Internet Engineering Task Force (IETF) N. Bindel
Request for Comments: 9955 SandboxAQ
Category: Informational B. Hale
ISSN: 2070-1721 Naval Postgraduate School
D. Connolly
SandboxAQ
F. Driscoll
UK National Cyber Security Centre
April
May 2026
Hybrid Signature Spectrums
Abstract
This document describes classification of design goals and security
considerations for hybrid digital signature schemes, including proof
composability, non-separability of the component signatures given a
hybrid signature, backwards and forwards compatibility, hybrid
generality, and Simultaneous Verification (SV).
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are candidates for any level of Internet
Standard; see Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
https://www.rfc-editor.org/info/rfc9955.
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Table of Contents
1. Introduction
1.1. Terminology
1.2. Motivation for Use of Hybrid Signature Schemes
1.2.1. Complexity
1.2.2. Time
1.3. Goals
1.3.1. Hybrid Authentication
1.3.2. Proof Composability
1.3.3. Weak Non-Separability
1.3.4. Strong Non-Separability
1.3.5. Backwards and Forwards Compatibility
1.3.6. Simultaneous Verification
1.3.7. Hybrid Generality
1.3.8. High Performance
1.3.9. High Space Efficiency
1.3.10. Minimal Duplicate Information
2. Non-Separability Spectrum
3. Artifacts
3.1. Artifacts vs. Separability
3.2. Artifact Locations
3.3. Artifact Location Comparison Example
4. Need for Approval Spectrum
5. EUF-CMA Challenges
6. Discussion of Advantages and Disadvantages
6.1. Backwards Compatibility vs. SNS
6.2. Backwards Compatibility vs. Hybrid Unforgeability
6.3. Simultaneous Verification vs. Low Need for Approval
7. Security Considerations
8. IANA Considerations
9. References
9.1. Normative References
9.2. Informative References
Acknowledgements
Authors' Addresses
1. Introduction
Plans to transition protocols to post-quantum cryptography sometimes
focus on confidentiality, given the potential risk of store and
decrypt attacks, where data encrypted today using traditional
algorithms could be decrypted in the future by an attacker with a
sufficiently powerful quantum computer, also known as a
Cryptographically Relevant Quantum Computer (CRQC).
It is important to also consider transitions to post-quantum
authentication; delaying such transitions creates risks. For
example, attackers may be able to carry out quantum attacks against
RSA-2048 [RSA] years before the public is aware of these
capabilities. Furthermore, there are applications where algorithm
turnover is complex or takes a long time. For example, root
certificates are often valid for about 20 years or longer. There are
also applications where future checks on past authenticity play a
role, such as long-lived digital signatures on legal documents.
Still, there have been successful attacks against algorithms using
post-quantum cryptography, as well as implementations of such
algorithms. Sometimes an attack exploits implementation issues, such
as [KYBERSLASH], which exploits timing variations, or [HQC_CVE],
which exploits implementation bugs. Sometimes an attack works for
all implementations of the specified algorithm. Research indicates
that implementation-independent attacks published in 2023 or earlier
had broken 48% of the proposals in Round 1 of the NIST Post-Quantum
Cryptography Standardization Project, 25% of the proposals not broken
by the end of Round 1, and 36% of the proposals selected by NIST for
Round 2 [QRCSP].
Such cryptanalysis and security concerns are one reason to consider
'hybrid' cryptographic algorithms, which combine both traditional and
post-quantum (or more generally a combination of two or more)
algorithms. A core objective of hybrid algorithms is to protect
against quantum computers while at the same time making clear that
the change is not reducing security. A security premise for these
algorithms is that if at least one of the two component algorithms of
the hybrid scheme holds, the confidentiality or authenticity offered
by that scheme is maintained. It should be noted that the word
'hybrid' has many uses, but this document uses 'hybrid' only in this
algorithm sense.
Whether or not hybridization is desired depends on the use case and
security threat model. Users may recognize a need to start post-
quantum transition, even while issues such as those described above
are a concern. For this, hybridization can support transition. It
should be noted that hybridization is not necessary for all systems;
recommendations on system types or analysis methods for such
determination are out of scope of this document. For cases where
hybridization is determined to be advantageous, a decision on how to
hybridize needs to be made. With many options available, this
document is intended to provide context on some of the trade-offs and
nuances to consider.
Hybridization of digital signatures, where the hybrid signature may
be expected to attest to both standard and post-quantum components,
is subtle to design and implement due to the potential separability
of the hybrid/dual signatures and the risk of downgrade/stripping
attacks. There are also a range of requirements and properties that
may be required from hybrid signatures, which will be discussed in
this document. Some of these are mutually exclusive, which
highlights the importance of considering use-case-specific
requirements.
This document focuses on explaining a spectrum of different hybrid
signature scheme design categories and different security goals for
them. It is intended as a resource for designers and implementers of
hybrid signature schemes to help them decide what properties they do
and do not require from their use case. In scope limitations, it
does not attempt to give concrete recommendations for any use case.
It also intentionally does not propose concrete hybrid signature
combiners or instantiations thereof. As with the data authenticity
guarantees provided by any digital signature, the security guarantees
discussed in this document are reliant on correct provisioning and
management of the keys involved, e.g., entity authentication, key
revocation, etc. This document only considers scenarios with a
single signer and a single verifier; constructions with multiple
signers or verifiers are out of scope.
1.1. Terminology
We follow existing documents on hybrid terminology [RFC9794] and
hybrid key encapsulation mechanisms (KEMs) [RFC9954] to enable
settling on a consistent language. We will make clear when this is
not possible. In particular, we follow the definitions of 'post-
quantum algorithm', 'traditional algorithm', and 'combiner'.
Moreover, we use the definition of 'certificate' to mean 'public-key
certificate' as defined in [RFC4949].
Signature scheme: A signature scheme is defined via the following
three algorithms:
KeyGen() -> (pk, sk):
A probabilistic key generation algorithm, which generates a
public verifying key pk and a secret signing key sk.
Sign(sk, m) -> (sig):
A probabilistic signature generation, which takes as input a
secret signing key sk and a message m, and outputs a signature
sig. In this document, the secret signing key sk is assumed to
be implicit for notational simplicity, and the following
notation is used: Sign(m) -> (sig). If the message m is
comprised of multiple fields, m1, m2, ..., mN, this is notated
as Sign(m) = Sign (m1, m2, ... mN) -> (sig).
Verify(pk, sig, m) -> b:
A verification algorithm, which takes as input a public
verifying key pk, a signature sig, and a message m, and outputs
a bit b indicating accept (b=1) or reject (b=0) of the
signature for the message m.
