This is a purely informative rendering of an RFC that includes verified errata. This rendering may not be used as a reference.
The following 'Verified' errata have been incorporated in this document:
EID 9039
Internet Engineering Task Force (IETF) A. Banerjee
Request for Comments: 9958 T. Reddy.K
Category: Informational D. Schoinianakis
ISSN: 2070-1721 Nokia
T. Hollebeek
DigiCert
M. Ounsworth
Entrust
June 2026
Post-Quantum Cryptography for Engineers
Abstract
The advent of a cryptographically relevant quantum computer (CRQC)
would render state-of-the-art, traditional public key algorithms
deployed today obsolete, as the mathematical assumptions underpinning
their security would no longer hold. To address this, protocols and
infrastructure must transition to post-quantum algorithms, which are
designed to resist both traditional and quantum attacks. This
document explains why engineers need to be aware of and understand
post-quantum cryptography (PQC), and it details the impact of CRQCs
on existing systems and the challenges involved in transitioning to
post-quantum algorithms. Unlike previous cryptographic updates, this
shift may require significant protocol redesign due to the unique
properties of post-quantum algorithms.
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/rfc9958.
Copyright Notice
Copyright (c) 2026 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
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to this document. Code Components extracted from this document must
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Trust Legal Provisions and are provided without warranty as described
in the Revised BSD License.
Table of Contents
1. Introduction
2. Terminology
3. Threat of CRQCs on Cryptography
3.1. Symmetric Cryptography
3.2. Asymmetric Cryptography
3.3. Quantum Side-Channel Attacks
4. Traditional Cryptographic Primitives That Could Be Replaced by
PQC
5. NIST PQC Algorithms
5.1. NIST Candidates Selected for Standardization
5.1.1. PQC Key Encapsulation Mechanisms (KEMs)
5.1.2. PQC Signatures
6. ISO Candidates Selected for Standardization
6.1. PQC Key Encapsulation Mechanisms (KEMs)
7. Timeline for Transition
8. PQC Categories
8.1. Lattice-Based Public Key Cryptography
8.2. Hash-Based Public Key Cryptography
8.3. Code-Based Public Key Cryptography
9. KEMs
9.1. Authenticated Key Exchange
9.2. Security Properties of KEMs
9.2.1. IND-CCA2
9.2.2. Binding
9.3. HPKE
10. PQC Signatures
10.1. Security Properties of PQC Signatures
10.1.1. EUF-CMA and SUF-CMA
10.2. Details of FN-DSA, ML-DSA, and SLH-DSA
10.3. Details of XMSS and LMS
10.3.1. LMS Key and Signature Sizes
10.4. Hash-then-Sign
11. NIST Recommendations for Security and Performance Trade-offs
12. Comparing PQC KEMs/Signatures against Traditional KEMs, Key
Exchanges, and Signatures
13. Post-Quantum and Traditional (PQ/T) Hybrid Schemes
13.1. PQ/T Hybrid Confidentiality
13.2. PQ/T Hybrid Authentication
13.3. Hybrid Cryptographic Algorithm Combinations:
Considerations and Approaches
13.3.1. Hybrid Cryptographic Combinations
13.3.2. Composite Keys in Hybrid Schemes
13.3.3. Key Reuse in Hybrid Schemes
13.3.4. Future Directions and Ongoing Research
14. Impact on Constrained Devices and Networks
15. Security Considerations
15.1. Cryptanalysis
15.2. Cryptographic Agility
15.3. Jurisdictional Fragmentation
15.4. Hybrid Key Exchange and Signatures: Bridging the Gap
Between PQ/T Cryptography
15.5. Caution: Ciphertext Commitment in KEM vs. DH
16. IANA Considerations
17. Further Reading and Resources
18. References
18.1. Normative References
18.2. Informative References
Acknowledgements
Authors' Addresses
1. Introduction
Quantum computing is no longer just a theoretical concept in
computational science and physics; it is now an active area of
research with practical implications. Considerable research efforts
and enormous corporate and government funding for the development of
practical quantum computing systems are currently being invested. At
the time this document is published, cryptographically relevant
quantum computers (CRQCs) that can break widely used asymmetric
algorithms (also known as public key algorithms) are not yet
available. However, there is ongoing research and development in the
field of quantum computing, with the goal of building more powerful
and scalable quantum computers.
One common myth is that quantum computers are faster than
conventional CPUs and GPUs in all areas. This is not the case; much
as GPUs outperform general-purpose CPUs only on specific types of
problems, quantum computers also have a niche set of problems on
which they excel. Unfortunately for cryptographers, integer
factorization and discrete logarithms, the mathematical problems
underpinning much of classical public key cryptography, happen to
fall within the niche in which quantum computers are expected to
excel. As quantum technology advances, there is the potential for
future quantum computers to have a significant impact on current
cryptographic systems. Predicting the date of emergence of a CRQC is
a challenging task, and there is ongoing uncertainty regarding when
they will become practically feasible [CRQCThreat].
Extensive research has produced several post-quantum cryptographic
algorithms that offer the potential to ensure cryptography's survival
in the quantum computing era. However, transitioning to a post-
quantum infrastructure is not a straightforward task, and there are
numerous challenges to overcome. It requires a combination of
engineering efforts, proactive assessment and evaluation of available
technologies, and a careful approach to product development and
deployment.
PQC is sometimes referred to as "quantum-proof", "quantum-safe", or
"quantum-resistant". It is the development of cryptographic
algorithms designed to secure communication and data in a world where
quantum computers are powerful enough to break traditional
cryptographic systems, such as RSA (Rivest-Shamir-Adleman) and ECC
(Elliptic Curve Cryptography). PQC algorithms are intended to be
resistant to attacks by quantum computers, which use quantum-
mechanical phenomena to solve mathematical problems that are
infeasible for classical computers.
As the threat of CRQCs draws nearer, engineers responsible for
designing, maintaining, and securing cryptographic systems must
prepare for the significant changes that the existence of CRQCs will
bring. Engineers need to understand how to implement post-quantum
algorithms in applications, how to evaluate the trade-offs between
security and performance, and how to ensure backward compatibility
with current systems where needed. This is not merely a one-for-one
replacement of algorithms; in many cases, the shift to PQC will
involve redesigning protocols and infrastructure to accommodate the
significant differences in resource utilization and key sizes between
traditional and PQC algorithms. Due to the wide-ranging nature of
these impacts, discussions of protocol changes are integrated
throughout this document rather than being confined to a single
section.
This document aims to provide general guidance to engineers working
on cryptographic libraries, network security, and infrastructure
development, where long-term security planning is crucial. The
document covers topics such as selecting appropriate PQC algorithms
and understanding the differences between PQC Key Encapsulation
Mechanisms (KEMs) and traditional Diffie-Hellman (DH) and RSA-style
key exchanges, and it provides insights into expected differences in
keys, ciphertext, signature sizes, and processing times between PQC
and traditional algorithms. Additionally, it discusses the potential
threat to symmetric cryptography and hash functions from CRQCs.
It is important to remember that asymmetric algorithms (also known as
public key algorithms) are largely used for secure communications
between organizations or endpoints that may not have previously
interacted, so a significant amount of coordination between
organizations, and within and between ecosystems, needs to be taken
into account. Such transitions are some of the most complicated in
the tech industry and will require staged migrations in which
upgraded agents need to coexist and communicate with non-upgraded
agents at a scale never before undertaken.
The National Security Agency (NSA) of the United States released an
article on future PQC algorithm requirements for US national security
systems [CNSA2-0] based on the need to protect against deployments of
CRQCs in the future. The German Federal Office for Information
Security (BSI) has also released a PQC migration and recommendations
document [BSI-PQC] that largely aligns with United States National
Institute of Standards and Technology (NIST) and NSA guidance but
differs in aspects such as specific PQC algorithm profiles.
CRQCs pose a threat to both symmetric and asymmetric cryptographic
schemes. However, the threat to asymmetric cryptography is
significantly greater due to Shor's algorithm [Shors], which can
break widely used public key schemes like RSA and ECC. Symmetric
cryptography and hash functions face a lower risk from Grover's
algorithm [Grovers], although the impact is less severe and can
typically be mitigated by doubling key and digest lengths where the
risk applies. It is crucial for the reader to understand that when
"PQC" is mentioned in the document, it means asymmetric cryptography
(or public key cryptography) and not any symmetric algorithms based
on stream ciphers, block ciphers, hash functions, Message
Authentication Codes (MACs), etc., which are less vulnerable to
quantum computers. This document does not cover topics such as when
traditional algorithms might become vulnerable (for that, see
documents such as [QC-DNS] and others).
This document does not cover unrelated technologies like quantum key
distribution (QKD) or quantum key generation, which use quantum
hardware to exploit quantum effects to protect communications and
generate keys, respectively. PQC is based on conventional math (not
on quantum mechanics) and software, and it can be run on any general-
purpose computer.
This document does not go into the deep mathematics or technical
specification of the PQC algorithms but rather provides an overview
to engineers on the current threat landscape and the relevant
algorithms designed to help prevent those threats. Also, the
cryptographic and algorithmic guidance given in this document should
be taken as non-authoritative if it conflicts with emerging and
evolving guidance from the IRTF's Crypto Forum Research Group (CFRG).
2. Terminology
Quantum computer: A computer that performs computations using
quantum-mechanical phenomena such as superposition and
entanglement.
Physical qubit: The basic physical unit in a quantum computer, which
is prone to noise and errors.
Logical qubit: A fault-tolerant qubit constructed from multiple
physical qubits using quantum error correction; it is the
effective unit for reliable quantum computation.
Post-Quantum Cryptography (PQC): Cryptographic algorithms designed
to be secure against quantum and classical attacks.
Cryptographically Relevant Quantum Computer (CRQC): A quantum
computer with sufficient logical qubits to break traditional
asymmetric cryptographic algorithms (e.g., RSA or ECC) within a
practical timeframe.
Public Key Cryptography (also called Asymmetric Cryptography): A
class of cryptographic algorithms in which separate keys are used
for encryption and decryption or for signing and verification.
Throughout this document, the terms Public Key Cryptography and
Asymmetric Cryptography are used interchangeably.
There is ongoing discussion about whether to use the term "post-
quantum", "quantum ready", "quantum resistant", or "quantum secure"
to describe algorithms that resist CRQCs, and a consensus has not yet
been reached. NIST has coined the term "post-quantum" to refer to
the algorithms that participated in its competition-like selection
process; in this context, the term can be interpreted to mean "the
set of algorithms that are designed to still be relevant after
quantum computers exist" and not a statement about their security.
"Quantum resistant" or "quantum secure" is obviously the goal of
these algorithms; however, some people have raised concerns that
labeling a class of algorithms as "quantum resistant" or "quantum
secure" could lead to confusion if one or more of those algorithms
are later found to be insecure or to not resist quantum computers as
much as theory predicted. "Quantum ready" is often used to refer to
a solution -- device, appliance, or software stack -- that has
reached maturity with regard to integration of these new
cryptographic algorithms. That said, the authors recognize that
there is great variability in how these terms are used. This
document uses these terms interchangeably to refer to such
algorithms.
