 ZGt6+mxFkyUmo8N1Vhm+mUwhHCoxwFs0R4NsshUL4YKdrmsExVNc/1RuOSunl0EX IPkk9JClrFSV8hNW1VC3gqZMFoi2tlW8x4Qhl6Q0wvZWO1t/CaeLzEiCMng1YdFv 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s7TAwcrR1drv9BRiaH2qytnr8PcAAAAAAAAAAAAAAAAAAAAAFSM2QA== -----ENDCERTIFICATE----- ]]></artwork>CERTIFICATE-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { [0] { INTEGER { 2 } } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } SEQUENCE { SET { SEQUENCE { # organizationName OBJECT_IDENTIFIER { 2.5.4.10 } PrintableString { "IETF" } } } SET { SEQUENCE { # commonName OBJECT_IDENTIFIER { 2.5.4.3 } PrintableString { "LAMPS WG" } } } } SEQUENCE { UTCTime { "200203043210Z" } UTCTime { "400129043210Z" } } SEQUENCE { SET { SEQUENCE { # organizationName OBJECT_IDENTIFIER { 2.5.4.10 } PrintableString { "IETF" } } } SET { SEQUENCE { # commonName OBJECT_IDENTIFIER { 2.5.4.3 } PrintableString { "LAMPS WG" } } } } SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 } } BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5 bcdbe487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b 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3e30fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497 980b1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3c c1600903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851b f02117f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a 26cdb33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf6 1baab71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987 ec37225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162 e0b324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede 0b81c3bc59a065a1b6d63b26c` } } [3] { SEQUENCE { SEQUENCE { # keyUsage OBJECT_IDENTIFIER { 2.5.29.15 } BOOLEAN { TRUE } OCTET_STRING { BIT_STRING { b`001` } } } SEQUENCE { # subjectKeyIdentifier OBJECT_IDENTIFIER { 2.5.29.14 } OCTET_STRING { OCTET_STRING { `0ec592a5971e7e8da078a86e4674f2fb11f6 e8d7` } } } SEQUENCE { # authorityKeyIdentifier OBJECT_IDENTIFIER { 2.5.29.35 } OCTET_STRING { SEQUENCE { [0 PRIMITIVE] { `329a07b1fabb48f52a309f11a1898f848 e2322ff` } } } } } } } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } BIT_STRING { `00` `dc57c2c0fc37bc4ace942f7b4c7075ca7348935da04 f3cbca80a2996286fc1859dbdf6a77283a42ffe158cc577ee40bbc120952213d 6e8214bc3247d41bf9abec015c33383dc6f9f396bdef67c1ecb8fbad363019ec e9e10446b27e1b30e507b4e4bff4c683f4b030f179440d297af4a80dfa337e09 a93e3d2d50dcebbe4e978cd9fa37d38fb7bd37c794d89e3d234eaa4775a73b36 9f05486d018859cb69175ac81c2ecd27f5ce3b766c3770abef9f0e2f2028b427 460919e3d7a161c61d6b27defa6facbe628f7a083320976da560f2688a19417a 4b8a738ba0904838bc913002d3e53286a8827ed725c5a42888462a9d4cee71bd 2af810c4246f21f45446e0f21da88e02439ac8af87a7ae00574da96d85ffc355 fd6d6d4a39e21de36114429176885bb78a53898b5266305c8c3fc959658abff1 f3efdca1993c5609a5deb2680ed178841a36216008cab1ee7c3f66d8bbb1ad9a e5da2bdd8a9846367c525254b9850ac4d0dd7bfbb8e969881064987329e93a21 186f27969975b8c9eeea853d50edb9853d5f0c8f39f7ad7cadcd4cd465facaf2 3f5c1f1028cd8b05ed10ee0666ae96261f5758daae809c1eba215539d24a248c 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The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIISnTCCBZqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMS MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggSyMAsGCWCGSAFlAwQEAgOCBKEAKYqhDUI8jdoGnQK8WebN8DoJ a4s9pMq5uAykoUkHZyzO8exPryNKC8W36dRz8rMTOzsmodF1y2engFkZaZwC92Ux uZxfiRgHBLtMpFNcW4lyZ5xmCgfF5RS4cAnIYuuPUVdpXvs/xAqd72uBwcwCokmu TwlK0Nm9NIXBwcaAgFIKfIxjIDLO5zgVTlxRdsB9pWAkd2pDD+durPZlo/e4MhAi