Hybrid signature scheme: Following [RFC9794], we define a hybrid
signature scheme to be "a multi-algorithm digital signature scheme
made up of two or more component digital signature algorithms".
While
For security purposes, it often makes sense for security purposes to require that the
security of the component schemes is be based on the hardness of
different cryptographic assumptions, assumptions. However, in other some cases,
hybrid schemes might be motivated, e.g., by interoperability of
variants on the same scheme, scheme and as such, such both component schemes are
would be based on the same hardness assumption (e.g., both post-quantum post-
quantum assumptions or even both of the same concrete assumption, assumption
such as Ring Learning With Errors (LWE)). (R-LWE)). We allow this
explicitly. In particular, this means that in contrast to
[RFC9794], we will use the more general term 'hybrid signature
scheme' instead of requiring one post-quantum and one traditional
algorithm (i.e.,
Post-Quantum Traditional Post-Quantum/Traditional (PQ/T) hybrid signature
schemes) to allow also the combination of several post-quantum
algorithms. The term 'composite scheme' has sometimes been used
as a synonym for 'hybrid scheme'. This is different from
[RFC9794] where the term is used as a specific instantiation of
hybrid schemes such that
"where multiple cryptographic algorithms are combined to form a
single key or signature such that they can be treated the "scheme is exposed as a single
atomic object at singular
interface of the protocol level". same type as the component algorithms". To avoid
confusion, we will avoid the term 'composite scheme'.
Hybrid signature: A hybrid signature is the output of the hybrid
signature scheme's signature generation. As a synonym, we might
use 'dual signature'. For example, NIST defines a dual signature
as "two or more signatures on a common message" [NIST_PQC_FAQ].
For the same reason as above, we will avoid using the term
'composite signature', although it sometimes appears as a synonym
for 'hybrid/dual signature'.
Component (signature) scheme: Component signature schemes are the
cryptographic algorithms contributing to the hybrid signature
scheme. This has a similar purpose as in [RFC9794]. 'Ingredient
(signature) scheme' may be used as a synonym.
Next-generation algorithms: Following [RFC9954], we define next-
generation algorithms to be "algorithms that are not yet widely
deployed but may eventually be widely deployed". Hybrid
signatures are mostly motivated by preparation for post-quantum
transition or use in long-term post-quantum deployment, hence the
reference to post-quantum algorithms in this document. However,
the majority of the discussion in this document applies equally
well to future transitions to other next-generation algorithms.
Policy: Throughout this document, we refer to 'policy' in the
context of, e.g., a system policy requiring verification of two
signatures, an RFC description, guidance documentation, etc.
Similar terminology may include 'security configuration settings'
or related phrasing. We treat these terms as equivalent for the
purposes of this document.
Artifact: An artifact is evidence of the sender's intent to
hybridize a signature that remains even if a component signature
is removed. Artifacts can be, e.g., at the algorithmic level
(e.g., within the digital signature), at the protocol level (e.g.,
within the certificate), or on the system policy level (e.g.,
within the message). Artifacts should be easily identifiable by
the receiver in the case of signature stripping.
Stripping attack: A stripping attack refers to a case where an
adversary takes a message and hybrid signature pair and attempts
to submit (a potential modification of) the pair to a component
algorithm verifier, meaning that the security is based only on the
remaining component scheme. A common example of a stripping
attack includes a message and hybrid signature, comprised of
concatenated post-quantum and traditional signatures, where an
adversary with a quantum computer simply removes the post-quantum
component signature and submits the (potentially changed) message
and traditional component signature to a traditional verifier.
This could include an authentic traditional certificate authority
signature on a certificate that was originally hybrid-signed. An
attribute of this is that an honest signer would attest to
generating the signature. Stripping attacks should not be
confused with component message forgery attacks.
Component message forgery attacks: A forgery attack refers to a case
where an adversary attempts to forge a (non-hybrid) signature on a
message using the public key associated with a component
algorithm. A common example of such an attack would be a quantum
attacker compromising the key associated with a traditional
component algorithm and forging a message and signature pair.
Message forgery attacks may be formalized with experiments such as
the Existential Unforgeability under Chosen Message Attack (EUF-
CMA) [EUFCMA], while the difference introduced in component
message forgery attacks is that the key is accepted for both
hybrid and single algorithm use. Further discussion of this
appears in Section 5.
1.2. Motivation for Use of Hybrid Signature Schemes
Before diving into the design goals for hybrid digital signatures, it
is worth taking a look at motivations for them. As many of the
arguments hold in general for hybrid algorithms, we again refer to
[RFC9954], which summarizes these well. In addition, we explicate
the motivation for hybrid signatures here.
1.2.1. Complexity
Next-generation algorithms and their underlying hardness assumptions
are often more complex than traditional algorithms. For example, the
signature scheme Module-Lattice-Based Digital Signature Algorithm
(ML-DSA) [MLDSA] (also known as CRYSTALS-DILITHIUM) follows the well-
known well-known Fiat-Shamir transform [FS] to
construct the signature scheme but also relies on rejection sampling
that is known to give cache side channel information (although this
does not lead to a known attack). Likewise, the signature scheme
FALCON [FALCON] uses complex sampling during signature generation.
Furthermore, attacks against the next-generation multivariate schemes
Rainbow [RAINBOW] and Great Multivariate Short Signature (GeMSS)
[GEMSS] might raise concerns for conservative adopters of other
algorithms, which could hinder adoption.
As such, some next-generation algorithms carry a higher risk of
implementation mistakes and revision of parameters compared to
traditional algorithms, such as RSA. RSA is a relatively simple
algorithm to understand and explain, yet during its existence and
use, there have been multiple attacks and refinements, such as adding
requirements to how padding and keys are chosen, and implementation
issues, such as cross-protocol attacks (e.g., component algorithm
forgeries). attacks. Thus, even in a relatively
simple algorithm, subtleties and caveats on implementation and use
can arise over time. Given the complexity of next-generation
algorithms, the chance of such discoveries and caveats needs to be
taken into account.
Of note, some next-generation algorithms have received considerable
analysis, for example, following attention gathered during the NIST
Post-Quantum Cryptography Standardization Process Project [NIST_PQC_FAQ].
However, if and when further information on caveats and
implementation issues come to light, it is quite possible that
vulnerabilities will represent a weakening of security rather than a
full "break". Such weakening may also be offset if a hybrid approach
has been used.