In this document, the terms "current", "state-of-the-art", and
"ongoing" refer to work, research, investigations, deployments, or
developments that are applicable at the time of publication.
3. Threat of CRQCs on Cryptography
When considering the security risks associated with the ability of a
quantum computer to attack traditional cryptography, it is important
to distinguish between the impact on symmetric algorithms and public
key ones. Dr. Peter Shor and Dr. Lov Grover developed two algorithms
that changed the way the world thinks of security under the presence
of a CRQC.
Quantum computers are, by their nature, hybrids of classical and
quantum computational units. For example, Shor's algorithm consists
of a combination of quantum and classical computational steps. Thus,
the term "quantum adversary" should be thought of as "quantum-
enhanced adversary", meaning they have access to both classical and
quantum computational techniques.
Although large-scale quantum computers do not yet exist to experiment
on, the theoretical properties of quantum computation are very well
understood. This allows engineers and researchers to reason about
the upper limits of quantum-enhanced computation and to design
cryptographic algorithms that are resistant to any conceivable form
of quantum cryptanalysis.
3.1. Symmetric Cryptography
For unstructured data such as symmetric encrypted data or
cryptographic hashes, although CRQCs can search for specific
solutions across all possible input combinations (e.g., Grover's
algorithm), no quantum algorithm is known to break the underlying
security properties of these classes of algorithms. Symmetric-key
cryptography, which includes keyed primitives such as block ciphers
(e.g., AES) and message authentication mechanisms (e.g., HMAC-
SHA256), relies on secret keys shared between the sender and receiver
and remains secure even in a post-quantum world. Symmetric
cryptography also includes hash functions (e.g., SHA-256) that are
used for secure message digesting without any shared key material.
Hashed Message Authentication Code (HMAC) is a specific construction
that utilizes a cryptographic hash function and a secret key shared
between the sender and receiver to produce a message authentication
code.
Grover's algorithm is a quantum search algorithm that provides a
theoretical quadratic speedup for searching an unstructured database,
compared to traditional search algorithms. This has led to the
common misconception that symmetric key lengths need to be doubled
for quantum security. When you consider the mapping of hash values
to their corresponding hash inputs (also known as pre-image) or of
ciphertext blocks to the corresponding plaintext blocks as an
unstructured database, then Grover's algorithm theoretically requires
doubling the key sizes of the symmetric algorithms that are currently
deployed at the time of publication to counter the quadratic speedup
and maintain the current security level. This is because Grover's
algorithm reduces the amount of operations to break 128-bit symmetric
cryptography to 2^64 quantum operations, which might sound
computationally feasible. However, quantum operations are
fundamentally different from classical ones, as 2^64 classical
operations can be efficiently parallelized but 2^64 quantum
operations must be performed serially, making them infeasible on
practical quantum computers.
Grover's algorithm is highly non-parallelizable and even if one
deploys 2^c computational units in parallel to brute-force a key
using Grover's algorithm, it will complete in time proportional to
2^((128-c)/2), or, put simply, using 256 quantum computers will only
reduce runtime by a factor of 16, 1024 quantum computers will only
reduce runtime by a factor of 32, and so forth (see [NIST] and
[Cloudflare]). Due to this inherent limitation, the general expert
consensus is that AES-128 remains secure in practice and key sizes do
not necessarily need to be doubled.
It would be natural to ask whether future research will develop a
superior algorithm that could outperform Grover's algorithm in the
general case. However, Christof Zalka has shown that Grover's
algorithm achieves the best possible complexity for this type of
search, meaning no significantly faster quantum approach is expected
[Grover-Search].
Finally, in their evaluation criteria for PQC, NIST is assessing the
security levels of proposed post-quantum algorithms by comparing them
against the equivalent traditional and quantum security of AES-128,
AES-192, and AES-256. This indicates that NIST is confident in the
stable security properties of AES, even in the presence of both
traditional and quantum attacks. As a result, 128-bit algorithms can
be considered quantum-safe for the foreseeable future. However, for
compliance purposes, some organizations, such as the French National
Agency for the Security of Information Systems (ANSSI) [ANSSI] and
the National Security Agency (NSA) (CNSA 2.0) [CNSA2-0], recommend
the use of AES-256.
3.2. Asymmetric Cryptography
"Shor's algorithm" efficiently solves the integer factorization
problem (and the related discrete logarithm problem), which underpin
the foundations of the vast majority of public key cryptography that
the world uses today. This implies that, if a CRQC is developed,
today's public key algorithms (e.g., RSA, Diffie-Hellman, and ECC, as
well as less commonly used variants such as ElGamal [RFC6090] and
Schnorr signatures [RFC8235]) and protocols would need to be replaced
by algorithms and protocols that can offer cryptanalytic resistance
against CRQCs. Note that Shor's algorithm cannot run solely on a
classical computer; it requires a CRQC.
For example, studies show that, if a CRQC existed, it could break
RSA-2048 in hours or even seconds depending on assumptions about
error correction [RSAShor] [RSA8HRS] [RSA10SC]. While such machines
are purely theoretical at the time of writing, this illustrates the
eventual vulnerability of RSA to CRQCs.
For structured data such as public keys and signatures, CRQCs can
fully solve the underlying hard problems used in traditional
cryptography (see Shor's algorithm). Because an increase in the size
of the key pair would not provide a secure solution (short of RSA
keys that are many gigabytes in size [PQRSA]), a complete replacement
of the algorithm is needed. Therefore, post-quantum public key
cryptography must rely on problems that are different from the ones
used in traditional public key cryptography (i.e., the integer
factorization problem, the finite-field discrete logarithm problem,
and the elliptic-curve discrete logarithm problem).
3.3. Quantum Side-Channel Attacks
Cryptographic side-channel attacks exploit physical implementations
(such as timing, power consumption, or electromagnetic leakage) to
recover secret keys.
The field of cryptographic side-channel attacks potentially stands to
gain a boost in attacker power once cryptanalytic techniques can be
enhanced with quantum computation techniques [QuantSide]. While a
full discussion of quantum side-channel techniques is beyond the
scope of this document, implementers of cryptographic hardware should
be aware that current best practices for side-channel resistance may
not be sufficient against quantum adversaries.
4. Traditional Cryptographic Primitives That Could Be Replaced by PQC
Any asymmetric cryptographic algorithm based on integer
factorization, finite field discrete logarithms, or elliptic-curve
discrete logarithms will be vulnerable to attacks using Shor's
algorithm on a CRQC. This document focuses on the principal
functions of asymmetric cryptography:
Key agreement and key transport: Key agreement schemes, typically
referred to as Diffie-Hellman (DH) or Elliptic Curve Diffie-
Hellman (ECDH), as well as key transport, typically using RSA
encryption, are used to establish a shared cryptographic key for
secure communication. They are one of the mechanisms that can be
replaced by PQC, as they are based on existing public key
cryptography and are therefore vulnerable to Shor's algorithm. A
CRQC can employ Shor's algorithm to efficiently find the prime
factors of a large public key (in the case of RSA), which, in
turn, can be exploited to derive the private key. In the case of
DH, a CRQC has the potential to calculate the discrete logarithm
of the (short- or long-term) DH public key. This, in turn, would
reveal the secret required to derive the symmetric encryption key.
Digital signatures: Digital signature schemes are used to
authenticate the identity of a sender, detect unauthorized
modifications to data, and underpin trust in a system. Similar to
key agreement, signatures also depend on a public-private key pair
based on the same mathematics as for key agreement and key
transport. Because of this, a break in existing public key
cryptography will also affect traditional digital signatures,
hence the importance of developing post-quantum digital
signatures.
Boneh-Boyen-Shacham (BBS) signatures: BBS signatures are a privacy-
preserving signature scheme that offers zero-knowledge proof-like
properties by allowing selective disclosure of specific signed
attributes without revealing the entire set of signed data. The
security of BBS signatures relies on the hardness of the discrete
logarithm problem, making them vulnerable to Shor's algorithm. A
CRQC can break the data authenticity security property of BBS but
not the data confidentiality (Section 6.9 of [BBS-SIG-SCHEME]).
Content encryption: Content encryption typically refers to the
encryption of the data using symmetric key algorithms, such as
AES, to ensure confidentiality. The threat to symmetric
cryptography is discussed in Section 3.1.
5. NIST PQC Algorithms
At the time of writing, NIST has standardized three PQC algorithms,
with more expected to be standardized in the future (see
[NISTFINAL]). These algorithms are not necessarily drop-in
replacements for traditional asymmetric cryptographic algorithms.
For instance, RSA [RSA] and ECC [RFC6090] can be used as both a KEM
and a signature scheme, whereas there is currently no post-quantum
algorithm that can perform both functions. When upgrading protocols,
it is important to replace the existing use of traditional algorithms
with either a PQC KEM or a PQC signature method, depending on how the
traditional algorithm was previously being used. Additionally, KEMs,
as described in Section 9, present a different API than either key
agreement or key transport primitives. As a result, they may require
protocol-level or application-level changes in order to be
incorporated.
5.1. NIST Candidates Selected for Standardization
5.1.1. PQC Key Encapsulation Mechanisms (KEMs)
ML-KEM: Module-Lattice-Based Key-Encapsulation Mechanism. See FIPS
203 [ML-KEM].
HQC: Hamming Quasi-Cyclic. See [HQC]. The coding algorithm based
on the hardness of the syndrome decoding problem for quasi-cyclic
concatenated Reed-Muller and Reed-Solomon (RMRS) codes in the
Hamming metric. Reed-Muller (RM) codes are a class of block
error-correcting codes commonly used in wireless and deep-space
communications, while Reed-Solomon (RS) codes are widely used to
detect and correct multiple-bit errors. HQC has been selected as
part of the NIST post-quantum cryptography project but has not yet
been standardized.
5.1.2. PQC Signatures
ML-DSA: Module-Lattice-Based Digital Signature Algorithm. See FIPS
204 [ML-DSA].
SLH-DSA: Stateless Hash-Based Digital Signature Algorithm. See FIPS
205 [SLH-DSA].
FN-DSA: Fast-Fourier Transform over NTRU-Lattice-Based Digital
Signature Algorithm. See [FN-DSA]; note that NIST has named this
algorithm "FN-DSA" and assigned "FIPS 206" for its specification,
but at the time of this document's publication, it has not yet
been released.
For more information about these, see Sections 8.1, 8.2, and 10.2.
6. ISO Candidates Selected for Standardization
At the time of writing, ISO has selected three PQC KEM algorithms as
candidates for standardization; these are mentioned in the following
subsection.
6.1. PQC Key Encapsulation Mechanisms (KEMs)
FrodoKEM: KEM based on the hardness of learning with errors in
algebraically unstructured lattices. See [FrodoKEM].
ClassicMcEliece: KEM based on the hardness of syndrome decoding of
Goppa codes. Goppa codes are a class of error-correcting codes
that can correct a certain number of errors in a transmitted
message. The decoding problem involves recovering the original
message from the received noisy codeword. See [ClassicMcEliece].
NTRU: KEM based on the "N-th degree Truncated polynomial Ring Units"
(NTRU) lattices. Variants include Streamlined NTRU Prime
(sntrup761), which is leveraged for use in SSH [RFC9941]. See
[NTRU].
