PQUIP A. Banerjee
Internet-Draft T. Reddy
Intended status: Informational D. Schoinianakis
Expires: 18 August 2025 Nokia
T. Hollebeek
DigiCert
M. Ounsworth
Entrust
14 February 2025
Post-Quantum Cryptography for Engineers
draft-ietf-pquip-pqc-engineers-09
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), detailing 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.
About This Document
This note is to be removed before publishing as an RFC.
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Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Threat of CRQCs on Cryptography . . . . . . . . . . . . . . . 6
2.1. Symmetric Cryptography . . . . . . . . . . . . . . . . . 7
2.2. Asymmetric Cryptography . . . . . . . . . . . . . . . . . 8
2.3. Quantum Side-channel Attacks . . . . . . . . . . . . . . 9
3. Traditional Cryptographic Primitives that Could Be Replaced by
PQC . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4. Invariants of PQC: Necessitating Compliance Adjustments . . . 10
5. NIST PQC Algorithms . . . . . . . . . . . . . . . . . . . . . 11
5.1. NIST Candidates Selected for Standardization . . . . . . 11
5.1.1. PQC Key Encapsulation Mechanisms (KEMs) . . . . . . . 11
5.1.2. PQC Signatures . . . . . . . . . . . . . . . . . . . 11
5.2. Candidates Advancing to the Fourth Round for
Standardization at NIST . . . . . . . . . . . . . . . . . 11
6. Timeline for Transition . . . . . . . . . . . . . . . . . . . 12
7. PQC Categories . . . . . . . . . . . . . . . . . . . . . . . 14
7.1. Lattice-Based Public-Key Cryptography . . . . . . . . . . 14
7.2. Hash-Based Public-Key Cryptography . . . . . . . . . . . 15
7.3. Code-Based Public-Key Cryptography . . . . . . . . . . . 16
8. KEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
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8.1. Authenticated Key Exchange . . . . . . . . . . . . . . . 18
8.2. Security Properties of KEMs . . . . . . . . . . . . . . . 21
8.2.1. IND-CCA2 . . . . . . . . . . . . . . . . . . . . . . 21
8.2.2. Binding . . . . . . . . . . . . . . . . . . . . . . . 21
8.3. HPKE . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9. PQC Signatures . . . . . . . . . . . . . . . . . . . . . . . 22
9.1. Security Properties of PQC Signatures . . . . . . . . . . 22
9.2. EUF-CMA and SUF-CMA . . . . . . . . . . . . . . . . . . . 22
9.3. Details of FN-DSA, ML-DSA, and SLH-DSA . . . . . . . . . 23
9.4. Details of XMSS and LMS . . . . . . . . . . . . . . . . . 25
9.4.1. LMS Key and Signature Sizes . . . . . . . . . . . . . 25
9.5. Hash-then-Sign . . . . . . . . . . . . . . . . . . . . . 26
10. Recommendations for Security / Performance Tradeoffs . . . . 27
11. Comparing PQC KEMs/Signatures vs Traditional KEMs
(KEXs)/Signatures . . . . . . . . . . . . . . . . . . . . 30
12. Post-Quantum and Traditional Hybrid Schemes . . . . . . . . . 32
12.1. PQ/T Hybrid Confidentiality . . . . . . . . . . . . . . 32
12.2. PQ/T Hybrid Authentication . . . . . . . . . . . . . . . 33
12.3. Hybrid Cryptographic Algorithm Combinations:
Considerations and Approaches . . . . . . . . . . . . . 34
12.3.1. Hybrid Cryptographic Combinations . . . . . . . . . 34
12.3.2. Composite Keys in Hybrid Schemes . . . . . . . . . . 34
12.3.3. Key Reuse in Hybrid Schemes . . . . . . . . . . . . 35
12.3.4. Jurisdictional Fragmentation . . . . . . . . . . . . 36
12.3.5. Future Directions and Ongoing Research . . . . . . . 36
13. Security Considerations . . . . . . . . . . . . . . . . . . . 36
13.1. Cryptanalysis . . . . . . . . . . . . . . . . . . . . . 36
13.2. Cryptographic Agility . . . . . . . . . . . . . . . . . 37
13.3. Hybrid Key Exchange and Signatures: Bridging the Gap
Between Post-Quantum and Traditional Cryptography . . . 38
13.4. Caution: Ciphertext commitment in KEM vs DH . . . . . . 39
14. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 39
15. Further Reading & Resources . . . . . . . . . . . . . . . . . 39
16. Informative References . . . . . . . . . . . . . . . . . . . 39
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 46
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 46
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 public-key
cryptographic algorithms are not yet available. However, there is
ongoing research and development in the field of quantum computing,
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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, so too will quantum computers have a niche set of problems
on which they excel. Unfortunately for cryptographers, integer
factorization and discrete logarithms, the mathematical problems
underpinning much of modern cryptography, happen to fall within the
niche that quantum computers are expected to excel at. As such, 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.