1.2.2. Time
In large systems, including national systems, space systems, large
healthcare support systems, and critical infrastructure, acquisition
and procurement time can be measured in years, and algorithm
replacement may be difficult or even practically impossible. Long-
term commitment creates further urgency for immediate post-quantum
algorithm selection, for example, when generating root certificates
with their long validity windows. Additionally, for some sectors,
future checks on past authenticity plays a role (e.g., many legal,
financial, auditing, and governmental systems). This means there is
a need to transition some systems to post-quantum signature
algorithms imminently. However, as described above, there is a need
to remain aware of potential, hidden subtleties in next-generation
algorithms' resistance to standard attacks, particularly in cases
where it is difficult to replace algorithms. This combination of
time pressure and complexity drives some transition designs towards
hybridization.
1.3. Goals
There are various security and usability goals that can be achieved
through hybridization. The following provides a summary of these
goals while also noting where goals are in conflict, i.e., that
achievement of one goal precludes another, such as backwards
compatibility.
1.3.1. Hybrid Authentication
One goal of hybrid signature schemes is security. As defined in
[RFC9794], ideally a hybrid signature scheme can achieve 'hybrid
authentication', which is the property that (cryptographic)
authentication is achieved by the hybrid signature scheme, provided
that a least one component signature algorithm remains 'secure'.
There might be, however, other goals in competition with this one,
such as backwards compatibility -- referring to the property where a
hybrid signature may be verified by only verifying one component
signature (see description below). Section 1.3.5). Hybrid authentication is an umbrella
term that encompasses more specific concepts of hybrid signature
security, such as 'hybrid unforgeability' described next.
1.3.1.1. Hybrid Unforgeability
Hybrid unforgeability is a specific type of hybrid authentication,
where the security assumption for the scheme (e.g., EUF-CMA) is
maintained as long as at least one of the component schemes maintains
that security assumption. We call this notion 'hybrid
unforgeability'; it is a specific type of hybrid authentication. For example, the concatenation combiner in
[HYBRIDSIG] is 'hybrid unforgeable'. As mentioned above, this might
be incompatible with backwards compatibility, where the EUF-CMA
security of the hybrid signature relies solely on the security of one
of the component schemes instead of relying on both, e.g., the dual
message combiner using nesting in [HYBRIDSIG]. For more details,
refer to the
discussion below.
Use cases where Section 1.3.5.
In some use cases, a hybrid scheme is used with, e.g., with (for example) EUF-CMA
security assumed for only one component scheme scheme; these cases generally
use hybrid techniques for their 'functional transition' pathway
support. For example, hybrid signatures may be used as a transition
step for gradual post-
quantum post-quantum adoption while ensuring
interoperability when a system includes both verifiers that only
support traditional signatures and verifiers that have been upgraded
to support post-quantum signatures.
In contrast, in other use cases where cases, a hybrid scheme is used with, e.g., EUF-
CMA with (for
example) EUF-CMA security assumed for both component schemes without
prioritization between them them; these cases can use hybrid techniques
for both functional transition and security transition (i.e., a
transition to ensure security even if it may not be known which
algorithm should be relied upon).
1.3.2. Proof Composability
Under proof composability, the component algorithms are combined in
such a way that it is possible to prove a security reduction from the
security properties of a hybrid signature scheme to the properties of
the respective component signature schemes and, potentially, other
building blocks such as hash functions, key derivation functions,
etc. Otherwise, an entirely new proof of security is required, and
there is a lack of assurance that the combination builds on the
standardization processes and analysis performed to date on component
algorithms. The resulting hybrid signature would be, in effect, an
entirely new algorithm of its own. The more the component signature
schemes are entangled, the more likely it is that an entirely new
proof is required, thus not meeting proof composability.
1.3.3. Weak Non-Separability
Non-separability was one of the earliest properties of hybrid digital
signatures to be discussed [HYBRIDSIG]. It was defined as the
guarantee that an adversary cannot simply "remove" one of the
component signatures without evidence left behind. For example,
there are artifacts that a carefully designed verifier may be able to
identify or that are identifiable in later audits. This was later
termed Weak Non-Separability (WNS) [HYBRIDSIGDESIGN]. Note that WNS
does not restrict an adversary from potentially creating a valid
component digital signature from a hybrid one (a signature stripping
attack) but rather implies that such a digital signature will contain
artifacts of the separation. Thus, authentication that is normally
assured under correct verification of digital signature(s) is now
potentially also reliant on further investigation on the receiver
side that may extend well beyond traditional signature verification
behavior. For instance, this can intuitively be seen in cases of a
message containing a context note on hybrid authentication that is
then signed by all component algorithms/the algorithms as part of the hybrid
signature scheme. If an adversary removes one component signature
but not the other, then artifacts in the message itself point to the
possible existence of a hybrid signature such as a label stating
"this message must be hybrid-signed". This might be a countermeasure
against stripping attacks if the verifier expects a hybrid signature
scheme to have this property. However, it places the responsibility
of signature validity not only on the correct format of the message,
as in a traditional signature security guarantee, but the precise
content thereof.
1.3.4. Strong Non-Separability
Strong Non-Separability (SNS) is a stronger notion of WNS, which is
introduced in [HYBRIDSIGDESIGN]. SNS guarantees that an adversary
cannot take a hybrid signature (and message) as input and output a
valid component signature (and potentially different message) that
will verify correctly. In other words, separation of the hybrid
signature into component signatures implies that the component
signature will fail verification (of the component signature scheme)
entirely. Therefore, authentication is provided by the sender to the
receiver through correct verification of the digital signature(s), as
in traditional signature security experiments. It is not dependent
on other components, such as message content checking, or protocol-
level aspects, such as public key provenance. As an illustrative
example distinguishing WNS from SNS, consider the case of component
algorithms Sigma_1.Sign and Sigma_2.Sign where the hybrid signature
is computed as a concatenation (sig_1, sig_2), where sig_1 =
Sigma_1.Sign(hybridAlgID, m) and sig_2 = Sigma_2.Sign(hybridAlgID,
m). In this case, a new message m' = (hybridAlgID, m) along with
signature sig_1 and Sigma_1.pk, with the hybrid artifact embedded in
the message instead of the signature, could be correctly verified.
The separation would be identifiable through further investigation,
but the signature verification itself would not fail. Thus, this
case shows WNS (assuming the verification algorithm is defined
accordingly) but not SNS.
Some work [COMP-MLDSA] has looked at reliance on the public key
certificate chains to explicitly define hybrid use of the public key,
namely that Sigma_1.pk cannot be used without Sigma_2.pk. This
implies pushing the hybrid artifacts into the protocol and system
level and a dependency on the security of other verification
algorithms (namely those in the certificate chain). This further
requires that security analysis of a hybrid digital signature
requires analysis of the key provenance, i.e., not simply that a
valid public key is used but how its hybridization and hybrid
artifacts have been managed throughout the entire chain. External
dependencies such as this may imply hybrid artifacts lie outside the
scope of the signature algorithm itself. SNS may potentially be
achievable based on dependencies at the system level.