7. Timeline for Transition
The timeline and driving motivation for transition differ slightly
between data confidentiality (e.g., encryption) and data
authentication (e.g., signature) use cases.
For data confidentiality, one is concerned with the so-called
"harvest now, decrypt later" (HNDL) attack where a malicious actor
with adequate resources can launch an attack to store sensitive
encrypted data today that they hope to decrypt once a CRQC is
available. This implies that, every day, sensitive encrypted data is
susceptible to the attack by not implementing quantum-safe
strategies, as it corresponds to data possibly being deciphered in
the future.
For authentication, it is often the case that signatures have a very
short lifetime between signing and verifying (such as during a TLS
handshake), but some authentication use cases do require long
lifetimes, such as signing firmware or software that will be active
for decades, signing legal documents, or signing certificates that
will be embedded into hardware devices such as smart cards. Even for
short-lived signature use cases, the infrastructure often relies on
long-lived root keys, which can be difficult to update or replace on
in-field devices.
+------------------------+----------------------------+
| | |
| y | x |
+------------------------+----------+-----------------+
| | <--------------->
| z | Security gap
+-----------------------------------+
Figure 1: Mosca Model
These challenges are illustrated nicely by the so-called Mosca model
discussed in [Threat-Report]. In Figure 1, "x" denotes the time that
systems and data need to remain secure, "y" the number of years to
fully migrate to a PQC infrastructure, and "z" the time until a CRQC
that can break current cryptography is available. The model assumes
either that encrypted data can be intercepted and stored before the
migration is completed in "y" years, or that signatures will still be
relied upon for "x" years after their creation. This data remains
vulnerable for the complete "x" years of their lifetime; thus, the
sum "x+y" gives us an estimate of the full timeframe that data
remains insecure. The model essentially asks how one is preparing IT
systems during those "y" years (in other words, how one can minimize
those "y" years) to minimize the transition phase to a PQC
infrastructure and hence minimize the risks of data being exposed in
the future.
Finally, other factors that could accelerate the introduction of a
CRQC should not be underestimated, for example, faster-than-expected
advances in quantum computing and more efficient versions of Shor's
algorithm requiring fewer qubits. Innovation often comes in waves,
so it is to the industry's benefit to remain vigilant and prepare as
early as possible. Also, bear in mind that while the industry tracks
advances from public research institutions such as universities and
companies that publish their results, there is also a great deal of
large-budget quantum research being conducted privately by various
national interests. Therefore, the true state of quantum computer
advancement is likely several years ahead of the publicly available
research at the date this document is published.
Organizations should also carefully and honestly consider what their
migration timeline "y" actually is. If you only think of the time
between receiving a patch from your technology vendor and rolling
that patch out, then "y" might seem as short as a few weeks.
However, this represents the minority of migration cases; more often,
a PQC migration will involve at least some amount of hardware
replacement. For example, performance-sensitive applications will
need CPUs with PQC hardware acceleration. Security-sensitive
applications will need PQC TPMs, Trusted Execution Environments
(TEEs), secure enclaves, and other cryptographic co-processors.
Smart card applications will require replacement of the cards and
readers. The readers can come in many form factors: tap-for-entry
door and turnstile readers, PIN pad machines, laptops with built-in
smart card readers, and many others.
Included in "y" is not only the deployment time but also the
preparation time: integration, testing, auditing, and recertification
of cryptographic environments. Also consider upstream effects that
contribute to "y", including lead times for vendors to produce PQC-
ready products, which may itself include auditing and certification
delays, time for regulating bodies to adopt PQC policies, time for
auditors to become familiar with the new requirements, etc. If you
measure the full migration time "y" from when your vendors begin
implementing PQC functionality to when you switch off your last non-
PQC-capable device, then "y" can be quite long, likely measured in
years for even most moderately sized organizations. This long tail
should not discourage early action.
Organizations responsible for protecting long-lived sensitive data or
operating critical infrastructure will need to begin transitioning
immediately, particularly in scenarios where data is vulnerable to
HNDL attacks. Post-quantum and traditional (PQ/T) Section 13 or PQ
key exchange is relatively self-contained, typically requiring
changes only to the cryptographic library (e.g., OpenSSL). In
contrast, migrating to post-quantum or PQ/T digital signatures
involves broader ecosystem changes, including updates to
certificates, certification authorities (CAs), Certificate Management
Protocols, HSMs, and trust anchors. Starting early with hybrid key
exchange deployments allows organizations to gain operational
experience, while prototyping and planning for PQ/T or PQ digital
signature integration helps identify ecosystem-wide impacts early.
This phased approach reduces long-term migration risks and ensures
readiness for more complex updates.
8. PQC Categories
The post-quantum cryptographic schemes standardized by NIST can be
categorized into three main groups: lattice-based, hash-based, and
code-based. Other approaches, such as isogeny-based, multivariate-
based, and MPC-in-the-Head-based cryptography, are also being
explored in research and standardization efforts. In addition, NIST
issued a call for additional digital signature proposals to expand
the set of post-quantum signatures under evaluation [AddSig].
8.1. Lattice-Based Public Key Cryptography
Lattice-based public key cryptography leverages the simple
construction of lattices (i.e., a regular collection of points in a
Euclidean space that are evenly spaced) to create "trapdoor"
problems. These problems are efficient to compute if you possess the
secret information but challenging to compute otherwise. Examples of
such problems include the shortest vector, closest vector, short
integer solution, learning with errors, module learning with errors,
and learning with rounding problems. All of these problems feature
strong proofs for worst-to-average case reduction, effectively
relating the hardness of the average case to the worst case.
Lattice-based public keys and signatures are larger than those of
classical schemes such as RSA or ECC, but typically by less than an
order of magnitude for public keys (about 6-10x) and by roughly one
to two orders of magnitude for signatures (about 10-100x) rather than
by several orders of magnitude, making them the best available
candidates for general-purpose use, such as replacing the use of RSA
in PKIX certificates.
Examples of this class of algorithms include ML-KEM, FN-DSA, ML-DSA,
and FrodoKEM.
It is noteworthy that lattice-based encryption schemes require a
rounding step during decryption, which has a non-zero probability of
"rounding the wrong way" and leading to a decryption failure, meaning
that valid encryptions are decrypted incorrectly. However, the
parameters of NIST PQC candidates are carefully chosen so that the
probability of such a failure is cryptographically negligible, far
lower than the probability of random transmission errors and
implementation bugs. In practical terms, these rare decryption
failures can be treated the same way as any fatal transport error:
Both sides simply perform a fresh KEM operation, generating a new
ciphertext and shared secret.
In cryptanalysis, an oracle refers to a system that an attacker can
query to learn whether decryption succeeded or failed. If such an
oracle exists, an attacker could significantly reduce the security of
lattice-based schemes that have a relatively high failure rate.
However, for most of the NIST PQC proposals, the number of required
oracle queries to force a decryption failure is above practical
limits, as shown in [LattFail1]. More recent works have improved
upon the results in [LattFail1], showing that the cost of searching
for additional failing ciphertexts after one or more have already
been found can be sped up dramatically [LattFail2]. Nevertheless, at
the time this document is published, the PQC candidates by NIST are
considered secure under these attacks, and constant monitoring as
cryptanalysis research is ongoing.
8.2. Hash-Based Public Key Cryptography
Hash-based Public Key Cryptography (Hash-based PKC) has been around
since the 1970s, when it was developed by Lamport and Merkle. It is
used to create digital signature algorithms, and its security is
based on the security of the underlying cryptographic hash function.
Many variants of hash-based signatures (HBSs) have been developed
since the 1970s, including the recent XMSS [RFC8391], HSS/LMS
[RFC8554], or BPQS [BPQS] schemes. Unlike many other digital
signature techniques, most hash-based signature schemes are stateful,
which means that signing necessitates the update and careful tracking
of the state of the secret key. Producing multiple signatures using
the same secret key state results in loss of security and may
ultimately enable signature forgery attacks against that key.
Stateful hash-based signatures with long service lifetimes require
additional operational complexity compared to other signature types.
For example, consider a 20-year root key; there is an expectation
that 20 years is longer than the expected lifetime of the hardware
that key is stored on, so the key will need to be migrated to new
hardware at some point. Disaster-recovery scenarios where the
primary node fails without warning can be similarly tricky. This
requires careful operational and compliance consideration to ensure
that no private key state can be reused across the migration or
disaster recovery event. One approach for avoiding these issues is
to only use stateful HBSs for short-term use cases that do not
require horizontal scaling, for example, signing a batch of firmware
images and then retiring the signing key.
The SLH-DSA algorithm, which was standardized by NIST, leverages the
HORST (Hash to Obtain Random Subset with Trees) technique and remains
the only standardized hash based signature scheme that is stateless,
thus avoiding the complexities associated with state management.
SLH-DSA is an advancement on SPHINCS that reduces the signature sizes
in SPHINCS and makes it more compact.
8.3. Code-Based Public Key Cryptography
This area of cryptography started in the 1970s and 1980s and was
based on the seminal work of McEliece and Niederreiter, which focuses
on the study of cryptosystems based on error-correcting codes. Some
popular error-correcting codes include Goppa codes (used in McEliece
cryptosystems), encoding and decoding syndrome codes used in HQC, or
quasi-cyclic moderate density parity check (QC-MDPC) codes.
Examples include all the unbroken NIST Round 4 finalists: Classic
McEliece, HQC (selected by NIST for standardization), and Bit
Flipping Key Encapsulation (BIKE) [BIKE].
9. KEMs
A Key Encapsulation Mechanism (KEM) is a cryptographic technique used
for securely exchanging symmetric key material between two parties
over an insecure channel. It is commonly used in hybrid encryption
schemes where a combination of asymmetric (public key) and symmetric
encryption is employed. The encapsulation operation of a KEM results
in a fixed-length symmetric key that can be used with a symmetric
algorithm, typically a block cipher, in one of two different ways:
* To derive a data encryption key (DEK) to encrypt the data
* To derive a key encryption key (KEK) used to wrap a DEK
These techniques are often referred to as the Hybrid Public Key
Encryption (HPKE) [RFC9180] mechanism.