Extensive research has produced several post-quantum cryptographic
(PQC) 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.
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 and ECC. 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.
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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,
understanding the differences between PQC key encapsulation
mechanisms (KEMs) and traditional Diffie-Hellman and RSA style key
exchanges, and provides insights into expected key sizes and
processing time differences between PQC and traditional algorithms.
Additionally, it discusses the potential threat to symmetric
cryptography 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 co-exist 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] which largely aligns with United States National
Institute of Standards and Technology (NIST) and NSA guidance, but
differs on some of the guidance.
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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, which can break
widely-used public key schemes like RSA and ECC. Symmetric
cryptography and hash functions also face some risk from Grover's
algorithm, although the impact is less severe and can typically be
mitigated by doubling key lengths. It is crucial for the reader to
understand that when the word "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, MACs, etc., which are less vulnerable to quantum
computers. This document does not cover such topics as when
traditional algorithms might become vulnerable (for that, see
documents such as [QC-DNS] and others). It also 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 (that is, not quantum) math and software and
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).
There is ongoing discussion about whether to use the term "post-
quantum", "quantum ready", or "quantum resistant", to describe
algorithms that resist CRQCs, and a consensus has not yet been
reached. It is important to clarify that "post-quantum" refers to
algorithms designed to withstand attacks by CRQCs and classical
computers alike. These algorithms are based on mathematically hard
cryptographic problems that neither CRQCs nor classical computers are
expected to break. This document uses any of these terms
interchangeably to refer to such algorithms.
2. 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.
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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.
Despite the fact that large-scale quantum computers do not yet exist
to experiment on, the theoretical properties of quantum computation
are very well understood. This allows us to reason today about the
upper limits of quantum-enhanced computation, and indeed to design
cryptographic algorithms that are resistant to any conceivable for of
quantum cryptanalysis.
2.1. 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.
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 today to counter the quadratic speedup and maintain 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, whereas 2^{64} classical operations can be
efficiently parallelized, 2^{64} quantum operations must be performed
serially, making them infeasible on practical quantum computers.
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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,
192, and 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 National Agency
for the Security of Information Systems (ANSSI), recommend the use of
AES-256 [ANSSI].
2.2. 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 cryptography algorithms (e.g., RSA, Diffie-Hellman
and elliptic curve cryptography, as well as less commonly-used
variants such as ElGamal and Schnorr signatures) 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, to provide some context, one would need around 20
million noisy qubits to break RSA-2048 in 8 hours [RSAShor] and
[RSA8HRS] or 4099 stable (or logical) qubits to break it [RSA10SC].
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
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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).
2.3. Quantum Side-channel Attacks
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. 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.
3. 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 sufficiently large general-purpose quantum computer,
known as 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 this is based on public key cryptography and
is 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 case of RSA), which in turn can be exploited to
derive the private key. In the case of Diffie-Hellman, a CRQC has
the potential to calculate the exponent or discrete logarithm of
the (short or long-term) Diffie-Hellman public key. This, in
turn, would reveal the secret required to derive the symmetric
encryption key.
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* 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, and hence a break in public key cryptography will also
affect traditional digital signatures, hence the importance of
developing post-quantum digital signatures.
* BBS signatures: BBS (Boneh-Boyen-Shacham) 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 quantum
attacks. A CRQC can break the data authenticity security property
of BBS but not the data confidentiality (Section 6.9 of
[I-D.irtf-cfrg-bbs-signatures]).
* 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 2.1.
4. Invariants of PQC: Necessitating Compliance Adjustments
In the context of PQC, symmetric-key cryptographic algorithms are
generally not directly impacted by quantum computing advancements.
Symmetric-key cryptography, which includes keyed primitives such as
block ciphers (e.g., AES) and message authentication mechanisms
(e.g., HMAC-SHA2), 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. HMAC is a specific construction that utilizes a
cryptographic hash function (such as SHA-2) and a secret key shared
between the sender and receiver to produce a message authentication
code.
Grover's algorithm does not pose a practical threat to symmetric
cryptography (see Section 2.1 for more details). As a result, CRQCs
offer no substantial advantages in breaking symmetric-key algorithms
compared to classical computers. However, for compliance purposes,
such as meeting the standards of CNSA 2.0 (Commercial National
Security Algorithm Suite 2.0) [CNSA2-0], AES-256 must be used to
ensure the highest level of security against both traditional and
quantum threats.