1.3.5. Backwards and Forwards Compatibility
Backwards compatibility refers to the property where a hybrid
signature may be verified by only verifying one component signature,
allowing the scheme to be used by legacy receivers. In general, this
means verifying the traditional component signature scheme,
potentially ignoring the post-quantum signature entirely. This
provides an option to transition sender systems to post-quantum
algorithms while still supporting select legacy receivers. Notably,
this is a verification property; the sender has provided a hybrid
digital signature, but the verifier is allowed, due to internal
policy and/or implementation, to only verify one component signature.
Forwards compatibility has also been a consideration in hybrid
proposals [NC-HYBRID-AUTH]. Forwards compatibility assumes that
hybrid signature schemes will be used for some time but that
eventually all systems will transition to use only one (particularly,
only one post-quantum) algorithm. As this is very similar to
backwards compatibility, it also may imply separability of a hybrid
algorithm; however, it could also simply imply capability to support
separate component signatures. Thus, the key distinction between
backwards and forwards compatibility is that backwards compatibility
may be needed for legacy systems that cannot use and/or process
hybrid or post-quantum signatures, whereas in forwards compatibility,
the system has those capabilities and can choose what to support
(e.g., for efficiency reasons).
Ideally, backwards and forwards compatibility is achieved using
redundant information as little as possible, as noted in [RFC9954].
1.3.6. Simultaneous Verification
Simultaneous Verification (SV) builds on SNS and was first introduced
in [HYBRIDSIGDESIGN]. SV requires that not only is the entire hybrid
signature (e.g., all component signature elements) needed to achieve
a successful verification present in the signature presented for
verification but also that verification of both component algorithms
occurs roughly simultaneously. Namely, "missing" information needs
to be computed by the verifier so that a normally functioning
verification algorithm cannot "quit" the verification process before
the hybrid signature elements attesting for both component algorithms
are verified. This may additionally cover some error-injection and
similar attacks, where an adversary attempts to make an otherwise
honest verifier skip component algorithm verification. SV mimics
traditional digital signatures guarantees, essentially ensuring that
the hybrid digital signature behaves as a single algorithm vs. two
separate component stages. Alternatively phrased, under an SV
guarantee, it is not possible for an otherwise honest verifier to
initiate termination of the hybrid verification upon successful
verification of one component algorithm without also knowing if the
other component succeeded. Note that SV does not prevent dishonest
verification, such as if a verifier maliciously implements a
customized verification algorithm that is designed with intention to
subvert the hybrid verification process or skips signature
verification altogether.
1.3.7. Hybrid Generality
Hybrid generality means that a general signature combiner is defined
based on inherent and common structures of component digital
signatures
signature "categories". For instance, since multiple signature
schemes use a Fiat-Shamir transform, a hybrid scheme based on the
transform can be made that is generalizable to all such signatures.
Such generality can also result in simplified constructions, whereas
more tailored hybrid variants might be more efficient in terms of
sizes and performance.
1.3.8. High Performance
Similar to performance goals noted for hybridization of other
cryptographic components [RFC9954], hybrid signature constructions
are expected to be as performant as possible. For most hybrid
signatures, this means that the computation time should only
minimally exceed the sum of the component signature computation time.
It is noted that performance of any variety may come at the cost of
other properties, such as hybrid generality.
1.3.9. High Space Efficiency
Similar to space considerations in [RFC9954], hybrid
Hybrid signature constructions are expected to be as space performant
as possible. This includes messages (as they might increase if
artifacts are used), public keys, and the hybrid signature. For the
hybrid signature, size should no more than minimally exceed the
signature size of the two component signatures. In some cases, it
may be possible for a hybrid signature to be smaller than the
concatenation of the two component signatures.
1.3.10. Minimal Duplicate Information
Duplicated information should be avoided when possible, as a general
point of efficiency. This might include repeated information in
hybrid certificates or in the communication of component certificates
in addition to hybrid certificates (for example, to achieve backwards
and forwards compatibility) or sending multiple public keys or
signatures of the same component algorithm.
2. Non-Separability Spectrum
Non-separability is not a singular definition but rather is a scale
spectrum representing degrees of separability hardness, visualized in
Figure 1.
| ----------------------------------------------------------|
| *No Non-Separability*
|
| No artifacts exist.
| ----------------------------------------------------------|
| *Weak Non-Separability*
|
| Artifacts exist in the message, signature, system,
| application, or protocol.
| ----------------------------------------------------------|
| *Strong Non-Separability*
|
| Artifacts exist in the hybrid signature.
| ----------------------------------------------------------|
| *Strong Non-Separability with Simultaneous Verification*
|
| Artifacts exist in the hybrid signature, and verification
| or failure of both components occurs simultaneously.
| ----------------------------------------------------------|
▼
Figure 1: Spectrum of Non-Separability from Weakest to Strongest
At one end of the spectrum are schemes in which one of the component
signatures can be stripped away with the verifier not being able to
detect the change during verification. An example of this includes
simple concatenation of signatures without any artifacts used.
Nested signatures (where a message is signed by one component
algorithm and then the message-signature combination is signed by the
second component algorithm) may also fall into this category,
dependent on whether the inner or outer signature is stripped off
without any artifacts remaining.
Next on the spectrum are weakly non-separable signatures. Under Weak
Non-Separability, if one of the component signatures of a hybrid
signature is removed, artifacts of the hybrid hybridization will remain (in
the message, in the signature, at the protocol level, etc.). This
may enable the verifier to detect if a component signature is
stripped away from a hybrid signature, but that detectability depends
highly on the type of artifact and permissions. For instance, if a
message contains a label artifact "This message must be signed with a
hybrid signature", then the system must be allowed to analyze the
message contents for possible artifacts. Whether a hybrid signature
offers (Weak/Strong) Non-Separability might also depend on the
implementation and policy of the protocol or application the hybrid
signature is used in on the verifier side. Such policies may be
further ambiguous to the sender, meaning that the type of
authenticity offered to the receiver is unclear. In another example,
under nested signatures, the verifier could be tricked into
interpreting a new message as the message/inner
signature combination of the message and
inner signature and verify only the outer signature. In this case,
the inner signature is an artifact.
Third on the scale spectrum is the Strong Non-Separability notion, in which
separability detection is dependent on artifacts in the signature
itself. Unlike in Weak Non-Separability, where artifacts may be in
the actual message, the certificate, or other non-signature
components, this notion more closely ties to traditional algorithm
security notions (such as EUF-CMA) where security is dependent on the
internal construct of the signature algorithm and its verification.
In this type, the verifier can detect artifacts on an algorithmic
level during verification. For example, the signature itself may
encode the information that a hybrid signature scheme is used.