The term "encapsulation" is chosen intentionally to indicate that KEM
algorithms behave differently at the API level from the key agreement
or key encipherment and key transport mechanisms that are in use
today. Key agreement schemes imply that both parties contribute a
public-private key pair to the exchange, while key encipherment and
key transport schemes imply that the symmetric key material is chosen
by one party and "encrypted" or "wrapped" for the other party. KEMs,
on the other hand, behave according to the following API primitives
[PQCAPI]:
* def kemKeyGen() -> (pk, sk)
* def kemEncaps(pk) -> (ss, ct)
* def kemDecaps(ct, sk) -> ss
where pk is the public key, sk is the secret key, ct is the
ciphertext representing an encapsulated key, and ss is the shared
secret. The following figure illustrates a sample flow of a KEM-
based key exchange:
+---------+ +---------+
| Client | | Server |
+---------+ +---------+
+----------------------+ | |
| pk, sk = kemKeyGen() |-| |
+----------------------+ | |
| |
| pk |
|---------->|
| | +-----------------------+
| |-| ss, ct = kemEncaps(pk)|
| | +-----------------------+
| |
| ct |
|<----------|
+------------------------+ | |
| ss = kemDecaps(ct, sk) |-| |
+------------------------+ | |
| |
Figure 2: KEM-Based Key Exchange
9.1. Authenticated Key Exchange
Authenticated Key Exchange (AKE) with KEMs where both parties
contribute a KEM public key to the overall session key is interactive
as described in Section 9.4 of [RFC9528]. However, a single-sided
KEM, such as when one peer has a KEM key in a certificate and the
other peer wants to encrypt for it (as in S/MIME or OpenPGP email),
can be achieved using non-interactive HPKE [RFC9180]. The following
figure illustrates the DH Key exchange:
+---------+ +---------+
| Client | | Server |
+---------+ +---------+
+-----------------------+ | |
| Long-term client key: | | |
| sk1, pk1 |-| |
+-----------------------+ | |
| |
| pk1 |
|---------->|
| | +------------------------+
| |-| Long-term server key: |
| | | sk2, pk2 |
| | | ss = KeyEx(pk1, sk2) |
| | +------------------------+
| |
| pk2|
|<----------|
+-------------------------+ | |
| ss = KeyEx(pk2, sk1) | | |
| encryptContent(ss) |-| |
+-------------------------+ | |
| encrypted |
| content |
|---------->|
| | +------------------------+
| | | decryptContent(ss) |
| | +------------------------+
Figure 3: DH-Based AKE
In the sample flow above, it is important to note that the shared
secret ss is derived using key material from both the client and the
server, which classifies it as an AKE. There is another property of
a key exchange, called Non-Interactive Key Exchange (NIKE), that
refers to whether the sender can compute the shared secret ss and
encrypt content without requiring active interaction (an exchange of
network messages) with the recipient. Figure 3 shows a DH key
exchange, which is an AKE since both parties are using long-term keys
that can have established trust (for example, via certificates), but
it is not a NIKE since the client needs to wait for the network
interaction to receive the receiver's public key pk2 before it can
compute the shared secret ss and begin content encryption. However,
a DH key exchange can be an AKE and a NIKE at the same time if the
receiver's public key is known to the sender in advance (see
Figure 4), and many Internet protocols rely on this property of DH-
based key exchanges.
+---------+ +---------+
| Client | | Server |
+---------+ +---------+
+-----------------------+ | |
| Long-term client key: | | |
| sk1, pk1 |-| |
| Long-term server key: | | |
| pk2 | | |
| ss = KeyEx(pk2, sk1) | | |
| encryptContent(ss) |-| |
+-----------------------+ | |
| |
| pk1, |
| encrypted |
| content |
|---------->|
| | +------------------------+
| |-| Long-term server key: |
| | | sk2, pk2 |
| | | ss = KeyEx(pk1, sk2) |
| | | decryptContent(ss) |
| | +------------------------+
Figure 4: Simultaneous DH-Based AKE and NIKE
The complication with KEMs is that a KEM Encaps() is non-
deterministic; it involves randomness chosen by the sender of that
message. Therefore, in order to perform an AKE, the client must wait
for the server to generate the needed randomness and perform Encaps()
against the client key, which necessarily requires a network round-
trip. Therefore, a KEM-based protocol can either be an AKE or a
NIKE, but it cannot be both at the same time. Consequently, certain
Internet protocols will necessitate a redesign to accommodate this
distinction, either by introducing extra network round trips or by
making trade-offs in security properties.
+---------+ +---------+
| Client | | Server |
+---------+ +---------+
+------------------------+ | |
| pk1, sk1 = kemKeyGen() |-| |
+------------------------+ | |
| |
|pk1 |
|---------->|
| | +--------------------------+
| |-| ss1, ct1 = kemEncaps(pk1)|
| | | pk2, sk2 = kemKeyGen() |
| | +--------------------------+
| |
| ct1,pk2|
|<----------|
+--------------------------+ | |
| ss1 = kemDecaps(ct1, sk1)| | |
| ss2, ct2 = kemEncaps(pk2)|-| |
| ss = Combiner(ss1, ss2) | | |
+--------------------------+ | |
| |
|ct2 |
|---------->|
| | +--------------------------+
| |-| ss2 = kemDecaps(ct2, sk2)|
| | | ss = Combiner(ss1, ss2) |
| | +--------------------------+
Figure 5: KEM-Based AKE
In the figure above, Combiner(ss1, ss2), often referred to as a KEM
combiner, is a cryptographic construction that takes in two shared
secrets and returns a single combined shared secret. The simplest
combiner is concatenation ss1 || ss2, but combiners can vary in
complexity depending on the cryptographic properties required. For
example, if the combination should preserve IND-CCA2 (see
Section 9.2.1) of either input, even if the other is chosen
maliciously, then a more complex construct is required. Another
consideration for combiner design is the so-called "binding
properties" introduced in [KEEPINGUP], which may require the
ciphertexts and recipient public keys to be included in the combiner.
KEM combiner security analysis becomes more complicated in hybrid
settings where the two KEMs represent different algorithms, for
example, where one is ML-KEM and the other is ECDH. For a more
thorough discussion of KEM combiners, see [KEEPINGUP],
[KEM-COMBINER], and [PQ-KEM].
9.2. Security Properties of KEMs
The security properties described in this section (IND-CCA2 and
binding) are not an exhaustive list of all possible KEM security
considerations. They were selected because they are fundamental to
evaluating KEM suitability in protocol design and are commonly
discussed in current PQC work.
9.2.1. IND-CCA2
IND-CCA2 (INDistinguishability under adaptive Chosen-Ciphertext
Attack) is an advanced security notion for encryption schemes. It
ensures the confidentiality of the plaintext and resistance against
chosen-ciphertext attacks. An appropriate definition of IND-CCA2
security for KEMs can be found in [CS01] and [BHK09]. ML-KEM
[ML-KEM] and Classic McEliece provide IND-CCA2 security.
Understanding IND-CCA2 security is essential for individuals involved
in designing or implementing cryptographic systems and protocols in
order to evaluate the strength of the algorithm, assess its
suitability for specific use cases, and ensure that data
confidentiality and security requirements are met. Understanding
IND-CCA2 security is generally not necessary for developers migrating
to using an IETF-vetted KEM within a given protocol or flow. IND-
CCA2 is a widely accepted security notion for public key encryption
mechanisms, making it suitable for a broad range of applications.
When an IETF specification defines a new KEM, its security
considerations should fully describe the relevant cryptographic
properties, including IND-CCA2.
9.2.2. Binding
KEMs also have an orthogonal set of properties to consider when
designing protocols around them: binding [KEEPINGUP]. This can be
"ciphertext binding", "public key binding", "context binding", or any
other property that is important to not be substituted between KEM
invocations. In general, a KEM is considered to bind a certain value
if substitution of that value by an attacker will necessarily result
in a different shared secret being derived. As an example, if an
attacker can construct two different ciphertexts that will
decapsulate to the same shared secret, can construct a ciphertext
that will decapsulate to the same shared secret under two different
public keys, or can substitute whole KEM exchanges from one session
into another, then the construction is not ciphertext binding, public
key binding, or context binding, respectively. Similarly, protocol
designers may wish to bind protocol state information such as a
transaction ID or nonce so that attempts to replay ciphertexts from
one session inside a different session will be blocked at the
cryptographic level because the server derives a different shared
secret and is thus is unable to decrypt the content.
The solution to binding is generally achieved at the protocol design
level: It is recommended to avoid using the KEM output shared secret
directly without integrating it into an appropriate protocol. While
KEM algorithms provide key secrecy, they do not inherently ensure
source authenticity, protect against replay attacks, or guarantee
freshness. These security properties should be addressed by
incorporating the KEM into a protocol that has been analyzed for such
protections. Even though modern KEMs such as ML-KEM produce full-
entropy shared secrets, it is still advisable for binding reasons to
pass the shared secret through a key derivation function (KDF) and
also include all values that you wish to bind; finally, you will have
a shared secret that is safe to use at the protocol level.
9.3. HPKE
Modern cryptography has long used the notion of "hybrid encryption"
where an asymmetric algorithm is used to establish a key and then a
symmetric algorithm is used for bulk content encryption. The
previous sections explained important security properties of KEMs,
such as IND-CCA2 security and binding, and emphasized that these
properties must be supported by proper protocol design. One widely
deployed scheme that achieves this is Hybrid Public Key Encryption
(HPKE) [RFC9180].
HPKE [RFC9180] works with a combination of KEMs, KDFs, and
Authenticated Encryption with Associated Data (AEAD) schemes. HPKE
includes three authenticated variants, including one that
authenticates possession of a pre-shared key and two optional ones
that authenticate possession of a KEM private key. HPKE can be
extended to support hybrid post-quantum KEM [PQ-HPKE]. ML-KEM does
not support the static-ephemeral key exchange that allows HPKE that
is based on DH-based KEMs and its optional authenticated modes as
discussed in Section 1.5 of [X-WING].
10. PQC Signatures
Any digital signature scheme that provides a construction defining
security under a post-quantum setting falls under this category of
PQC signatures.
10.1. Security Properties of PQC Signatures
10.1.1. EUF-CMA and SUF-CMA
EUF-CMA (existential unforgeability under chosen message attack)
[GMR88] is a security notion for digital signature schemes. It
guarantees that an adversary, even with access to a signing oracle,
cannot forge a valid signature for an arbitrary message. EUF-CMA
provides strong protection against forgery attacks, ensuring the
integrity and authenticity of digital signatures by preventing
unauthorized modifications or fraudulent signatures. ML-DSA, FN-DSA,
and SLH-DSA provide EUF-CMA security.
SUF-CMA (strong unforgeability under chosen message attack) builds
upon EUF-CMA by requiring that an adversary cannot produce a
different valid signature for a message that has already been signed
by the signing oracle. Like EUF-CMA, SUF-CMA provides robust
assurances for digital signature schemes, further enhancing their
security posture. ML-DSA, FN-DSA, and SLH-DSA also achieve SUF-CMA
security.
Understanding EUF-CMA and SUF-CMA security is essential for designing
or implementing cryptographic systems in order to ensure the
security, reliability, and robustness of digital signature schemes.
These notions allow for informed decision making, vulnerability
analysis, compliance with standards, and designing systems that
provide strong protection against forgery attacks. For developers
migrating to an IETF-vetted PQC signature scheme within a given
protocol or flow, a deep understanding of EUF-CMA and SUF-CMA
security may not be necessary, as the schemes vetted by IETF adhere
to these stringent security standards.
EUF-CMA and SUF-CMA are considered strong security benchmarks for
public key signature algorithms, making them suitable for most
applications. Authors of IETF specifications should include all
security concerns in the "Security Considerations" section of the
relevant RFC and should not assume that implementers are experts in
cryptographic theory.
10.2. Details of FN-DSA, ML-DSA, and SLH-DSA
ML-DSA [ML-DSA] is a digital signature algorithm based on the
hardness of lattice problems over module lattices (i.e., the Module
Learning with Errors (MLWE) problem). The design of the algorithm is
based on the "Fiat-Shamir with Aborts" [Lyu09] framework introduced
by Lyubashevsky that leverages rejection sampling to render lattice-
based Fiat-Shamir (FS) schemes compact and secure. ML-DSA uses
uniformly distributed random number sampling over small integers to
compute coefficients in error vectors, which makes the scheme easier
to implement compared to FN-DSA [FN-DSA], which uses Gaussian-
distributed numbers, necessitating the need to use floating-point
arithmetic during signature generation.