FbyC8Qk5yDVXBDNqj6wdgeS7BIWqXXx01rWbvlxelyoNi6xBG1W11VV81oChqPcb TrhrxIyaBQlzGlS9nXKQsnlj5DctybGZz9ysCwGs0opiOVES5MQ2SNYixIyCNNAU QOjMN2ySfyOlr8msBHTGYidOQkUlyFUuzjs/4mUW3pAbx9UVveiVWOYmyVyAuTNC +AEABPOebGyUhxxeNEyrOWbINfmpalmv0xxAKGs4scGnhHC6uUdRiTRFPOhnNqkZ 8fWm1RCob1RU/DmAy1x2W9K9X3s2sUENZjXIzrR8TdoNdqKOrJOcccMCSASGbHFi 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The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIIZQzCCBxqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMT MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggYyMAsGCWCGSAFlAwQEAwOCBiEAS5TClFAREZGCOzUUyaweo9mC XMuGOTot+wRlT6IZLTe/rRxJfGUC7uXKgKc7/OC69aVKiFhaQBOXo9Iy9Canr7CC vCGkQxcJDqrHWSwuqIplPESR6hk5MTNfUumJo8TMVtnFU3MtV8Rw+0GrdZtl0tBE RTgvzZxONEoRKPqeEeBDWOGS7QFLIyMqfuKyLiNxf0QRHuM1dTmcN2RtqYE+ybIS r+lOXcXCMwpylMwfQjSm0/u08WhauIksBKyxfNHBcNewYRtqcXbHlMyMZ/VfySPC rSAxAPNlmRiCwwJD13gThDtex8lkAyJjcGCS7PAMdRa+ZORZjKQibAabteZ+QXXP IobI3VxIimxYYfMbqgvQJpRw6LVR3TvNOMhsEvnNsXbHfci2wCpwH0eJAshVP2lM DYJye0xKXCwQQSEqoSdICLghEbN37HUhTpsZePdgBNQTnZhhP0uOmNIK97U0BzpQ mpWbenVk+bQMohi/YYKTIKhQIBeVTTKNesbHaewpcAdW57BoWzQNXhGAWVBKSaml 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a2644c7f4a5fc3cc5f2a03778b1ccd31151da4bc7b27fb9001e6e732d9938917 65bd5eec1849404fa11ae674858a4180bcfcc0f93ed64ca94a041af1e5ea3169 7db3baf913fa35a92903eab84e5e31b8337278aa8e743f7e5dd13769c591febf 89b1e8ab7066810c39298c1125718819b8b7ea2abc75f86e62eadea05a8a5c36 d2e655cb805af1d54fce7838890d214a2a7e7112383adccdbdc2e648c9db7d1d 7f8575e7aa8c6c9070c1c245b737f939bc8edf272777f90d820229e000000000 000000000000000000000000000000000000000000004080f171d292e31` }} ]]></artwork>}]]></artwork> </section> <section anchor="example-bad"> <name>Examples of Bad Private Keys</name><aside> <t>WARNING:<!-- [rfced] Please confirm that the WARNING should be tagged as an <aside>, which 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> <t>WARNING: These private keys are purposely bad. Do not use them in production systems.</t> </aside> <t>The following examples demonstrate inconsistent seed and expanded private keys.</t> <section anchor="ml-kem-inconsistent-seed-and-expanded-private-keys"> <name>ML-KEM Inconsistent Seed and Expanded Private Keys</name> <t>Four <tt>ML-KEM-512-PrivateKey</tt> examples of inconsistent seed and expanded private keysfollow:</t>are shown as follows:</t> <ol spacing="normal" type="1"><li> <t>The first <tt>ML-KEM-512-PrivateKey</tt> example includes the <tt>bothCHOICE</tt> ,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 for inconsistencies.</t> </li> <li> <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> and a valid public key hash, but a pairwise consistency check would find that the public key fails to match private.</t> </li> <li> <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 a public key digest check and a pairwise consistency check should fail.</t> </li> <li> <t>The fourth <tt>ML-KEM-512-PrivateKey</tt> example includes the <tt>bothCHOICE</tt> ,CHOICE</tt>, i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are included. There is mismatch of the seed and expanded private key in only the <tt>z</tt> implicit rejection secret;herehere, the private and public vectors match and the pairwise consistency check passes, but z is different.