Examples of this type may be found in [HYBRIDSIGDESIGN].
For schemes achieving the most demanding security notion, Strong Non-
Separability with Simultaneous Verification, verification succeeds
only when both of the component signatures are present and the
verifier has verified both signatures. Moreover, no information is
leaked to the receiver during the verification process on the
possible validity of the component signatures until both verify (or
verification failure may or may not be attributable to a specific
component algorithm). This construct most closely mirrors
traditional digital signatures where, assuming that the verifier does
verify a signature at all, the result is either a positive
verification of the full signature or a failure if the signature is
not valid. For fused hybrid signatures, a full signature implies the
fusion of both component algorithms; therefore, this type of
construction has the potential to achieve the strongest non-
separability notion, which ensures an all-or-nothing approach to
verification, regardless of adversarial action. Examples of
algorithms providing this type of security can be found in
[HYBRIDSIGDESIGN].
3. Artifacts
Hybridization benefits from the presence of artifacts as evidence of
the sender's intent to decrease the risk of successful stripping
attacks. This, however, depends strongly on where such evidence
resides (e.g., in the message, in the signature, or somewhere on the
protocol level instead of at the algorithmic level). Even commonly
discussed hybrid approaches, such as concatenation, are not
inherently tied to one type of security (e.g., WNS or SNS). This can
lead to ambiguities when comparing different approaches and
assumptions about security or lack thereof. Thus, in this section,
we cover artifact locations and also walk through a high-level
comparison of a few hybrid categories to show how artifact location
can differ within a given approach. Artifact location is tied to
non-separability notions as described above; thus, the selection of a
given security guarantee and general hybrid approach must also
include a finer-grained selection of artifact placement.
3.1. Artifacts vs. Separability
Note that non-separability is a security notion of the signature
scheme and not directly related to artifacts -- however, artifacts
may be used for detection of separation. For instance, under strong
non-separability, the scheme would fail verification if separation
occurs, while for weak non-separability, some artifacts exist if
separation occurs but verification would not necessarily fail. The
verifier could indeed ignore the artifact, resulting in the scheme
achieving only weak non-separability and not strong non-separability.
It is rather that
However, if an investigation occurred, then an artifact exists that could be
identified if an
investigation occurred, etc. in the separated signature. Under weak non-separability,
detection of separation may depend on non-cryptographic
configurations or other dependencies. Also, strong non-separability
and weak non-
separability non-separability are properties of the signature scheme --
artifacts are not necessarily in the signature and may appear in the
signed message, certificate, protocol, or policy (hence them not
necessarily being related to the strong non-separability and weak non-
separability
non-separability security notions). Artifacts may still be useful
(albeit dependent on system configurations) even if separable
signatures are used.
3.2. Artifact Locations
There are a variety of artifact locations possible, ranging from
within the message to the signature algorithm to the protocol level
and even into policy, as shown in Table 1. For example, one artifact
location could be in the message to be signed, e.g., containing a
label artifact. Depending on the hybrid type, it might be possible
to strip this away. For example, a quantum attacker could strip away
the post-quantum signature of a concatenated dual signature, and,
being able to forge the traditional signature, it could remove the
label artifact from the message as well. So, for many applications
and threat models, adding an artifact in the message might be
insufficient under stripping attacks. Another artifact location
could be in the public key certificates as described in [COMP-MLDSA].
In such a case, the artifacts are still present even if a stripping
attack occurs. In yet another case, artifacts may be present through
the fused hybrid method, thus making them part of the signature at
the algorithmic level. Note that in this latter case, it is not
possible for an adversary to strip one of the component signatures or
use a component of the hybrid signature to create a forgery for a
component algorithm. Such signatures provide SNS. Consequently,
this also implies that the artifacts of hybridization are absolute in
that verification failure would occur if an adversary tries to remove
them.
Eventual security analysis may be a consideration in choosing between
levels. For example, if the security of the hybrid scheme is
dependent on system policy, then cryptographic analysis must
necessarily be reliant on specific policies, and it may not be
possible to describe a scheme's security in a standalone sense. In
this case, it is necessary to consider the configuration of a
particular implementation or use to assess security, which could
increase the risk of unknown and unanticipated vulnerabilities,
regardless of the algorithms in use.
+========================================+===========+
| Location of Artifacts of Hybrid Intent | Level |
+========================================+===========+
| Signature | Algorithm |
+----------------------------------------+-----------+
| Certificate | Protocol |
+----------------------------------------+-----------+
| Algorithm agreement / negotiation | Protocol |
+----------------------------------------+-----------+
| Message | Policy |
+----------------------------------------+-----------+
Table 1: Artifact Placement Levels
3.3. Artifact Location Comparison Example
Here we provide a high-level example of how artifacts can appear in
different locations even within a single, common approach. We look
at the following categories of approaches: concatenation, nesting,
and fusion. This is to illustrate that a given approach does not
inherently imply a specific non-separability notion and that there
are subtleties to the selection decision, since hybrid artifacts are
related to non-separability guarantees. Additionally, this
comparison highlights how artifact placement can be identical in two
different hybrid approaches.
We briefly summarize the hybrid approach categories (concatenation,
nesting, and fusion) for clarity in description before showing how
each one may have artifacts in different locations in Table 2.
* Concatenation: Variants of hybridization where, for component
algorithms Sigma_1.Sign and Sigma_2.Sign, the hybrid signature is
calculated as a concatenation (sig_1, sig_2) such that sig_1 =
Sigma_1.Sign(hybridAlgID || m) and sig_2 =
Sigma_2.Sign(hybridAlgID || m).
* Nesting: Variants of hybridization where, for component algorithms
Sigma_1.Sign and Sigma_2.Sign, the hybrid signature is calculated
in a layered approach as (sig_1, sig_2) such that, e.g., sig_1 =
Sigma_1.Sign(hybridAlgID || m) and sig_2 =
Sigma_2.Sign(hybridAlgID || (m || sig_1)).
* Fused hybrid: Variants of hybridization, where for component
algorithms Sigma_1.Sign and Sigma_2.Sign, the hybrid signature is
calculated to generate a single hybrid signature sig_h that cannot
be cleanly separated to form one or more valid component
constructs. For example, if both signature schemes are
constructed through the Fiat-Shamir transform, the component
signatures would include responses r_1 and r_2 and challenges c_1
and c_2, where c_1 and c_2 are hashes computed over the respective
commitments comm_1 and comm_2 (and the message). A fused hybrid
signature could consist of the component responses r_1 and r_2 and
a challenge c that is computed as a hash over both commitments,
i.e., c = Hash((comm_1 || comm_2) || Hash2(message)). As such, c
does not belong to either of the component signatures but rather
both, meaning that the signatures are 'entangled'.