ML-DSA offers both deterministic and randomized signing and is
instantiated with three parameter sets providing different security
levels. Security properties of ML-DSA are discussed in Section 9 of
[RFC9881].
FN-DSA [FN-DSA] is based on the GPV hash-and-sign lattice-based
signature framework introduced by Gentry, Peikert, and
Vaikuntanathan, which is a framework that requires a certain class of
lattices and a trapdoor sampler technique.
The main design principle of FN-DSA is compactness, i.e., it was
designed in a way that achieves minimal total memory bandwidth
requirement (the sum of the signature size plus the public key size).
This is possible due to the compactness of NTRU lattices. FN-DSA
also offers very efficient signing and verification procedures. The
main potential downsides of FN-DSA refer to the non-triviality of its
algorithms and the need for floating-point arithmetic support in
order to support Gaussian-distributed random number sampling where
the other lattice schemes use the less efficient but easier to
support uniformly distributed random number sampling.
Implementers of FN-DSA need to be aware that FN-DSA signing is highly
susceptible to side-channel attacks unless constant-time 64-bit
floating-point operations are used. This requirement is extremely
platform-dependent, as noted in NIST's report [NIST].
The performance characteristics of ML-DSA and FN-DSA may differ based
on the specific implementation and hardware platform. Generally, ML-
DSA is known for its relatively fast signature generation, while FN-
DSA can provide more efficient signature verification. The choice
may depend on whether the application requires more frequent
signature generation or signature verification (see [LIBOQS]). For
further clarity on the sizes and security levels, please refer to the
tables in Sections 11 and 12.
SLH-DSA [SLH-DSA] utilizes the concept of stateless hash-based
signatures, where each signature is unique and unrelated to any
previous signature (as discussed in Section 8.2). This property
eliminates the need for maintaining state information during the
signing process. SLH-DSA was designed to sign up to 2^64 messages
under a given key pair, and it offers three security levels. The
parameters for each of the security levels were chosen to provide 128
bits of security, 192 bits of security, and 256 bits of security.
SLH-DSA offers smaller public key sizes, larger signature sizes,
slower signature generation, and slower verification when compared to
ML-DSA and FN-DSA. SLH-DSA does not introduce a new hardness
assumption beyond those inherent to the underlying hash functions.
It builds upon established foundations in cryptography, making it a
reliable and robust digital signature scheme for a post-quantum
world.
All of these algorithms (ML-DSA, FN-DSA, and SLH-DSA) include two
signature modes: pure mode, where the entire content is signed
directly, and pre-hash mode, where a digest of the content is signed.
10.3. Details of XMSS and LMS
The eXtended Merkle Signature Scheme (XMSS) [RFC8391] and
Hierarchical Signature Scheme (HSS) / Leighton-Micali Signature (LMS)
[RFC8554] are stateful hash-based signature schemes, where the secret
key state changes over time. In both schemes, reusing a secret key
state compromises cryptographic security guarantees.
XMSS and LMS can be used for signing a potentially large but fixed
number of messages, and the number of signing operations depends upon
the size of the tree. XMSS and LMS provide cryptographic digital
signatures without relying on the conjectured hardness of
mathematical problems, instead leveraging the properties of
cryptographic hash functions. Multi-tree XMSS and LMS (i.e., XMSS-MT
and HSS, respectively) use a hyper-tree-based hierarchical approach
with a Merkle tree at each level of the hierarchy. [RFC8391]
describes both single-tree and multi-tree variants of XMSS, while
[RFC8554] describes the Leighton-Micali One-Time Signature (LM-OTS)
system as well as the LMS and HSS N-time signature systems.
Comparison of XMSS and LMS is discussed in Section 10 of [RFC8554].
The number of tree layers in multi-tree XMSS and HSS provides a
trade-off between signature size on the one side and key generation
and signing speed on the other side. Increasing the number of layers
reduces key generation time exponentially and signing time linearly
at the cost of increasing the signature size linearly. HSS allows
for customization of each subtree, whereas XMSS-MT does not, electing
instead to use the same structure for each subtree.
Due to the complexities described above, XMSS and LMS are not
suitable replacements for traditional signature schemes like RSA or
ECDSA. Applications that expect a long lifetime of a signature, like
firmware update or secure boot, are typical use cases where those
schemes can be successfully applied.
10.3.1. LMS Key and Signature Sizes
The LMS scheme is characterized by four distinct parameter sets: the
underlying hash function (SHA2-256 or SHAKE-256), the length of the
digest (24 or 32 bytes), the LMS tree height parameter that controls
a maximal number of signatures that the private key can produce, and
the width of the Winternitz coefficients (see [RFC8554], Section 4.1)
that can be used to trade-off signing time for signature size.
Parameters can be mixed, providing 80 possible parameterizations of
the scheme.
The public (PK) and private (SK) key size depends on the length of
the digest (M). The signature size depends on the digest, the
Winternitz parameter (W), the LMS tree height (H), and the length of
the digest. The table below provides key and signature sizes for
parameterization with the digest size M=32 of the scheme.
+====+====+===+======+======+======+======+======+
| PK | SK | W | H=5 | H=10 | H=15 | H=20 | H=25 |
+====+====+===+======+======+======+======+======+
| 56 | 52 | 1 | 8684 | 8844 | 9004 | 9164 | 9324 |
+----+----+---+------+------+------+------+------+
| 56 | 52 | 2 | 4460 | 4620 | 4780 | 4940 | 5100 |
+----+----+---+------+------+------+------+------+
| 56 | 52 | 4 | 2348 | 2508 | 2668 | 2828 | 2988 |
+----+----+---+------+------+------+------+------+
| 56 | 52 | 8 | 1292 | 1452 | 1612 | 1772 | 1932 |
+----+----+---+------+------+------+------+------+
Table 1
10.4. Hash-then-Sign
Within the hash-then-sign paradigm, the message is hashed before
signing it. By pre-hashing, the onus of resistance to existential
forgeries becomes heavily reliant on the collision-resistance of the
hash function in use. The hash-then-sign paradigm has the ability to
improve application performance by reducing the size of signed
messages that need to be transmitted between application and
cryptographic module and making the signature size predictable and
manageable. As a corollary, hashing remains mandatory even for short
messages and assigns a further computational requirement onto the
verifier. This makes the performance of hash-then-sign schemes more
consistent, but not necessarily more efficient.
Using a hash function to produce a fixed-size digest of a message
ensures that the signature is compatible with a wide range of systems
and protocols, regardless of the specific message size or format.
Crucially for hardware security modules, hash-then-sign also
significantly reduces the amount of data that needs to be transmitted
and processed by a Hardware Security Module (HSM). Consider
scenarios such as a networked HSM located in a different data center
from the calling application or a smart card connected over a USB
interface. In these cases, streaming a message that is megabytes or
gigabytes long can result in notable network latency, on-device
signing delays, or even depletion of available on-device memory.
Note that the vast majority of Internet protocols that sign large
messages already perform some form of content hashing at the protocol
level, so this tends to be more of a concern with proprietary
cryptographic protocols and protocols from non-IETF standards bodies.
Protocols like TLS 1.3 and DNSSEC use the hash-then-sign paradigm.
In TLS 1.3 [RFC8446] CertificateVerify messages, the content that is
covered under the signature includes the transcript hash output
(Section 4.4.1 of [RFC8446]) while DNSSEC [RFC4034] uses it to
provide origin authentication and integrity assurance services for
DNS data. Similarly, the Cryptographic Message Syntax (CMS)
[RFC5652] includes a mandatory message digest step before invoking
the signature algorithm.
In the case of ML-DSA, it internally incorporates the necessary hash
operations as part of its signing algorithm. ML-DSA directly takes
the original message, applies a hash function internally, and then
uses the resulting hash value for the signature generation process.
In the case of SLH-DSA, it internally performs randomized message
compression using a keyed hash function that can process arbitrary
length messages. In the case of FN-DSA, the SHAKE-256 hash function
is used as part of the signature process to derive a digest of the
message being signed.
Therefore, ML-DSA, FN-DSA, and SLH-DSA offer enhanced security over
the traditional hash-then-sign paradigm because, by incorporating
dynamic key material into the message digest, a pre-computed hash
collision on the message to be signed no longer yields a signature
forgery. Applications requiring the performance and bandwidth
benefits of hash-then-sign may still pre-hash at the protocol level
prior to invoking ML-DSA, FN-DSA, or SLH-DSA, but protocol designers
should be aware that doing so reintroduces the weakness that hash
collisions directly yield signature forgeries. Signing the full un-
digested message is recommended where applications can tolerate it.
11. NIST Recommendations for Security and Performance Trade-offs
This information is a reprint of information provided in the NIST PQC
project [NIST] as of the time this document is published. Table 2
denotes the five security levels provided by NIST for PQC algorithms.
Neither NIST nor the IETF makes any specific recommendations about
which security level to use. In general, protocols will include
algorithm choices at multiple levels so that users can choose the
level appropriate to their policies and data classification, similar
to how organizations today choose which size of RSA key to use. The
security levels are defined as requiring computational resources
comparable to or greater than an attack on AES (128, 192, and 256)
and SHA2/SHA3 algorithms, i.e., exhaustive key recovery for AES and
optimal collision search for SHA2/SHA3.
+=============+=====================+===========================+
| PQ Security | AES/SHA(2/3) | PQC Algorithm |
| Level | hardness | |
+=============+=====================+===========================+
| 1 | AES-128 (exhaustive | ML-KEM-512, FN-DSA-512, |
| | key recovery) | SLH-DSA-SHA2/SHAKE-128f/s |
+-------------+---------------------+---------------------------+
| 2 | SHA-256/SHA3-256 | ML-DSA-44 |
| | (collision search) | |
+-------------+---------------------+---------------------------+
| 3 | AES-192 (exhaustive | ML-KEM-768, ML-DSA-65, |
| | key recovery) | SLH-DSA-SHA2/SHAKE-192f/s |
+-------------+---------------------+---------------------------+
| 4 | SHA-384/SHA3-384 | No algorithm tested at |
| | (collision search) | this level |
+-------------+---------------------+---------------------------+
| 5 | AES-256 (exhaustive | ML-KEM-1024, FN-DSA-1024, |
| | key recovery) | ML-DSA-87, SLH-DSA-SHA2/ |
| | | SHAKE-256f/s |
+-------------+---------------------+---------------------------+
Table 2
The SLH-DSA-x-yf/s "f/s" in the above table denotes whether SLH-DSA
is using SHAKE or SHA-2 as an underlying hash function "x" and
whether it is the fast (f) or small (s) version for "y" bit AES
security level. Refer to [RFC9814] for further details on SLH-DSA
algorithms.
The following table compares the signature sizes for different SLH-
DSA algorithm categories at equivalent security levels using the
"simple" version. The categories include "f" for fast signature
generation and "s" for smaller signature size and faster
verification, although with slower signature generation. Both
SHA-256 and SHAKE-256 parameterizations produce the same signature
sizes and are therefore included together in the table.