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5. NIST PQC Algorithms
At time of writing, NIST have standardized three PQC algorithms, with
more expected to be standardised in the future ([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 key encapsulation method (KEM) and as
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 8, 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
Standard (FIPS-203).
5.1.2. PQC Signatures
* [ML-DSA]: Module-Lattice-Based Digital Signature Standard (FIPS-
204).
* [SLH-DSA]: Stateless Hash-Based Digital Signature (FIPS-205).
* [FN-DSA]: FN-DSA is a lattice signature scheme (Section 7.1 and
Section 9.3).
5.2. Candidates Advancing to the Fourth Round for Standardization at
NIST
The fourth-round of the NIST process focuses only on KEMs. The goal
of that round is to select an alternative algorithm that is based on
different hard problem than ML-KEM. The candidates still advancing
for standardization are:
* [ClassicMcEliece]: 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.
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* [BIKE]: Based on the hardness of syndrome decoding of Quasi-Cyclic
Moderate Density Parity Check (QC-MDPC) codes. QC-MDPC codes are
a class of error-correcting codes that leverages bit flipping
techniques to efficiently correct errors.
* [HQC]: Based on the hardness of syndrome decoding of Quasi-cyclic
concatenated Reed Muller Reed Solomon (RMRS) codes in the Hamming
metric. Reed Muller (RM) codes are a class of block error-
correcting codes used especially in wireless and deep space
communications. Reed Solomon (RS) are a class of block error
correcting codes that are used to detect and correct multiple bit
errors.
* [SIKE] (Broken): Supersingular Isogeny Key Encapsulation (SIKE) is
a specific realization of the SIDH (Supersingular Isogeny Diffie-
Hellman) protocol. Recently, a mathematical attack [SIDH-Attack]
based on the "glue-and-split" theorem from 1997 from Ernst Kani
was found against the underlying chosen starting curve and torsion
information. In practical terms, this attack allows for the
efficient recovery of the private key. NIST announced that SIKE
was no longer under consideration, but the authors of SIKE had
asked for it to remain in the list so that people are aware that
it is broken. While SIKE is broken, isogenies in general remain
an active area of cryptographic research due to their very
attractive bandwidth usage, and yet more cryptographic primitives
in the future may appear from this research area.
6. Timeline for Transition
The timeline, and driving motivation for transition differs 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" 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.
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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 smartcards. Even for
short-lived signatures 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 remain
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 under-estimated, like 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. Bear in mind also 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.
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Organizations should also consider carefully and honestly what their
migration timeline "y" actually is. If you think only 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, TEEs, Secure Enclaves, and other
cryptographic co-processors. Smartcard applications will require
replacement of the cards as well as of the readers which can come in
many form-factors: tap-for-entry door and turnstile readers, PIN pad
machines, laptops with built-in smartcard readers, and many others.
Included in "y" is not only the deployment time, but also preparation
time: integration, testing, auditing, and re-certification of
cryptographic environments. Consider also upstream effects that
contribute to "y", including lead-times for your 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 or decades for even most moderately-
sized organizations.
7. PQC Categories
The post-quantum cryptographic schemes standardized by NIST, along
with the ongoing Round 4 candidates, 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.
7.1. 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.
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Lattice-based schemes usually have good performances and average size
public keys and signatures (average within the PQC primitives at
least; they are still several orders of magnitude larger than e.g.,
RSA or ECC signatures), 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 and ML-
DSA.
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; as such, 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 has been
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.
7.2. 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 mathematically based on the security
of the selected cryptographic hash function. Many variants of hash-
based signatures (HBS) have been developed since the 70s including
the recent XMSS [RFC8391], HSS/LMS [RFC8554] or 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 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 with 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, and therefore 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.
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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 HBS 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 leverages the HORST (hash to obtain random
subset with trees) technique and remains the only hash based
signature scheme that is stateless, thus avoiding the complexities
associated with state management.
SLH-DSA is an advancement on SPHINCS which reduces the signature
sizes in SPHINCS and makes it more compact. SLH-DSA was recently
standardized by NIST.
7.3. Code-Based Public-Key Cryptography
This area of cryptography started in the 1970s and 80s 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 Hamming
quasi-cyclic (HQC), or quasi-cyclic moderate density parity check
(QC-MDPC) codes.
Examples include all the NIST Round 4 (unbroken) finalists: Classic
McEliece, HQC, BIKE.
8. 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 KEM encapsulation 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:
* Derive a data encryption key (DEK) to encrypt the data
* Derive a key encryption key (KEK) used to wrap a DEK
These techniques are often referred to as "hybrid public key
encryption (HPKE)" [RFC9180] mechanism.