+====+=======================+=============================+
+====+=========================+==================================+
| # | Location of Artifacts | Category |
| | of Hybrid Intent | |
+====+=======================+=============================+
+====+=========================+==================================+
| | | *Concatenated* |
+----+-----------------------+=============================+
+----+-------------------------+==================================+
| 1 | None | No label in message, public keys |
| | | keys are in separate certs certificates |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 2 | In message | Label in message, public keys |
| | | keys are in separate certs certificates |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 3 | In cert certificate | No label in message, public keys |
| | | keys are in combined cert certificate |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 4 | In message and cert | Label in message, public keys |
| | certificate | keys are in combined cert certificate |
+----+-----------------------+=============================+
+----+-------------------------+==================================+
| | | *Nested* |
+----+-----------------------+=============================+
+----+-------------------------+==================================+
| 5 | In message | Label in message, public keys |
| | | keys are in separate certs certificates |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 6 | In cert certificate | No label in message, public keys |
| | | keys are in combined cert certificate |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 7 | In message and cert | Label in message, public keys |
| | certificate | keys are in combined cert certificate |
+----+-----------------------+=============================+
+----+-------------------------+==================================+
| | | *Fused* |
+----+-----------------------+=============================+
+----+-------------------------+==================================+
| 8 | In signature | Public keys are in separate |
| | | certs certificates |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 9 | In signature and | Label in message, public keys |
| | message | keys are in separate certs certificates |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 10 | In signature and cert | Public keys are in combined |
| | certificate | cert certificate |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
| 11 | In signature and | Label in message, public keys |
| | message and cert certificate | keys are in combined cert certificate |
+----+-----------------------+-----------------------------+
+----+-------------------------+----------------------------------+
Table 2: Artifact Locations Depending on the Hybrid Signature Type
As can be seen, shown in Table 2, while concatenation may appear to refer to a
single type of combiner, there are in fact several possible artifact
locations depending on implementation choices. Artifacts help to
support detection in the case of stripping attacks, which means that
different artifact locations imply different overall system
implementation considerations to be able to achieve such detection.
Case 1 provides the weakest guarantees of hybrid identification, as
there are no prescribed artifacts and therefore non-separability is
not achieved. However, as can be seen, this does not imply that every implementation
using concatenation fails to achieve non-
separability. non-separability. Thus, it is
advisable for implementers to be transparent about artifact
locations.
In cases 2 and 5, the artifacts lie within the message. This is
notable as the authenticity of the message relies on the validity of
the signature, and the artifact location means that the signature in
turn relies on the authentic content of the message (the artifact
label). This creates a risk of circular dependency. Alternative
approaches, such as cases 3, 4, 6, and 7, solve this circular
dependency by provisioning keys in a combined certificate.
Another observation from this comparison is that artifact locations
may be similar among some approaches. For instance, cases 3 and 6
both contain artifacts in the certificate. Naturally, these are
high-level examples and further specification on concrete schemes in
the categories are needed before prescribing non-separability
guarantees to each, but this does indicate how there could be a
strong similarity between such guarantees. Such comparisons allow
for a systematic decision process, where security is compared and
identified, and if schemes are similar in the desired security goal,
then decisions between schemes can be based on performance and
implementation ease.
A final observation that this type of comparison provides is how
various combiners may change the security analysis assumptions in a
system. For instance, cases 3, 4, 6, and 7 all push artifacts -- and
therefore the signature validity -- into the certificate chain.
Naturally, the entire chain must then also use a similar combiner if
a straightforward security argument is to be made. Other cases, such
as 8, 9, 10, and 11, put artifacts within the signature itself,
meaning that these bear the closest resemblance to traditional
schemes where message authenticity is dependent on signature
validity.
4. Need for Approval Spectrum
In practice, use of hybrid digital signatures relies on standards
where applicable. This is particularly relevant in the cases where
use of FIPS-approved software modules is required but applies equally
to any guidance or policy direction that specifies that at least one
component algorithm of the hybrid scheme has passed some
certification type while not specifying requirements on the other
component. NIST provides the following guidance in [NIST_PQC_FAQ]
(emphasis added):
| Assume that in a [hybrid] signature, _one signature is generated
| with a NIST-approved signature scheme as specified in FIPS 186,
| while another signature(s) can be generated using different
| schemes_, e.g., ones that are not currently specified in NIST
| standards ... _[hybrid] _hybrid signatures can be accommodated by current
| standards in "FIPS mode", as defined in FIPS 140, provided at
| least one of the component methods is a properly implemented,
| NIST-approved signature algorithm_. For the purposes of FIPS 140
| validation, any signature that is generated by a non-approved
| component scheme would not be considered a security function,
| since the NIST-approved component is regarded as assuring the
| validity of the [hybrid] hybrid signature.
This document does not define a formal interpretation of the NIST
statement; however, we use it as motivation to highlight some points
that implementers of hybrids hybrid signature schemes may wish to consider
when following any guidance documents that specify that 1) the
signature scheme for one of the component algorithms must be approved
and 2) the said algorithm must be a well-implemented or certified
implementation. This type of need for approval (i.e., a requirement
that an implementer is looking to follow regarding approval or
certification of the software module implementation of a hybrid or
its component algorithms) can drive some logistical decisions on what
types of
hybrids hybrid signature schemes an implementer should consider.
In this respect, there is a scale spectrum of approval that developers may
consider as to whether they are using at least one approved component
algorithm implementation (1-out-of-n approved software module) or
whether every component algorithm implementation is individually
approved (all approved software module).
We provide a scale spectrum for the different nuances of approval of the
hybrid combiners, where "approval" means that a software
implementation of a component algorithm can be used unmodified for
creation of the hybrid signature. This may be related to whether a
hybrid combiner is likely to need dedicated certification.
| ---------------------------------------------------------|
| *New Algorithm*
|
| New signature scheme based on a selection of hardness
| assumptions.
|
| Separate approval needed.
| ---------------------------------------------------------|
| *No Approved Software Module*
|
| Hybrid combiner supports security analysis that can be
| reduced to approved component algorithms, potentially
| changing the component implementations.
|
| Uncertainty about whether separate approval is needed.
| ---------------------------------------------------------|
| *1-out-of-n Approved Software Module*
|
| Combiner supports one component algorithm and
| implementation in a black-box way but potentially
| changes the other component algorithm implementation(s).
|
| No new approval needed if the black-box component
| (implementation) is approved.
| ---------------------------------------------------------|
| *All Approved Software Modules*
|
| Hybrid combiner acts as a wrapper, fully independent of
| the component signature scheme implementations.
|
| No new approval needed if at least one component
| implementation is approved.
| ---------------------------------------------------------|
▼
Figure 2: Generality / Need for Approval Spectrum
The first listed "combiner" would be a new construction with a
security reduction to different hardness assumptions but not
necessarily to approved (or even existing) signature schemes. Such a
new, singular algorithm relies on both traditional and next-
generation principles.