+==========+===========================+========+=======+===========+
| PQ | Algorithm | Public |Private| Signature |
| Security | | key |key | size (in |
| Level | | size |size | bytes) |
| | | (in |(in | |
| | | bytes) |bytes) | |
+==========+===========================+========+=======+===========+
| 1 | SLH-DSA-{SHA2,SHAKE}-128f | 32 |64 | 17088 |
+----------+---------------------------+--------+-------+-----------+
| 1 | SLH-DSA-{SHA2,SHAKE}-128s | 32 |64 | 7856 |
+----------+---------------------------+--------+-------+-----------+
| 3 | SLH-DSA-{SHA2,SHAKE}-192f | 48 |96 | 35664 |
+----------+---------------------------+--------+-------+-----------+
| 3 | SLH-DSA-{SHA2,SHAKE}-192s | 48 |96 | 16224 |
+----------+---------------------------+--------+-------+-----------+
| 5 | SLH-DSA-{SHA2,SHAKE}-256f | 64 |128 | 49856 |
+----------+---------------------------+--------+-------+-----------+
| 5 | SLH-DSA-{SHA2,SHAKE}-256s | 64 |128 | 29792 |
+----------+---------------------------+--------+-------+-----------+
Table 3
The following table illustrates the impact of performance on
different security levels in terms of private key sizes, public key
sizes, and ciphertext/signature sizes.
+==========+=============+============+============+================+
| PQ | Algorithm | Public key | Private | Ciphertext/ |
| Security | | size (in | key size | signature |
| Level | | bytes) | (in bytes) | size (in |
| | | | | bytes) |
+==========+=============+============+============+================+
| 1 | ML-KEM-512 | 800 | 1632 | 768 |
+----------+-------------+------------+------------+----------------+
| 1 | FN-DSA-512 | 897 | 1281 | 666 |
+----------+-------------+------------+------------+----------------+
| 2 | ML-DSA-44 | 1312 | 2560 | 2420 |
+----------+-------------+------------+------------+----------------+
| 3 | ML-KEM-768 | 1184 | 2400 | 1088 |
+----------+-------------+------------+------------+----------------+
| 3 | ML-DSA-65 | 1952 | 4032 | 3309 |
+----------+-------------+------------+------------+----------------+
| 5 | FN-DSA-1024 | 1793 | 2305 | 1280 |
+----------+-------------+------------+------------+----------------+
5 | ML-KEM-1024 | 1568 | 3168 | 1568 |
Notes:
Table 4 states that ML-KEM-1024 'Ciphertext/signature size (in bytes)' is 1588. The correct value appears to be 1568. Source: NIST FIPS 203 https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.203.pdf
+----------+-------------+------------+------------+----------------+
| 5 | ML-DSA-87 | 2592 | 4896 | 4627 |
+----------+-------------+------------+------------+----------------+
Table 4
12. Comparing PQC KEMs/Signatures against Traditional KEMs, Key
Exchanges, and Signatures
This section provides two tables for comparison of different KEMs and
signatures, respectively, in the traditional and post-quantum
scenarios. These tables focus on the secret key sizes, public key
sizes, and ciphertext/signature sizes for the PQC algorithms and
their traditional counterparts of similar security levels.
The first table compares traditional and PQC KEMs in terms of
security, public and private key sizes, and ciphertext sizes.
+=============+=====================+========+=========+============+
| PQ Security | Algorithm | Public | Private | Ciphertext |
| Level | | key | key | size (in |
| | | size | size | bytes) |
| | | (in | (in | |
| | | bytes) | bytes) | |
+=============+=====================+========+=========+============+
| Traditional | P256_HKDF_SHA-256 | 65 | 32 | 65 |
+-------------+---------------------+--------+---------+------------+
| Traditional | P521_HKDF_SHA-512 | 133 | 66 | 133 |
+-------------+---------------------+--------+---------+------------+
| Traditional | X25519_HKDF_SHA-256 | 32 | 32 | 32 |
+-------------+---------------------+--------+---------+------------+
| 1 | ML-KEM-512 | 800 | 1632 | 768 |
+-------------+---------------------+--------+---------+------------+
| 3 | ML-KEM-768 | 1184 | 2400 | 1088 |
+-------------+---------------------+--------+---------+------------+
| 5 | ML-KEM-1024 | 1568 | 3168 | 1568 |
+-------------+---------------------+--------+---------+------------+
Table 5
The next table compares traditional and PQC signature schemes in
terms of security, public, private key sizes, and signature sizes.
+=============+=============+============+============+===========+
| PQ Security | Algorithm | Public key | Private | Signature |
| Level | | size (in | key size | size (in |
| | | bytes) | (in bytes) | bytes) |
+=============+=============+============+============+===========+
| Traditional | RSA2048 | 256 | 256 | 256 |
+-------------+-------------+------------+------------+-----------+
| Traditional | ECDSA-P256 | 64 | 32 | 64 |
+-------------+-------------+------------+------------+-----------+
| 1 | FN-DSA-512 | 897 | 1281 | 666 |
+-------------+-------------+------------+------------+-----------+
| 2 | ML-DSA-44 | 1312 | 2560 | 2420 |
+-------------+-------------+------------+------------+-----------+
| 3 | ML-DSA-65 | 1952 | 4032 | 3309 |
+-------------+-------------+------------+------------+-----------+
| 5 | FN-DSA-1024 | 1793 | 2305 | 1280 |
+-------------+-------------+------------+------------+-----------+
| 5 | ML-DSA-87 | 2592 | 4896 | 4627 |
+-------------+-------------+------------+------------+-----------+
Table 6
As is clear from the above table, PQC KEMs and signature schemes
typically have significantly larger keys and ciphertexts/signatures
than their traditional counterparts. These increased key and
signatures sizes could introduce problems in protocols. As an
example, the Internet Key Exchange Protocol Version 2 (IKEv2) uses
UDP as the transport protocol for its messages. One challenge with
integrating a PQC KEM into IKEv2 is that IKE fragmentation cannot be
utilized in the initial IKE_SA_INIT exchange. To address this issue,
[RFC9242] introduces a solution by defining a new exchange called the
"Intermediate Exchange", which can be fragmented using the IKE
fragmentation mechanism. [RFC9370] then uses this Intermediate
Exchange to carry out the PQC key exchange after the initial IKEv2
exchange and before the IKE_AUTH exchange. Another example from
Section 6.3.3 of [SP-1800-38C] shows that increased key and signature
sizes cause protocol key exchange messages to span more network
packets, which results in a higher total loss probability per packet.
In lossy network conditions, this may increase the latency of the key
exchange.
13. Post-Quantum and Traditional (PQ/T) Hybrid Schemes
The migration to PQC is unique in the history of modern digital
cryptography in that neither the traditional algorithms nor the post-
quantum algorithms are fully trusted to protect data for the required
lifetimes. The traditional algorithms, such as RSA and ECDH, will
fall to quantum cryptanalysis, while the post-quantum algorithms face
uncertainty about the underlying mathematics, compliance issues,
unknown vulnerabilities, and hardware and software implementations
that have not had sufficient maturing time to rule out traditional
cryptanalytic attacks and implementation bugs.
During the transition from traditional to post-quantum algorithms,
there may be a desire or a requirement for protocols that use both
algorithm types. [RFC9794] defines the terminology for PQ/T hybrid
schemes.
13.1. PQ/T Hybrid Confidentiality
The PQ/T Hybrid Confidentiality property can be used to mitigate both
"harvest now, decrypt now" and HNDL attacks described in Section 7.
If the PQ portion were to have a flaw, the traditional (T) algorithm,
which is secure against today's attackers, prevents immediate
decryption ("harvest now, decrypt now"). If the T algorithm is
broken in the future by CRQCs, the PQ portion, assuming it remains
secure, prevents later decryption (i.e., HNDL). A hybrid
construction therefore provides confidentiality as long as at least
one component remains secure. Two types of hybrid key agreement
schemes are discussed below.
Concatenated hybrid key agreement scheme: The final shared secret
that will be used as an input of the key derivation function is
the result of the concatenation of the secrets established with
each key agreement scheme. For example, in [TLS-HYB-KEY-EXCH],
the client uses the TLS supported groups extension to advertise
support for a PQ/T hybrid scheme, and the server can select this
group if it supports the scheme. The hybrid-aware client and
server establish a hybrid secret by concatenating the two shared
secrets, which is used as the shared secret in the existing TLS
1.3 key schedule.
Cascaded hybrid key agreement scheme: The final shared secret is
computed by applying as many iterations of the key derivation
function as the number of key agreement schemes composing the
hybrid key agreement scheme. For example, [RFC9370] extends IKEv2
to allow one or more PQC algorithms in addition to the traditional
algorithm to derive the final IKE Security Association (SA) keys
using the cascade method as explained in Section 2.2.2 of
[RFC9370].
Various instantiations of these two types of hybrid key agreement
schemes have been explored. One must be careful when selecting which
hybrid scheme to use. The chosen scheme for protocols like TLS 1.3
[TLS-HYB-KEY-EXCH] has IND-CCA2 robustness. That is, IND-CCA2
security is guaranteed for the scheme as long as at least one of the
component algorithms is IND-CCA2 secure.
13.2. PQ/T Hybrid Authentication
The PQ/T hybrid authentication property provides resilience against
catastrophic breaks or unforeseen vulnerabilities in PQC algorithms,
allowing systems additional time to stabilize before migrating fully
to pure PQ deployments.
This property ensures authentication using a PQ/T hybrid scheme as
long as at least one component algorithm remains secure. For
example, a PQ/T hybrid certificate [ML-DSA-X.509] can be employed to
facilitate a PQ/T hybrid authentication protocol. However, a PQ/T
hybrid authentication protocol does not need to use a PQ/T hybrid
certificate; separate certificates could be used for individual
component algorithms [RFC9763]. When separate certificates are used,
it may be possible for attackers to take them apart or put them
together in unexpected ways, including enabling cross-protocol
attacks. The exact risks this presents are highly dependent on the
protocol and use case, so a full security analysis is needed. Best
practices for ensuring that pairs of certificates are only used as
intended are discussed in more detail in Sections 13.3.2 and 13.3.3
of this document.
The frequency and duration of system upgrades and the time when CRQCs
will become widely available need to be weighed to determine whether
and when to support the PQ/T Hybrid Authentication property.
13.3. Hybrid Cryptographic Algorithm Combinations: Considerations and
Approaches
13.3.1. Hybrid Cryptographic Combinations
It is also possible to use more than two algorithms together in a
hybrid scheme, with various methods for combining them. For post-
quantum transition purposes, the combination of a post-quantum
algorithm with a traditional algorithm is the most straightforward
and recommended. The use of multiple post-quantum algorithms with
different mathematical bases has also been considered. Combining
algorithms in a way that requires both to be used together ensures
stronger security, while combinations that do not require both will
sacrifice security but offer other benefits like backwards
compatibility and crypto agility. Including a traditional key
alongside a post-quantum key often has minimal bandwidth impact.