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The term "encapsulation" is chosen intentionally to indicate that KEM
algorithms behave differently at the API level from the key agreement
or key encipherment / 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 / 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:
KEM relies on the following 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
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8.1. 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 [I-D.draft-ietf-lake-edhoc]. However, 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 Diffie-Hellman (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: Diffie-Hellman based AKE
What's important to note about the sample flow above is 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) which 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
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a Diffie-Hellman key exchange which is an AKE, since both parties are
using long-term keys which 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, 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: Diffie-Hellman based AKE and NIKE simultaneously
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 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.
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+---------+ +---------+
| 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
Here, 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 of either input even if the
other is chosen maliciously, then a more complex construct is
required. Another consideration for combiner design is 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],
[I-D.draft-ounsworth-cfrg-kem-combiners], and
[I-D.draft-connolly-cfrg-xwing-kem].
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8.2. Security Properties of KEMs
8.2.1. 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 key establishment method (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. IETF specification authors should include all
security concerns in the "Security Considerations" section of the
relevant RFC and not rely on implementers being experts in
cryptographic theory.
8.2.2. 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 which will
decapsulate to the same shared secret; or can construct a ciphertext
which 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.
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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 it through a key derivation function (KDF) and also include all
values that you wish to bind; then finally you will have a shared
secret that is safe to use at the protocol level.
8.3. 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.
HPKE (hybrid public key encryption) [RFC9180] is a specific
instantiation of this which works with a combination of KEMs, KDFs
and AEAD (authenticated encryption with additional data) 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 key encapsulation mechanism (KEM)
private key. HPKE can be extended to support hybrid post-quantum KEM
[I-D.draft-connolly-cfrg-xwing-kem]. ML-KEM does not support the
static-ephemeral key exchange that allows HPKE based on DH based KEMs
and its optional authenticated modes as discussed in section 1.5 of
[I-D.draft-connolly-cfrg-xwing-kem].
9. PQC Signatures
Any digital signature scheme that provides a construction defining
security under a post-quantum setting falls under this category of PQ
signatures.
9.1. Security Properties of PQC Signatures
9.2. 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,
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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 using 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. IETF specification authors 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.
9.3. Details of FN-DSA, ML-DSA, and SLH-DSA
ML-DSA [ML-DSA] is a digital signature algorithm (part of the
CRYSTALS suite) based on the hardness of lattice problems over module
lattices (i.e., the Module Learning with Errors problem (MLWE)). 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 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 with FN-DSA [FN-DSA]
which uses Gaussian-distributed numbers.
ML-DSA offers both deterministic and randomized signing and is
instantiated with 3 parameter sets providing different security
levels. Security properties of ML-DSA are discussed in Section 9 of
[I-D.ietf-lamps-dilithium-certificates].
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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.
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 Section 10 and Section 11.
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 7.2). 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.
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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.
9.4. 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 changes over time. In both schemes, reusing a secret key state
compromises cryptographic security guarantees.
Multi-tree 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. XMSS and HSS use a 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 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.
Due to the complexities described above, the XMSS and LMS are not a
suitable replacement 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.
9.4.1. 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.
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The public (PK) and private (SK) key size depends on the length of
the digest (M). The signature size depends on 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
9.5. 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.
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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 [RFC4033] 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 re-introduces the weakness that hash
collisions directly yield signature forgeries. Signing the full un-
digested message is recommended where applications can tolerate it.
10. Recommendations for Security / Performance Tradeoffs
The table below denotes the five security levels provided by NIST for
PQC algorithms. Neither NIST nor the IETF make 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. This
information is a re-print of information provided in the NIST PQC
project [NIST] as of time this document is published.
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+=============+=====================+===========================+
| 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 [I-D.ietf-lamps-cms-sphincs-plus] for
further details on SLH-DSA algorithms.
The following table discusses the signature size differences for
similar SLH-DSA algorithm security levels with the "simple" version
but for different categories i.e., (f) for fast verification and (s)
for compactness/smaller. Both SHA-256 and SHAKE-256 parameterization
output the same signature sizes, so both have been included.
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+==========+===========================+========+=======+===========+
| 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 discusses the impact of performance on different
security levels in terms of private key sizes, public key sizes, and
ciphertext/signature sizes.
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+==========+=============+============+============+================+
| 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 | 2528 | 2420 |
+----------+-------------+------------+------------+----------------+
| 3 | ML-KEM-768 | 1184 | 2400 | 1088 |
+----------+-------------+------------+------------+----------------+
| 3 | ML-DSA-65 | 1952 | 4000 | 3309 |
+----------+-------------+------------+------------+----------------+
| 5 | FN-DSA-1024 | 1793 | 2305 | 1280 |
+----------+-------------+------------+------------+----------------+
| 5 | ML-KEM-1024 | 1568 | 3168 | 1588 |
+----------+-------------+------------+------------+----------------+
| 5 | ML-DSA-87 | 2592 | 4864 | 4627 |
+----------+-------------+------------+------------+----------------+
Table 4
11. Comparing PQC KEMs/Signatures vs Traditional KEMs (KEXs)/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 vs. PQC KEMs in terms of
security, public and private key sizes, and ciphertext sizes.