</t> </li> </ol> <t>The following is the first example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR EhMUFRYXGBkaGxwdHh8hIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/QASC BmDvsn6JOEO1+bZhFYaTegU33BzhWY5u8TDVVBiwaUFnGLk3E4KY1lkkOQvUIErq c6VzJCCGVwzLkAdwiCoTOZIeHEYlqwgwpJUosrxyCyFgSFL9d57oFT3+QyRXG5tG Z6yFlUbOoVEPV5ltPMMKMY3QBrartJ/LOwD2QT6F4hF5wXkl2bU8dgwLDAJYxZhd eQNgMTo6rLojsTCL939wAcA1ks/zfCXBJD+J8FAzBikeocuHoaM49HaPzIzm95fE co8AWycN0JG8djQHiqjfaMYpNg0ldjW82ZycuxOtenMbZsc+GLFUmWiqZjxgupeV G4+lQZpRmsKU0ptIymHRcsMUCMHicS+19miPXIOPEQvORmEOqa0e12RZkkLj6y27 Uk4kZ5TB82bpqjccBB1Oq4lQ88ns0V2fYMVt5UFCoM153A8tBBNbfAPnIWrpRQHa +TdRbDHeyhTHg2/GExQ8lhhfB4DP/C+v+XBY4F5xMh4euYjsWXsPC5MPyX1n6aDe eYnB9q61wWkTK6indGy1clrZwQX70Ta7I8brALnFQDuUlzhqE8f51osDoBUHqCEm eh0Za60KkLtpppJFWElopV7adFlUSzNG8IIV8p2hk5PxN6gYGBcLtsrp1ruBYkLg GaZp1MWYIEiMc4nv4jOYO7yTZCRkwJN8e4wBlyr6ysU17FdsuxI7wJRHYa26pyxh 6h0kg1utBI8xSTZXA4/Ep0JZmMOdAxP97IsoF2IpPE8AlTqsKkZSSH99ZCyg2aLT 5JsFAVw5wQbHuYwaUgFWM2Z4xk81IJKVbKZD4SCboXaeYRSjdkCCp0oItlz8t8cF WVw9G29Otkqcu8Y5jJzMYwSUARi5VmuIdKK4JLGshait+hvQ2xCzEEPQqbn7rIZ3 ecO4uKllgS/og7cVtb6tSFdSElRfxBLw024tYiKszHLKB0hbVzR2Gy0xKVef8Xsi CJg8GxdrunLDlrfe237IW7VX4UvBdp3V4YGG+scfw1tMV0o7FWK8+sEMd1VVhBZX q0aRqxBRo8uY5m1IG2pIYDqSZmlIRr/zGygxEYYCeK+p2x5YyDpt2IEIoVWu8cCm loiUsRuop7njMsrudKX/hipV3DfkmwHUtKe6BaAb2MKLprTD1T+QCyWMgpBoImQW I2F6qEbx4pGmwhssh0iF9ikVUnA7GQSpNyPpV4LuksVV28LwDBdfLJuwuIo4R5Xg 1Ju86oha8Qz7xHKpQ7MKRS7l7I+D4V2Uopy/MrLU/Hxeg5Go663FkA+2QJ76km8y +qE8o28vM25KSgdLAnsUeIPgnIkXfGWc0Sc5ZytrscTGIcXAQsiQhxWLcz2IFylr ODGwJXVnN2Dt+a2QV46nFX8kF2LUo0OEy0j/XEMJ8MqgmQTaNhgtLCUpCIYwS3S7 Fz/HRj/+AzbZISXgNV5dQF700VAsjEfftEN3AcGIgWzZ5D0+waOM98MejCU5vLyF lbe4gXyv9jmgw1cI6wsGsFtIHBzwwIc8Oy+PWqNswRPIGHJWNn+ZKTaetmrspooj wme20LlsCg2asSt6gTs/C7BWVbAZcwTuR2hadCelkhKC0zz4Jmyqhim4GMQTnEGG wYcd92UvxsLZZMaOBGUG4y1oUnmy1hoKORa2y8xCVs7saBUDaanfGivRaoTByGal EG4ugDqhfI6RG7A2CCKkfLsdNDGBuRLqYg6RZXN0ai679nnZYsJTV0m/YV8iioKU mFhvgx4sK44rMAIKgmC+7LxHvHGra45wtjgwpg8NYH/vcbxvYwk/IyaOmQKGiGIA zLqF+4OEVlMQlUOxeh3spjJtm4rV2kUshji24i9h4ROPZ8DVZq4lqTfxJcsaVnJQ 4HhdomaWKnJ6lEpgMreOQlyYxp2GOAJf52GdIyKsAV9y2bfWMmuHhAniYarDxz0N +6JY0Q67VTT7AVHVx1aeVh3Vg6qVi7XX447eQoMy230pwnAMSI4fARfjZwA/5mev 42xo+n6QWhj1BC8iEafPhBz/F5BtGVQwjMSii111xw/9+lygBlJOSR+8Gbu45oQ/ uRoNz67mpuEldXK2fWtiQmYsoAnY0qhOArxWajY+/0pEdTMpOV105HVzD50LQ05m hHpZnF6s80FNh4KdUx3AVX9XISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+ P0A= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <t>The following is the second example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHFVT9Q2NE8nhbGzsbrBhLZnkAMz bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x yuCGIGs0MCtSD10Xet7Vs8zgKszoCOomvMByYl/bk/F0WKX8HU2jlDgKH1fpzGYQ lDigdfDSgT/MShmcx22zgj8nCwBhWUGSlAQRo3/7r64sFQFlzsXGv3PFlfuSzRUx JgfaBwd4ZSvZlEvEi8fRpTQzi60LrWZWxdUCznhQqxWHJE7rWPQ5q14IV0pxjIqs PXfHmLuhVCczvnNEjyP7cMDlNTonyIMixSGEk6+7OAhkNNbWCla6iH3UmMOrJqCH CZOBWqakCXXyGK3KFYLWT/yGUvuzqab7wwT5GUX6Sq7yh4/XFd9wET0jefRIhvgS yD/ytxmmnh7HSuSxWszTrtWlPOdqewmCRxYzuXPLQKGgAV0KQk+hGkecAjAXQ20q KQDpk+taCgZ0AMf0qt8gH8T6MSZKY7rpXMjWXDmVgV5ZfRBDVc8pqlMzyTJRhp1b zb5IcST2Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHm vG+QsOSbaTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbW f/mqvJdQPyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lA k0Frg7gSTmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8 XSCVcuD8dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoE ZM5BqLtEwtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRr evpsRZMlJqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5 JPSQpaxUlfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6 tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2 NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <t>The following is the third example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x 