13.3.2. Composite Keys in Hybrid Schemes
When combining keys in an "and" mode, it may make more sense to
consider them to be a single composite key instead of two keys. This
generally requires fewer changes to various components of PKI
ecosystems, many of which are not prepared to deal with two keys or
dual signatures. To those protocol- or application-layer parsers, a
"composite" algorithm composed of two "component" algorithms is
simply a new algorithm, and support for adding new algorithms
generally already exists. Treating multiple "component" keys as a
single "composite" key also has security advantages, such as
preventing cross-protocol reuse of the individual component keys and
guarantees about revoking or retiring all component keys together at
the same time, especially if the composite is treated as a single
object all the way down into the cryptographic module.
All that needs to be done is to standardize the formats of how the
two keys from the two algorithms are combined into a single data
structure and how the two resulting signatures or KEMs are combined
into a single signature or KEM. The answer can be as simple as
concatenation if the lengths are fixed or easily determined. At the
time this document is published, security research is ongoing as to
the security properties of concatenation-based composite signatures
and KEMs versus more sophisticated signature and KEM combiners and
protocol contexts in which those simpler combiners are sufficient.
One last consideration is the specific pairs of algorithms that can
be combined. A recent trend in protocols is to only allow a small
number of "known good" configurations that make sense, often referred
to in cryptography as a "ciphersuite", instead of allowing arbitrary
combinations of individual configuration choices that may interact in
dangerous ways. The current consensus is that the same approach
should be followed for combining cryptographic algorithms and that
"known good" pairs should be explicitly listed ("explicit composite")
instead of just allowing arbitrary combinations of any two
cryptographic algorithms ("generic composite").
The same considerations apply when using multiple certificates to
transport a pair of related keys for the same subject. Exactly how
two certificates should be managed in order to avoid some of the
pitfalls mentioned above is still an active area of investigation.
Using two certificates keeps the certificate tooling simple and
straightforward, but in the end, this simply moves problems (i.e.,
problems with the requirement that both certificates be used as a
pair, that two signatures that must be carried separately, and that
both validate) to the certificate management layer, where addressing
these concerns in a robust way can be difficult.
At least one scheme has been proposed that allows the pair of
certificates to exist as a single certificate when being issued and
managed but dynamically split into individual certificates when
needed (see [ENC-PAIR-CERTS]).
13.3.3. Key Reuse in Hybrid Schemes
An important security note, particularly when using hybrid signature
keys, but also to a lesser extent hybrid KEM keys, is key reuse. In
traditional cryptography, problems can occur with so-called "cross-
protocol attacks" when the same key can be used for multiple
protocols; for example, signing TLS handshakes and signing S/MIME
emails. While it is not best practice to reuse keys within the same
protocol, e.g., using the same key for multiple S/MIME certificates
for the same user, it is not generally catastrophic for security.
However, key reuse becomes a large security problem within hybrid
schemes.
Consider an {RSA, ML-DSA} hybrid key where the RSA key also appears
within a single-algorithm certificate. In this case, an attacker
could perform a "stripping attack" where they take some piece of data
signed with the {RSA, ML-DSA} key, remove the ML-DSA signature, and
present the data as if it was intended for the RSA only certificate.
This leads to a set of security definitions called "non-separability
properties", which refers to how well the signature scheme resists
various complexities of downgrade/stripping attacks
[HYBRID-SIG-SPECT]. Therefore, it is recommended that implementers
either reuse the entire hybrid key as a whole or perform fresh key
generation of all component keys per usage, and must not take an
existing key and reuse it as a component of a hybrid key.
13.3.4. Future Directions and Ongoing Research
Many aspects of hybrid cryptography are still under investigation.
The LAMPS Working Group at IETF is actively exploring the security
properties of these combinations, and future standards will reflect
the evolving consensus on these issues.
14. Impact on Constrained Devices and Networks
PQC algorithms generally have larger keys, ciphertext, and signature
sizes than traditional public key algorithms. This has particular
impact on constrained devices that operate with limited data rates.
In the IoT space, these constraints have historically driven
significant optimization efforts in the IETF (e.g., in the LAKE and
CoRE Working Groups) to adapt security protocols to resource-
constrained environments.
As the transition to PQC progresses, these environments will face
similar challenges. Larger message sizes can increase handshake
latency, raise energy consumption, and require fragmentation logic.
Work is ongoing in the IETF to study how PQC can be deployed in
constrained devices (see [CONSTRAIN-DEV-PCQ]).
15. Security Considerations
15.1. Cryptanalysis
Traditional cryptanalysis exploits weaknesses in algorithm design,
mathematical vulnerabilities, or implementation flaws that are
exploitable with classical (i.e., non-quantum) hardware, whereas
quantum cryptanalysis harnesses the power of CRQCs to solve specific
mathematical problems more efficiently. Quantum side-channel attacks
are another form of quantum cryptanalysis. In such attacks, a device
under threat is directly connected to a quantum computer, which then
injects entangled or superimposed data streams to exploit hardware
that lacks protection against quantum side channels. Both pose
threats to the security of cryptographic algorithms, including those
used in PQC. It is crucial to develop and adopt new cryptographic
algorithms resilient against these threats to ensure long-term
security in the face of advancing cryptanalysis techniques.
Recent attacks on the side-channel implementations using deep
learning-based power analysis have also shown that one needs to be
cautious while implementing the required PQC algorithms in hardware.
Two of the most recent works include one attack on ML-KEM [KyberSide]
and one attack on Saber [SaberSide]. An evolving threat landscape
points to the fact that lattice-based cryptography is indeed more
vulnerable to side-channel attacks as in [SideCh] and [LatticeSide].
Consequently, some mitigation techniques for side-channel attacks
have been proposed; see [Mitigate1], [Mitigate2], and [Mitigate3].
15.2. Cryptographic Agility
Cryptographic agility is recommended for both traditional and quantum
cryptanalysis as it enables organizations to adapt to emerging
threats, adopt stronger algorithms, comply with standards, and plan
for long-term security in the face of evolving cryptanalytic
techniques and the advent of CRQCs.
Several PQC schemes are available that need to be tested;
cryptography experts around the world are pushing for the best
possible solutions, and the first standards that will ease the
introduction of PQC are being prepared. This is of paramount
importance and is a call for imminent action for organizations,
bodies, and enterprises to start evaluating their cryptographic
agility, assess the complexity of implementing PQC into their
products, processes, and systems, and develop a migration plan that
achieves their security goals to the best possible extent.
An important and often overlooked step in achieving cryptographic
agility is maintaining a cryptographic inventory. Modern software
stacks incorporate cryptography in numerous places, making it
challenging to identify all instances. Therefore, cryptographic
agility and inventory management take two major forms. First,
application developers responsible for software maintenance should
actively search for instances of hard-coded cryptographic algorithms
within applications. When possible, they should design the choice of
algorithm to be dynamic, based on application configuration. Second,
administrators, policy officers, and compliance teams should take
note of any instances where an application exposes cryptographic
configurations. These instances should be managed through either
organization-wide written cryptographic policies or automated
cryptographic policy systems.
Numerous commercial solutions are available for detecting hard-coded
cryptographic algorithms in source code and compiled binaries, as
well as providing cryptographic policy management control planes for
enterprise and production environments.
15.3. Jurisdictional Fragmentation
Another potential application of hybrid schemes bears mentioning,
even though it is not directly related to PQC: using hybrids to
navigate inter-jurisdictional cryptographic connections. Traditional
cryptography is already fragmented by jurisdiction. Consider that
while most jurisdictions support ECDH, those in the United States
will prefer the NIST curves while those in Germany will prefer the
Brainpool curves. China, Russia, and other jurisdictions have their
own national cryptography standards. This situation of fragmented
global cryptography standards is unlikely to improve with PQC. If
"and" mode hybrid schemes become standardized for the reasons
mentioned above, then one could imagine leveraging them to create
ciphersuites in which a single cryptographic operation simultaneously
satisfies the cryptographic requirements of both endpoints.
15.4. Hybrid Key Exchange and Signatures: Bridging the Gap Between PQ/T
Cryptography
Post-quantum algorithms selected for standardization are relatively
new and have not been subject to the same depth of study as
traditional algorithms. PQC implementations will also be new and
therefore more likely to contain implementation bugs than the battle-
tested crypto implementations that are relied on today. In addition,
certain deployments may need to retain traditional algorithms due to
regulatory constraints, e.g., FIPS [SP-800-56C] or Payment Card
Industry (PCI) compliance [PCI]. Hybrid key exchange is recommended
to enhance security against the HNDL attack. Additionally, hybrid
signatures provide for time to react in the case of the announcement
of a devastating attack against any one algorithm, while not fully
abandoning traditional cryptosystems.
Hybrid key exchange performs both a classical and a post-quantum key
exchange in parallel. It provides security redundancy against
potential weaknesses in PQC algorithms, allows for a gradual
transition of trust in PQC algorithms, and, in backward-compatible
designs, enables gradual adoption without breaking compatibility with
existing systems. For instance, in TLS 1.3, a hybrid key exchange
can combine a widely supported classical algorithm, such as X25519,
with a post-quantum algorithm like ML-KEM. This allows legacy
clients to continue using the classical algorithm while enabling
upgraded clients to proceed with hybrid key exchange. In contrast,
overhead-spreading hybrid designs focus on reducing the PQ overhead.
For example, approaches like those described in [PQ-MLS] amortize PQ
costs by selectively applying PQ updates in key exchange processes,
allowing systems to balance security and efficiency. This strategy
ensures a post-quantum secure channel while keeping the overhead
manageable, making it particularly suitable for constrained
environments.
While some hybrid key exchange options introduce additional
computational and bandwidth overhead, the impact of traditional key
exchange algorithms (e.g., key size) is typically small, helping to
keep the overall increase in resource usage manageable for most
systems. In highly constrained environments, however, those hybrid
key exchange protocols may be impractical due to their higher
resource requirements compared to pure post-quantum or traditional
key exchange approaches. However, some hybrid key exchange designs
distribute the PQC overhead, making them more suitable for
constrained environments. The choice of hybrid key exchange design
depends on the specific system requirements and use case, so the
appropriate approach may vary.
15.5. Caution: Ciphertext Commitment in KEM vs. DH
The ciphertext generated by a KEM is not necessarily directly linked
to the shared secret it produces. KEMs allow for multiple
ciphertexts to encapsulate the same shared secret, which enables
flexibility in key management without enforcing a strict one-to-one
correspondence between ciphertexts and shared secrets. This allows
for secret reuse across different recipients, sessions, or
operational contexts without the need for new secrets for each use,
simplifying key distribution and reducing computational overhead. In
contrast, cryptographic schemes like Diffie-Hellman inherently link
the public key to the derived shared secret, meaning any change in
the public key results in a different shared secret.
16. IANA Considerations
This document has no IANA actions.
17. Further Reading and Resources
A good book on modern cryptography is "Serious Cryptography, 2nd
Edition" by Jean-Philippe Aumasson [Serious-Crypt].
The Open Quantum Safe (OQS) Project [OQS] is an open-source project
that aims to support the transition to quantum-resistant
cryptography.
The IETF's PQUIP Working Group [PQUIP-WG] maintains a list of PQC-
related protocol work within the IETF.
18. References
18.1. Normative References
[ClassicMcEliece]
"Classic McEliece", <https://classic.mceliece.org/>.