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+=============+=====================+========+=========+============+
| 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 vs. 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 | P256 | 64 | 32 | 64 |
+-------------+-------------+------------+------------+-----------+
| 1 | FN-DSA-512 | 897 | 1281 | 666 |
+-------------+-------------+------------+------------+-----------+
| 2 | ML-DSA-44 | 1312 | 2528 | 768 |
+-------------+-------------+------------+------------+-----------+
| 3 | ML-DSA-65 | 1952 | 4000 | 3293 |
+-------------+-------------+------------+------------+-----------+
| 5 | FN-DSA-1024 | 1793 | 2305 | 1280 |
+-------------+-------------+------------+------------+-----------+
| 5 | ML-DSA-87 | 2592 | 4864 | 4627 |
+-------------+-------------+------------+------------+-----------+
Table 6
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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, IKEv2 uses UDP as the transport 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 [SP-1800-38C] section 6.3.3 shows that increased
key and signature sizes cause protocol key exchange messages to span
more network packets, therefore it results in a higher total loss
probability per packet. In lossy network conditions, this may
increase the latency of the key exchange.
12. Post-Quantum and Traditional 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. [I-D.ietf-pquip-pqt-hybrid-terminology] defines the
terminology for the post-quantum and traditional hybrid schemes.
12.1. PQ/T Hybrid Confidentiality
The PQ/T Hybrid Confidentiality property can be used to protect from
a "harvest now, decrypt later" attack described in Section 6, which
refers to an attacker collecting encrypted data now and waiting for
quantum computers to become powerful enough to break the encryption
later. Two types of hybrid key agreement schemes are discussed
below:
* Concatenate 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
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[I-D.ietf-tls-hybrid-design], 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.
* Cascade 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 the
Internet Key Exchange Protocol Version 2 (IKEv2) to allow one or
more PQC algorithms in addition to the traditional algorithm to
derive the final IKE 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
[I-D.ietf-tls-hybrid-design] 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.
12.2. PQ/T Hybrid Authentication
The PQ/T hybrid authentication property can be utilized in scenarios
where an on-path attacker possesses network devices equipped with
CRQCs, capable of breaking traditional authentication protocols, or
where an attacker can attack long-lived authenticated data such as CA
certificates or signed software images. This property ensures
authentication through a PQ/T hybrid scheme or a PQ/T hybrid
protocol, as long as at least one component algorithm remains secure
to provide the intended security level. For instance, a PQ/T hybrid
certificate [I-D.ietf-lamps-pq-composite-sigs] 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 [I-D.ietf-lamps-cert-binding-for-multi-auth].
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 12.3.2 and 12.3.3 of this document.
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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.
12.3. Hybrid Cryptographic Algorithm Combinations: Considerations and
Approaches
12.3.1. 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.
12.3.2. 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 vs more sophisticated signature and KEM combiners, and in
which protocol contexts those simpler combiners are sufficient.
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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 simply moves the problems with
requiring that both certs are intended to be used as a pair, must
produce two signatures which must be carried separately, and both
must 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 ([I-D.draft-bonnell-lamps-chameleon-certs].
12.3.3. 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, for example 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
hybrids.
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
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[I-D.draft-ietf-pquip-hybrid-signature-spectrums]. 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.
12.3.4. Jurisdictional Fragmentation
Another potential application of hybrids bears mentioning, even
though it is not directly PQC-related. That is using hybrids to
navigate inter-jurisdictional cryptographic connections. Traditional
cryptography is already fragmented by jurisdiction: consider that
while most jurisdictions support Elliptic Curve Diffie-Hellman, 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 hybrids 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.
12.3.5. Future Directions and Ongoing Research
Many aspects of hybrid cryptography are still under investigation.
LAMPS WG at IETF is actively exploring the security properties of
these combinations, and future standards will reflect the evolving
consensus on these issues.
13. Security Considerations
13.1. 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. Another form of quantum
cryptanalysis is "quantum side-channel" attacks. 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. Developing and adopting new cryptographic
algorithms resilient against these threats is crucial for ensuring
long-term security in the face of advancing cryptanalysis techniques.
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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], [LatticeSide].
Consequently, there were some mitigation techniques for side channel
attacks that have been proposed as in [Mitigate1], [Mitigate2], and
[Mitigate3].