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tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2 NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g uBw7xZoGWhttY7Jsg/EB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw== -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <t>The following is the fourth example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF 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Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0 VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9 Pj4= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> </section> </section> </section> <section numbered="false" anchor="acknowledgments"> <name>Acknowledgments</name> <t>The authors wish to thank the following people for their contributions to this document:Corey Bonnell, Deirdre Connolly, Viktor Dukhovni, Alicja Kario, Russ Housley, Mike Ounsworth, Daniel<contact fullname="Corey Bonnell"/>, <contact fullname="Deirdre Connolly"/>, <contact fullname="Viktor Dukhovni"/>, <contact fullname="Alicja Kario"/>, <contact fullname="Russ Housley"/>, <contact fullname="Mike Ounsworth"/>, <contact fullname="Daniel VanGeest, Thom Wiggers,Geest"/>, <contact fullname="Thom Wiggers"/>, andCarl Wallace.</t><contact fullname="Carl Wallace"/>.</t> <t>In addition, we would like to thank those who contributed to the private key format discussion:Tony Arcieri, Bob Beck, Dmitry Belyavskiy, David Benjamin, Daniel Bernstein, Uri Blumenthal, Theo Buehler, Stephen Farrell, Jean-Pierre Fiset, Scott Fluhrer, Alex Gaynor, John Gray, Peter Gutmann, David Hook, Tim Hudson, Paul Kehrer, John Kemp, Watson Ladd, Adam Langley, John Mattsson, Damien Miller, Robert Relyea, Michael Richardson, Markku-Juhani<contact fullname="Tony Arcieri"/>, <contact fullname="Bob Beck"/>, <contact fullname="Dmitry Belyavskiy"/>, <contact fullname="David Benjamin"/>, <contact fullname="Daniel Bernstein"/>, <contact fullname="Uri Blumenthal"/>, <contact fullname="Theo Buehler"/>, <contact fullname="Stephen Farrell"/>, <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, Rich Salz, Roland Shoemaker, Sophie Schmieg, Simo Sorce, MichaelSaarinen"/>, <contact fullname="Rich Salz"/>, <contact fullname="Roland Shoemaker"/>, <contact fullname="Sophie Schmieg"/>, <contact fullname="Simo Sorce"/>, <contact fullname="Michael St.Johns, Falko Strenzke, Filippo Valsorda, and Wei-Jun Wang.</t>Johns"/>, <contact fullname="Falko Strenzke"/>, <contact fullname="Filippo Valsorda"/>, and <contact fullname="Wei-Jun Wang"/>.</t> </section> </back> <!--##markdown-source: H4sIAAG0d2gAA+S955bjSJYm+B9PwYk6ZzaiXBBaREsQVKAmQV2nTofBIAgS ggRAGZX9LPMs+2R7DaD08MjMSu/qnd3xrEx3Aqau+q4wM9bLywuVeqlvfy38 K1Uo6GFqx6GdFqavAq0UelvT93ChaR/hjROjJI23ON3GduGloPpuFHvpIijo 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Please let us know any objections. --> <!-- [rfced] Please review the "Inclusive Language" portion of the online Style Guide <https://www.rfc-editor.org/styleguide/part2/#inclusive_language> and let us know if any changes are needed. Updates of this nature typically result in more precise language, which is helpful for readers. Note that our script did not flag any words in particular, but this should still be reviewed as a best practice. In addition, please consider whether "tradition" should be updated for clarity. While the NIST website <https://web.archive.org/web/20250214092458/https://www.nist.gov/nist-research-library/nist-technical-series-publications-author-instructions#table1> 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>