Next is a combiner that might take inspiration from existing/approved
signature schemes such that its security can be reduced to the
security of the approved algorithms. The combiner may, however,
alter the implementations. As such, it is uncertain whether new
approval would be needed as it might depend on the combiner and
changes. Such a case may potentially imply a distinction between a
need for fresh approval of the algorithm(s) and approval of the
implementation(s).
The 1-out-of-n combiner uses at least one approved algorithm
implementation in a black-box way (i.e., without modification to the
software module implementation for that algorithm). It may
potentially change the specifics of the other component algorithm
implementations. If the premise is that no new approval is needed so
long as at least one component is approved, then this is likely
considered sufficient.
In an all-approved combiner, every algorithm implementation is used
in a black-box way. A concatenation combiner is a simple example
(where a signature is valid if all component signatures are valid).
Thus, as all algorithm implementations are approved, a requirement
that at least one of hybrid component algorithms is approved would be
satisfied.
5. EUF-CMA Challenges
Unforgeability properties for hybrid signature schemes are more
nuanced than for single-algorithm schemes.
Under the traditional EUF-CMA security assumption, an adversary
requests signatures for messages of their choosing and succeeds if
they are able to produce a valid signature for a message that was not
part of an earlier request. EUF-CMA can be seen as applying to the
hybrid signature scheme in the same way as single-algorithm schemes.
Namely, the most straightforward extension of the traditional EUF-CMA
security game would be that an adversary requests hybrid signatures
for messages of their choosing and succeeds if they are able to
produce a valid hybrid signature for a message that was not part of
an earlier request. However, this has several layers of nuance under
a hybrid construct.
Consider, for example, a simplistic hybrid approach using
concatenated component algorithms. If the hybrid signature is
stripped, such that a single component signature is submitted to a
verification algorithm for that component along with the message that
was signed by the hybrid, hybrid signature scheme, the result would be an
EUF-CMA forgery for the component signature. This is because as the
component signing algorithm was not previously called for the
message, the hybrid signing algorithm was used to generate the
signature. This is an example of a component algorithm forgery, a.k.a. a case an
example of cross-
algorithm a cross-algorithm attack or cross-protocol attack.
The component algorithm forgery verifier target does not need to be
the intended recipient of the hybrid-signed message and may even be
in an entirely different system. This vulnerability is particularly
an issue among concatenated or nested hybrid signature schemes where
individual component verification could be possible. It should be
noted that policy enforcement of a hybrid verification does not
mitigate the issue on the intended message recipient: The component
forgery could occur on any system that accepts the component keys.
Thus, if EUF-CMA security for hybrids is informally defined in the
straightforward way as that an adversary requests hybrid signatures for messages of their choosing and succeeds if they are able to
produce a valid hybrid signature for a message that was not part of
an earlier request, implicit scheme to be EUF-CMA secure, certain
requirements must hold in order to avoid
real-world implications. hold. Namely, either component algorithm
forgeries, a.k.a. cross-protocol attacks, forgeries
must be out of scope for the use case or the hybrid signature choice
must be strongly non-
separable. non-separable. Otherwise, component algorithm
forgeries, which can be seen as a type of cross-protocol attack,
affect the type of EUF-CMA properties offered and are a practical
consideration that system designers and managers should be aware of
when selecting among hybrid approaches for their use case.
There are a couple approaches to alleviating this issue, as noted
above. One is on restricting key reuse. As described in
[COMP-MLDSA], prohibiting hybrid algorithm and component algorithm
signers and verifiers from using the same keys can help ensure that a
component verifier cannot be tricked into verifying the hybrid
signature. This would effectively put component forgeries out of
scope for a use case. One means for restricting key reuse is through
allowed key use descriptions in certificates. While prohibiting key
reuse reduces the risk of such component forgeries, and is the
mitigation described in [COMP-MLDSA], it is still a policy
requirement and not a cryptographic assurance. Component forgery
attacks may be possible if the policy is not followed or is followed
inconsistently across all entities that might verify signatures using
those keys. This needs to be accounted for in any security analysis.
Since cryptographic provable security modeling has not historically
accounted for key reuse in this way, it should not be assumed that
systems with existing analyses are robust to this issue.
The other approach noted for alleviating the component forgery risk
is through hybrid signature selection of a scheme that provides
strong non-separability. Under this approach, the hybrid signature
cannot be separated into component algorithm signatures that will
verify correctly, thereby preventing the signature separation
required for the component forgery attack to be successful.
It should be noted that weak non-separability is insufficient for
mitigating risks of component forgeries. As noted in Section 9.3 of
[COMP-MLDSA], in cases of hybrid algorithm selection that provide
only weak non-separability, key reuse should be avoided, as mentioned
above, to mitigate risks of introducing EUF-CMA vulnerabilities for
component algorithms.
6. Discussion of Advantages and Disadvantages
The design (and hence security guarantees) of hybrid signature
schemes depend heavily on the properties needed for the application
or protocol using hybrid signatures. It seems that not all goals can
be achieved simultaneously as exemplified below.
6.1. Backwards Compatibility vs. SNS
There is an inherent mutual exclusion between backwards compatibility
and SNS. While WNS allows for a valid separation under leftover
artifacts, SNS will ensure verification failure if a receiver
attempts separation.
6.2. Backwards Compatibility vs. Hybrid Unforgeability
Similarly, there is an inherent mutual exclusion between backwards
compatibility, when acted upon, and hybrid unforgeability, as briefly
mentioned above. Since the goal of backwards compatibility is
usually to allow legacy systems without any software change to be
able to process hybrid signatures, all differences between the legacy
signature format and the hybrid signature format must be allowed to
be ignored, including skipping verification of signatures additional in addition
to the classical signature. As such, if a system does skip a
component signature, security does not rely on the security of all
component signatures. Note that this mutual exclusion occurs at the
verification stage, as a hybrid signature that is verified by a
system that can process both component schemes can provide hybrid
unforgeability even if another (legacy) system, processing the same
hybrid signature, loses that property.