13.2. 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. It is of paramount
importance and 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 either through
organization-wide written cryptographic policies or automated
cryptographic policy systems.
Numerous commercial solutions are available for both 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.
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13.3. Hybrid Key Exchange and Signatures: Bridging the Gap Between
Post-Quantum and Traditional Cryptography
Post-quantum algorithms selected for standardization are relatively
new and they 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, for example FIPS [SP-800-56C] or PCI
compliance. Hybrid key exchange is recommended to enhance security
against the "harvest now, decrypt later" 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 PQ 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
[I-D.hale-mls-combiner] 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.
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13.4. 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.
14. IANA Considerations
This document has no IANA considerations.
15. Further Reading & Resources
A good book on modern cryptography is Serious Cryptography, 2nd
Edition, by Jean-Philippe Aumasson, ISBN 9781718503847.
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.
16. Informative References
[ANSSI] "ANSSI views on the Post-Quantum Cryptography transition",
n.d., <https://cyber.gouv.fr/sites/default/files/document/
follow_up_position_paper_on_post_quantum_cryptography.pdf>
.
[BHK09] "Subtleties in the Definition of IND-CCA: When and How
Should Challenge-Decryption be Disallowed?",
<https://eprint.iacr.org/2009/418>.
[BIKE] "BIKE", n.d., <http://pqc-hqc.org/>.
[BSI-PQC] "Quantum-safe cryptography – fundamentals, current
developments and recommendations", May 2022,
<https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/
Publications/Brochure/quantum-safe-
cryptography.html?nn=916626>.
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[ClassicMcEliece]
"Classic McEliece", n.d., <https://classic.mceliece.org/>.
[Cloudflare]
"NIST’s pleasant post-quantum surprise",
<https://blog.cloudflare.com/nist-post-quantum-surprise/>.
[CNSA2-0] "Announcing the Commercial National Security Algorithm
Suite 2.0", <https://media.defense.gov/2022/
Sep/07/2003071834/-1/-1/0/CSA_CNSA_2.0_ALGORITHMS_.PDF>.
[CS01] "Design and Analysis of Practical Public-Key Encryption
Schemes Secure against Adaptive Chosen Ciphertext Attack",
<https://eprint.iacr.org/2001/108>.
[FN-DSA] "Fast Fourier lattice-based compact signatures over NTRU",
<https://falcon-sign.info/>.
[GMR88] "A digital signature scheme secure against adaptive
chosen-message attacks.",
<https://people.csail.mit.edu/silvio/
Selected%20Scientific%20Papers/Digital%20Signatures/
A_Digital_Signature_Scheme_Secure_Against_Adaptive_Chosen-
Message_Attack.pdf>.
[Grover-search]
"C. Zalka, “Grover’s quantum searching algorithm is
optimal,†Physical Review A, vol. 60, pp. 2746-2751,
1999.".
[HQC] "HQC", n.d., <http://pqc-hqc.org/>.
[I-D.draft-bonnell-lamps-chameleon-certs]
Bonnell, C., Gray, J., Hook, D., Okubo, T., and M.
Ounsworth, "A Mechanism for Encoding Differences in Paired
Certificates", Work in Progress, Internet-Draft, draft-
bonnell-lamps-chameleon-certs-05, 21 October 2024,
<https://datatracker.ietf.org/doc/html/draft-bonnell-
lamps-chameleon-certs-05>.
[I-D.draft-connolly-cfrg-xwing-kem]
Connolly, D., Schwabe, P., and B. Westerbaan, "X-Wing:
general-purpose hybrid post-quantum KEM", Work in
Progress, Internet-Draft, draft-connolly-cfrg-xwing-kem-
06, 21 October 2024,
<https://datatracker.ietf.org/doc/html/draft-connolly-
cfrg-xwing-kem-06>.
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[I-D.draft-ietf-lake-edhoc]
Selander, G., Mattsson, J. P., and F. Palombini,
"Ephemeral Diffie-Hellman Over COSE (EDHOC)", Work in
Progress, Internet-Draft, draft-ietf-lake-edhoc-23, 22
January 2024, <https://datatracker.ietf.org/doc/html/
draft-ietf-lake-edhoc-23>.
[I-D.draft-ietf-pquip-hybrid-signature-spectrums]
Bindel, N., Hale, B., Connolly, D., and F. D, "Hybrid
signature spectrums", Work in Progress, Internet-Draft,
draft-ietf-pquip-hybrid-signature-spectrums-06, 9 January
2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
pquip-hybrid-signature-spectrums-06>.
[I-D.draft-ounsworth-cfrg-kem-combiners]
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,
<https://datatracker.ietf.org/doc/html/draft-ounsworth-
cfrg-kem-combiners-05>.