[FN-DSA] "FALCON: Fast Fourier lattice-based compact signatures
over NTRU", <https://falcon-sign.info/>.
[FrodoKEM] "FrodoKEM", <https://frodokem.org/>.
[Grovers] Grover, L. K., "A fast quantum mechanical algorithm for
database search", STOC '96: Proceedings of the twenty-
eighth annual ACM symposium on Theory of Computing, pp.
212-219, DOI 10.1145/237814.237866, 1 July 1996,
<https://dl.acm.org/doi/10.1145/237814.237866>.
[ML-DSA] 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>.
[ML-KEM] NIST, "Module-Lattice-Based Key-Encapsulation Mechanism
Standard", NIST FIPS 203, DOI 10.6028/nist.fips.203,
August 2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.203.pdf>.
[NTRU] "NTRU", <https://ntru.org/index.shtml>.
[RFC4034] Arends, R., Austein, R., Larson, M., Massey, D., and S.
Rose, "Resource Records for the DNS Security Extensions",
RFC 4034, DOI 10.17487/RFC4034, March 2005,
<https://www.rfc-editor.org/info/rfc4034>.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
Curve Cryptography Algorithms", RFC 6090,
DOI 10.17487/RFC6090, February 2011,
<https://www.rfc-editor.org/info/rfc6090>.
[RFC8235] Hao, F., Ed., "Schnorr Non-interactive Zero-Knowledge
Proof", RFC 8235, DOI 10.17487/RFC8235, September 2017,
<https://www.rfc-editor.org/info/rfc8235>.
[RFC8391] Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A.
Mohaisen, "XMSS: eXtended Merkle Signature Scheme",
RFC 8391, DOI 10.17487/RFC8391, May 2018,
<https://www.rfc-editor.org/info/rfc8391>.
[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/info/rfc8446>.
[RFC8554] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
April 2019, <https://www.rfc-editor.org/info/rfc8554>.
[RFC9180] Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
February 2022, <https://www.rfc-editor.org/info/rfc9180>.
[RFC9242] Smyslov, V., "Intermediate Exchange in the Internet Key
Exchange Protocol Version 2 (IKEv2)", RFC 9242,
DOI 10.17487/RFC9242, May 2022,
<https://www.rfc-editor.org/info/rfc9242>.
[RFC9370] Tjhai, CJ., Tomlinson, M., Bartlett, G., Fluhrer, S., Van
Geest, D., Garcia-Morchon, O., and V. Smyslov, "Multiple
Key Exchanges in the Internet Key Exchange Protocol
Version 2 (IKEv2)", RFC 9370, DOI 10.17487/RFC9370, May
2023, <https://www.rfc-editor.org/info/rfc9370>.
[RFC9881] Massimo, J., Kampanakis, P., Turner, S., and B. E.
Westerbaan, "Internet X.509 Public Key Infrastructure --
Algorithm Identifiers for the Module-Lattice-Based Digital
Signature Algorithm (ML-DSA)", RFC 9881,
DOI 10.17487/RFC9881, October 2025,
<https://www.rfc-editor.org/info/rfc9881>.
[RSA] Rivest, R. L., Shamir, A., and L. Adleman, "A Method for
Obtaining Digital Signatures and Public-Key
Cryptosystems", Communications of the ACM, vol. 21, no. 2,
pp. 120-126, DOI 10.1145/359340.359342, February 1978,
<https://dl.acm.org/doi/pdf/10.1145/359340.359342>.
[Shors] Shor, P., "Polynomial-Time Algorithms for Prime
Factorization and Discrete Logarithms on a Quantum
Computer", arXiv:quant-ph/9508027v2, 25 January 1996,
<https://arxiv.org/pdf/quant-ph/9508027>.
[SLH-DSA] NIST, "Stateless Hash-Based Digital Signature Standard",
NIST FIPS 205, DOI 10.6028/NIST.FIPS.205, August 2024,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.205.pdf>.
18.2. Informative References
[AddSig] NIST, "Post-Quantum Cryptography: Additional Digital
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signature spectrums", Work in Progress, Internet-Draft,
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[KEEPINGUP]
Cremers, C., Dax, A., and N. Medinger, "Keeping Up with
the KEMs: Stronger Security Notions for KEMs and automated
analysis of KEM-based protocols", Cryptology ePrint
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[KEM-COMBINER]
Ounsworth, M., Wussler, A., and S. Kousidis, "Combiner
function for hybrid key encapsulation mechanisms (Hybrid
KEMs)", Work in Progress, Internet-Draft, draft-ounsworth-
cfrg-kem-combiners-05, 31 January 2024,
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[KyberSide]
Ji, Y., Wang, R., Ngo, K., Dubrova, E., and L. Backlund,
"A Side-Channel Attack on a Hardware Implementation of
CRYSTALS-Kyber", Cryptology ePrint Archive, Paper
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D'Anvers, J., Guo, Q., Johansson, T., Nilsson, A.,
Vercauteren, F., and I. Verbauwhede, "Decryption Failure
Attacks on IND-CCA Secure Lattice-Based Schemes", Public-
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[LattFail2]
D'Anvers, J., Rossi, M., and F. Virdia, "(One) Failure Is
Not an Option: Bootstrapping the Search for Failures in
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[LatticeSide]
Ravi, P., Roy, S. S., Chattopadhyay, A., and S. Bhasin,
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to Lattice and Factoring-Based Signatures", ASIACRYPT
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[Mitigate1]
Hoffmann, C., Libert, B., Momin, C., Peters, T., and F.
Standaert, "POLKA: Towards Leakage-Resistant Post-Quantum
CCA-Secure Public Key Encryption", Cryptology ePrint
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[Mitigate2]
Tsai, T., Huang, S., Tseng, Y., Chuang, Y., and Y. Hung,
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Exchange Protocol", IEEE Open Journal of the Computer
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[Mitigate3]
Azouaoui, M., Kuzovkova, Y., Schneider, T., and C. V.
Vredendaal, "Post-Quantum Authenticated Encryption against
Chosen-Ciphertext Side-Channel Attacks", Cryptology ePrint
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[ML-DSA-X.509]
Ounsworth, M., Gray, J., Pala, M., Klaußner, J., and S.
Fluhrer, "Composite Module-Lattice-Based Digital Signature
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Infrastructure", Work in Progress, Internet-Draft, draft-
ietf-lamps-pq-composite-sigs-19, 21 April 2026,
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[NIST] NIST, "Post-Quantum Cryptography Standardization",
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[NISTFINAL]
NIST, "NIST Releases First 3 Finalized Post-Quantum
Encryption Standards", 13 August 2024,
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releases-first-3-finalized-post-quantum-encryption-
standards>.
[OQS] "Open Quantum Safe Project",
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[PCI] PCI Security Standards Council, "Payment Card Industry
Data Security Standard", PCI DSS: v4.0.1, <https://docs-
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v4_0_1.pdf>.
[PQ-HPKE] Barnes, R. and D. Connolly, "Post-Quantum and Post-
Quantum/Traditional Hybrid Algorithms for HPKE", Work in
Progress, Internet-Draft, draft-ietf-hpke-pq-04, 2 March
2026, <https://datatracker.ietf.org/doc/html/draft-ietf-
hpke-pq-04>.
[PQ-KEM] Connolly, D., Barnes, R., and P. Grubbs, "Hybrid PQ/T Key
Encapsulation Mechanisms", Work in Progress, Internet-
Draft, draft-irtf-cfrg-hybrid-kems-11, 7 May 2026,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
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[PQ-MLS] Tian, X., Hale, B., Mularczyk, M., and J. Alwen,
"Amortized PQ MLS Combiner", Work in Progress, Internet-
Draft, draft-ietf-mls-combiner-02, 22 October 2025,
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[PQCAPI] NIST, "PQC - API notes",
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Cryptography/documents/example-files/api-notes.pdf>.
[PQRSA] Bernstein, D. J., Heninger, N., Lou, P., and L. Valenta,
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[QuantSide]
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[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
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<https://www.rfc-editor.org/info/rfc5652>.
[RFC9528] Selander, G., Preuß Mattsson, J., and F. Palombini,
"Ephemeral Diffie-Hellman Over COSE (EDHOC)", RFC 9528,
DOI 10.17487/RFC9528, March 2024,
<https://www.rfc-editor.org/info/rfc9528>.
[RFC9763] Becker, A., Guthrie, R., and M. Jenkins, "Related
Certificates for Use in Multiple Authentications within a
Protocol", RFC 9763, DOI 10.17487/RFC9763, June 2025,
<https://www.rfc-editor.org/info/rfc9763>.
[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>.
[RFC9814] Housley, R., Fluhrer, S., Kampanakis, P., and B.
Westerbaan, "Use of the SLH-DSA Signature Algorithm in the
Cryptographic Message Syntax (CMS)", RFC 9814,
DOI 10.17487/RFC9814, July 2025,
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[RFC9941] Friedl, M., Mojzis, J., and S. Josefsson, "Secure Shell
(SSH) Key Exchange Method Using Hybrid Streamlined NTRU
Prime sntrup761 and X25519 with SHA-512:
sntrup761x25519-sha512", RFC 9941, DOI 10.17487/RFC9941,
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[SaberSide]
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[SP-1800-38C]
Newhouse, W., Souppaya, M., Barke, W., Brown, C.,
Kampanakis, P., Goodman, J., Prat, J., Larrieu, R., Gray,
J., Ounsworth, M., Viana, C., Gong, H. L. V., Kwiatkowsk,
K., Hu, A., Burns, R., Paquin, C., Gilbert, J., Scinta,
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[SP-800-56C]
Barker, E., Chen, L., and R. Davis, "Recommendation for
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exchange in TLS 1.3", Work in Progress, Internet-Draft,
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general-purpose hybrid post-quantum KEM", Work in
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draft-connolly-cfrg-xwing-kem-10>.
Acknowledgements
This document leverages text from an earlier Internet-Draft by Paul
Hoffman. Thanks to Dan Wing, Florence D, Thom Wiggers, Sophia
Grundner-Culemann, Panos Kampanakis, Ben S, Sofia Celi, Melchior
Aelmans, Falko Strenzke, Deirdre Connolly, Hani Ezzadeen, Britta
Hale, Scott Rose, Hilarie Orman, Thomas Fossati, Roman Danyliw, Mike
Bishop, Mališa Vučinić, Éric Vyncke, Deb Cooley, Dirk Von Hugo, and
Daniel Van Geest for the discussion, review and comments.
In particular, the authors would like to acknowledge the
contributions to this document by Kris Kwiatkowski.
Authors' Addresses
Aritra Banerjee
Nokia
London
United Kingdom
Email: aritra.banerjee@nokia.com
Tirumaleswar Reddy.K
Nokia
Bangalore
Karnataka
India
Email: k.tirumaleswar_reddy@nokia.com
Dimitrios Schoinianakis
Nokia
Athens
Greece
Email: dimitrios.schoinianakis@nokia-bell-labs.com
Timothy Hollebeek
DigiCert
Pittsburgh, PA
United States of America
Email: tim.hollebeek@digicert.com
Mike Ounsworth
Entrust Limited
2500 Solandt Road, Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: mike@ounsworth.ca