6.3. Simultaneous Verification vs. Low Need for Approval
Hybrid algorithms that achieve simultaneous verification tend to fuse
(or 'entangle') the verification of component algorithms such that
verification operations from the different component schemes depend
on each other in some way. Consequently, there may be a natural
connection between achieving simultaneous verification and a higher
need for approval. As a contrasting example, NIST accommodates
concatenation of a FIPS-approved signature and another (potentially
non-FIPS approved) signature without any artifacts in FIPS 140
validation [NIST_PQC_FAQ]; however, as the component signatures are
verified separately, it is not possible to enforce 'simultaneous
verification'.
7. Security Considerations
This document discusses digital signature constructions that may be
used in security protocols. It is an Informational document and does
not directly affect any other documents. The security considerations
for any specific implementation or incorporation of a hybrid scheme
should be discussed in the relevant specification documents.
8. IANA Considerations
This document has no IANA actions.
9. References
9.1. Normative References
[RFC4949] Shirey, R., "Internet Security Glossary, Version 2",
FYI 36, RFC 4949, DOI 10.17487/RFC4949, August 2007,
<https://www.rfc-editor.org/info/rfc4949>.
[RFC9794] Driscoll, F., Parsons, M., and B. Hale, "Terminology for
Post-Quantum Traditional Hybrid Schemes", RFC 9794,
DOI 10.17487/RFC9794, June 2025,
<https://www.rfc-editor.org/info/rfc9794>.
[RFC9954] Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid Key
Exchange in TLS 1.3", RFC 9954, DOI 10.17487/RFC9954,
April May
2026, <https://www.rfc-editor.org/info/rfc9954>.
9.2. Informative References
[COMP-MLDSA]
Ounsworth, M., Gray, J., Pala, M., Klaußner, J., and S.
Fluhrer, "Composite ML-DSA Module-Lattice-Based Digital Signature
Algorithm (ML-DSA) for use in X.509 Public Key
Infrastructure", Work in Progress, Internet-Draft, draft-
ietf-lamps-pq-composite-sigs-15, 24 February
ietf-lamps-pq-composite-sigs-19, 21 April 2026,
<https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
pq-composite-sigs-15>.
pq-composite-sigs-19>.
[EUFCMA] Green, M., "EUF-CMA and SUF-CMA",
<https://blog.cryptographyengineering.com/euf-cma-and-suf-
cma/>.
[FALCON] Fouque, P., Hoffstein, J., Kirchner, P., Lyubashevsky, V.,
Pornin, T., Prest, T., Ricosset, T., Seiler, G., Whyte,
W., and Z. Zhang, "FALCON: Fast-Fourier Lattice-based
Compact Signatures over NTRU", Specification v1.2, 10
January 2020, <https://falcon-sign.info/falcon.pdf>.
[FS] Fiat, A. and A. Shamir, "How To Prove Yourself: Practical
Solutions to Identification and Signature Problems",
Advances in Cryptology -- CRYPTO' 86, Lecture Notes in
Computer Science, vol. 263, pp. 186-194,
DOI 10.1007/3-540-47721-7_12, 1986,
<https://doi.org/10.1007%2F3-540-47721-7_12>.
[GEMSS] "GeMSS: A Great Multivariate Short Signature", 15 April
2020, <https://www-polsys.lip6.fr/Links/NIST/
GeMSS_specification_round2_V2.pdf>.
[HQC_CVE] NIST, "CVE-2024-54137: liboqs has a correctness error in
HQC decapsulation", 6 December 2024,
<https://nvd.nist.gov/vuln/detail/CVE-2024-54137>.
[HYBRIDSIG]
Bindel, N., Herath, U., McKague, M., and D. Stebila,
"Transitioning to a Quantum-Resistant Public Key
Infrastructure", Cryptology ePrint Archive, Paper
2017/460, May 2017, <https://eprint.iacr.org/2017/460>.
[HYBRIDSIGDESIGN]
Bindel, N. and B. Hale, "A Note on Hybrid Signature
Schemes", Cryptology ePrint Archive, Paper 2023/423, March
2023, <https://eprint.iacr.org/2023/423>.
[KYBERSLASH]
Bernstein, D. J., Bhargavan, K., Bhasin, S.,
Chattopadhyay, A., Chia, T. K., Kannwischer, M. J.,
Kiefer, F., Ravi, P., and G. Tamvada, "KyberSlash:
Exploiting secret-dependent division timings in Kyber
implementations", Cryptology ePrint Archive, Paper
2024/1049, June 2024, <https://eprint.iacr.org/2024/1049>.
[MLDSA] NIST, "Module-Lattice-Based Digital Signature Standard",
NIST FIPS 204, DOI 10.6028/NIST.FIPS.204, August 2024,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.204.pdf>.
[NC-HYBRID-AUTH]
Becker, A., Guthrie, R., and M. J. Jenkins, "Non-Composite
Hybrid Authentication in PKIX and Applications to Internet
Protocols", Work in Progress, Internet-Draft, draft-
becker-guthrie-noncomposite-hybrid-auth-00, 22 March 2022,
<https://datatracker.ietf.org/doc/html/draft-becker-
guthrie-noncomposite-hybrid-auth-00>.
[NIST_PQC_FAQ]
NIST, "Post-Quantum Cryptography FAQs", 5 July 2022,
<https://csrc.nist.gov/Projects/post-quantum-cryptography/
<https://web.archive.org/web/20220705163944/
https://csrc.nist.gov/Projects/ post-quantum-cryptography/
faqs>.
[QRCSP] Bernstein, D. J., "Quantifying risks in cryptographic
selection processes", 24 November 2023,
<https://cr.yp.to/papers/qrcsp-20231124.pdf>.
[RAINBOW] "PQC Rainbow", <https://www.pqcrainbow.org/>.
[RSA] Rivest, R. L., Shamir, A., and L. Adleman, "A Method for
Obtaining Digital Signatures and Public-Key
Cryptosystems",
<https://people.csail.mit.edu/rivest/Rsapaper.pdf>. Communications of the ACM, vol. 21, no. 2,
pp. 120-126, DOI 10.1145/359340.359342,
<https://doi.org/10.1145/359340.359342>.
Acknowledgements
This document is based on the template of used for [RFC9954].
We would like to acknowledge the following people in alphabetical
order who have contributed to pushing this document forward, offered
useful insights and perspectives, and/or stimulated work in the area:
D.J. Bernstein, Scott Fluhrer, John Gray, Felix Günther, Serge
Mister, Mike Ounsworth, Max Pala, Douglas Stebila, Falko Strenzke,
and Brendan Zember
Authors' Addresses
Nina Bindel
SandboxAQ
Email: nina.bindel@sandboxaq.com
Britta Hale
Naval Postgraduate School
Email: britta.hale@nps.edu
Deirdre Connolly
SandboxAQ
Email: durumcrustulum@gmail.com
Florence Driscoll
UK National Cyber Security Centre
Email: flo.d@ncsc.gov.uk