[I-D.hale-mls-combiner]
Joël, Hale, B., Mularczyk, M., and X. Tian, "Flexible
Hybrid PQ MLS Combiner", Work in Progress, Internet-Draft,
draft-hale-mls-combiner-01, 26 September 2024,
<https://datatracker.ietf.org/doc/html/draft-hale-mls-
combiner-01>.
[I-D.ietf-lamps-cert-binding-for-multi-auth]
Becker, A., Guthrie, R., and M. J. Jenkins, "Related
Certificates for Use in Multiple Authentications within a
Protocol", Work in Progress, Internet-Draft, draft-ietf-
lamps-cert-binding-for-multi-auth-06, 10 December 2024,
<https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
cert-binding-for-multi-auth-06>.
[I-D.ietf-lamps-cms-sphincs-plus]
Housley, R., Fluhrer, S., Kampanakis, P., and B.
Westerbaan, "Use of the SLH-DSA Signature Algorithm in the
Cryptographic Message Syntax (CMS)", Work in Progress,
Internet-Draft, draft-ietf-lamps-cms-sphincs-plus-19, 13
January 2025, <https://datatracker.ietf.org/doc/html/
draft-ietf-lamps-cms-sphincs-plus-19>.
[I-D.ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B.
Westerbaan, "Internet X.509 Public Key Infrastructure:
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Algorithm Identifiers for ML-DSA", Work in Progress,
Internet-Draft, draft-ietf-lamps-dilithium-certificates-
07, 2 February 2025,
<https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
dilithium-certificates-07>.
[I-D.ietf-lamps-pq-composite-sigs]
Ounsworth, M., Gray, J., Pala, M., Klaußner, J., and S.
Fluhrer, "Composite ML-DSA For use in X.509 Public Key
Infrastructure and CMS", Work in Progress, Internet-Draft,
draft-ietf-lamps-pq-composite-sigs-03, 21 October 2024,
<https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
pq-composite-sigs-03>.
[I-D.ietf-pquip-pqt-hybrid-terminology]
D, F., P, M., and B. Hale, "Terminology for Post-Quantum
Traditional Hybrid Schemes", Work in Progress, Internet-
Draft, draft-ietf-pquip-pqt-hybrid-terminology-06, 10
January 2025, <https://datatracker.ietf.org/doc/html/
draft-ietf-pquip-pqt-hybrid-terminology-06>.
[I-D.ietf-tls-hybrid-design]
Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid key
exchange in TLS 1.3", Work in Progress, Internet-Draft,
draft-ietf-tls-hybrid-design-12, 14 January 2025,
<https://datatracker.ietf.org/doc/html/draft-ietf-tls-
hybrid-design-12>.
[I-D.irtf-cfrg-bbs-signatures]
Looker, T., Kalos, V., Whitehead, A., and M. Lodder, "The
BBS Signature Scheme", Work in Progress, Internet-Draft,
draft-irtf-cfrg-bbs-signatures-07, 23 September 2024,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
bbs-signatures-07>.
[KEEPINGUP]
"Keeping Up with the KEMs: Stronger Security Notions for
KEMs and automated analysis of KEM-based protocols", n.d.,
<https://eprint.iacr.org/2023/1933>.
[KyberSide]
"A Side-Channel Attack on a Hardware Implementation of
CRYSTALS-Kyber", <https://eprint.iacr.org/2022/1452>.
[LattFail1]
"Decryption Failure Attacks on IND-CCA Secure Lattice-
Based Schemes", <https://link.springer.com/
chapter/10.1007/978-3-030-17259-6_19#chapter-info>.
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[LattFail2]
"(One) Failure Is Not an Option: Bootstrapping the Search
for Failures in Lattice-Based Encryption Schemes.",
<https://link.springer.com/
chapter/10.1007/978-3-030-45727-3_1>.
[LatticeSide]
"Generic Side-channel attacks on CCA-secure lattice-based
PKE and KEM schemes", <https://eprint.iacr.org/2019/948>.
[LIBOQS] "LibOQS - Open Quantum Safe",
<https://github.com/open-quantum-safe/liboqs>.
[Lyu09] "V. Lyubashevsky, “Fiat-Shamir With Aborts: Applications
to Lattice and Factoring-Based Signatures“, ASIACRYPT
2009", <https://www.iacr.org/archive/
asiacrypt2009/59120596/59120596.pdf>.
[Mitigate1]
"POLKA: Towards Leakage-Resistant Post-Quantum CCA-Secure
Public Key Encryption",
<https://eprint.iacr.org/2022/873>.
[Mitigate2]
"Leakage-Resilient Certificate-Based Authenticated Key
Exchange Protocol",
<https://ieeexplore.ieee.org/document/9855226>.
[Mitigate3]
"Post-Quantum Authenticated Encryption against Chosen-
Ciphertext Side-Channel Attacks",
<https://eprint.iacr.org/2022/916>.
[ML-DSA] "FIPS-204: Module-Lattice-Based Digital Signature
Standard", <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.204.pdf>.
[ML-KEM] "FIPS-203: Module-Lattice-based Key-Encapsulation
Mechanism Standard",
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.203.pdf>.
[NIST] "Post-Quantum Cryptography Standardization",
<https://csrc.nist.gov/projects/post-quantum-cryptography/
post-quantum-cryptography-standardization>.
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[NISTFINAL]
"NIST Releases First 3 Finalized Post-Quantum Encryption
Standards", n.d., <https://www.nist.gov/news-
events/news/2024/08/nist-releases-first-3-finalized-post-
quantum-encryption-standards>.
[OQS] "Open Quantum Safe Project", n.d.,
<https://openquantumsafe.org/>.
[PQCAPI] "PQC - API notes",
<https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-
Cryptography/documents/example-files/api-notes.pdf>.
[PQRSA] "Post-quantum RSA", April 2017,
<https://cr.yp.to/papers/pqrsa-20170419.pdf>.
[PQUIP-WG] "Post-Quantum Use In Protocols (pquip) Working Group",
n.d.,
<https://datatracker.ietf.org/group/pquip/documents/>.
[QC-DNS] "Quantum Computing and the DNS",
<https://www.icann.org/octo-031-en.pdf>.
[RFC4033] Arends, R., Austein, R., Larson, M., Massey, D., and S.
Rose, "DNS Security Introduction and Requirements",
RFC 4033, DOI 10.17487/RFC4033, March 2005,
<https://www.rfc-editor.org/rfc/rfc4033>.
[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
<https://www.rfc-editor.org/rfc/rfc5652>.
[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/rfc/rfc6090>.
[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/rfc/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/rfc/rfc8446>.
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[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/rfc/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/rfc/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/rfc/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/rfc/rfc9370>.
[RSA] "A Method for Obtaining Digital Signatures and Public-Key
Cryptosystems+",
<https://dl.acm.org/doi/pdf/10.1145/359340.359342>.
[RSA10SC] "Breaking RSA Encryption - an Update on the State-of-the-
Art", <https://www.quintessencelabs.com/blog/breaking-rsa-
encryption-update-state-art>.
[RSA8HRS] "How to factor 2048 bit RSA integers in 8 hours using 20
million noisy qubits", <https://arxiv.org/abs/1905.09749>.
[RSAShor] "Circuit for Shor’s algorithm using 2n+3 qubits",
<https://arxiv.org/pdf/quant-ph/0205095.pdf>.
[SaberSide]
"A side-channel attack on a masked and shuffled software
implementation of Saber",
<https://link.springer.com/article/10.1007/
s13389-023-00315-3>.
[SideCh] "Side-Channel Attacks on Lattice-Based KEMs Are Not
Prevented by Higher-Order Masking",
<https://eprint.iacr.org/2022/919>.
[SIDH-Attack]
"An efficient key recovery attack on SIDH", n.d.,
<https://eprint.iacr.org/2022/975.pdf>.
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[SIKE] "SIKE – Supersingular Isogeny Key Encapsulation", n.d.,
<https://sike.org/>.
[SLH-DSA] "FIPS-205: Stateless Hash-Based Digital Signature
Standard", <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.205.pdf>.
[SP-1800-38C]
"Migration to Post-Quantum Cryptography Quantum Readiness:
Quantum-Resistant Cryptography Technology Interoperability
and Performance Report",
<https://www.nccoe.nist.gov/sites/default/files/2023-12/
pqc-migration-nist-sp-1800-38c-preliminary-draft.pdf>.
[SP-800-56C]
"Recommendation for Key-Derivation Methods in Key-
Establishment Schemes",
<https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-56Cr2.pdf>.
[Threat-Report]
"Quantum Threat Timeline Report 2020",
<https://globalriskinstitute.org/publications/quantum-
threat-timeline-report-2020/>.
Acknowledgements
This document leverages text from an earlier 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, 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
Munich
Germany
Email: aritra.banerjee@nokia.com
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Tirumaleswar Reddy
Nokia
Bangalore
Karnataka
India
Email: kondtir@gmail.com
Dimitrios Schoinianakis
Nokia
Athens
Greece
Email: dimitrios.schoinianakis@nokia-bell-labs.com
Timothy Hollebeek
DigiCert
Pittsburgh,
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@entrust.com
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