Caution

This ML-DSA implementation is conformant with ML-DSA standard @ https://doi.org/10.6028/NIST.FIPS.204. I also try to make it timing leakage free, but be informed that this implementation is not yet audited. If you consider using it in production, be careful !

ML-DSA (formerly known as Dilithium)

Module-Lattice-Based Digital Signature Standard by NIST i.e. FIPS 204.

Motivation

ML-DSA has been standardized by NIST as post-quantum secure digital signature algorithm (DSA), which can be used for verifying the authenticity of digital messages, giving recipient party confidence that the message indeed came from the known sender. ML-DSA's security is based on hardness of finding short vectors in lattice i.e. it's a lattice-based Post Quantum Cryptographic (PQC) construction.

ML-DSA offers following three algorithms.

Algorithm	What does it do ?
KeyGen	It takes a 32 -bytes seed, which is used for deterministically computing a ML-DSA keypair i.e. both public key and secret key.
Sign	It takes a 32 -bytes seed, a ML-DSA secret key, a N (>=0) -bytes message and an optional context (of max 255 -bytes) as input, producing ML-DSA signature bytes. For default and recommended hedged message signing, one must provide with 32B random seed. For deterministic message signing, one should simply fill seed with 32 zero bytes.
Verify	It takes a ML-DSA public key, N (>=0) -bytes message, an optional context (of max 255 -bytes) and ML-DSA signature, returning boolean value, denoting status of successful signature verification operation.

Here I'm maintaining ml-dsa as a C++20 header-only constexpr library, implementing NIST FIPS 204 ML-DSA, supporting ML-DSA-{44, 65, 87} parameter sets, as defined in table 1 of ML-DSA standard. For more details on using this library, see below. It shows following performance characteristics on desktop and server grade CPUs.

ML-DSA-65 Algorithm	Time taken on "12th Gen Intel(R) Core(TM) i7-1260P"	Time taken on "Raspberry Pi 4B"	Time taken on "AWS EC2 Instance c8g.large"
keygen	94.4 us	442.9 us	143 us
sign	115.7 us	2364.7 us	427 us
verify	98.5 us	492.1 us	151 us

Note

Find ML-DSA standard @ https://doi.org/10.6028/NIST.FIPS.204, which you should refer to when understanding intricate details of this implementation.

Caution

This implementation of ML-DSA doesn't yet implement "prehash" version i.e. where hashing of message can be outsourced to another cryptographic module and hash of the mesasge is signed instead of signing the original message.

Prerequisites

• A C++ compiler which can compiled C++20 program.

# I'm using
$ g++ --version
g++ (Ubuntu 14.2.0-4ubuntu2) 14.2.0

• Build utilities such as make, cmake.
• For testing correctness and compatibility of this ML-DSA implementation, you need to globally install google-test library and headers. Follow guide @ https://github.com/google/googletest/tree/main/googletest#standalone-cmake-project, if you don't have it installed.
• For benchmarking ML-DSA algorithms, you must have google-benchmark header and library globally installed. I found guide @ https://github.com/google/benchmark#installation helpful.

Note

If you are on a machine running GNU/Linux kernel and you want to obtain CPU cycle count for ML-DSA routines, you should consider building google-benchmark library with libPFM support, following https://gist.github.com/itzmeanjan/05dc3e946f635d00c5e0b21aae6203a7, a step-by-step guide. Find more about libPFM @ https://perfmon2.sourceforge.net.

Tip

Git submodule based dependencies will normally be imported automatically, but in case that doesn't work, you can manually initialize and update them by issuing $ git submodule update --init --recursive from inside the root of this repository.

Testing

For ensuring functional correctness of this library implementation of ML-DSA and conformance with the ML-DSA standard FIPS 204, issue following command.

Note

ML-DSA Known Answer Tests, living in this directory, are generated following the procedure, described in https://gist.github.com/itzmeanjan/d14afc3866b82119221682f0f3c9822d.

make test -j               # Run tests without any sort of sanitizers, with default C++ compiler.
CXX=clang++ make test -j   # Switch to non-default compiler, by setting variable `CXX`.

make debug_asan_test -j    # Run tests with AddressSanitizer enabled, with `-O1`.
make release_asan_test -j  # Run tests with AddressSanitizer enabled, with `-O3 -march=native`.
make debug_ubsan_test -j   # Run tests with UndefinedBehaviourSanitizer enabled, with `-O1`.
make release_ubsan_test -j # Run tests with UndefinedBehaviourSanitizer enabled, with `-O3 -march=native`.

PASSED TESTS (22/22):
       4 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth18
       4 ms: build/test/test.out ML_DSA.SampleInBallFor_ML_DSA_87
       4 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth3
       5 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth20
       5 ms: build/test/test.out ML_DSA.SampleInBallFor_ML_DSA_65
       5 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth13
       6 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth10
       6 ms: build/test/test.out ML_DSA.HintBitPolynomialEncodingDecodingFor_ML_DSA_65
       6 ms: build/test/test.out ML_DSA.HintBitPolynomialEncodingDecodingFor_ML_DSA_87
       6 ms: build/test/test.out ML_DSA.SampleInBallFor_ML_DSA_44
       7 ms: build/test/test.out ML_DSA.HintBitPolynomialEncodingDecodingFor_ML_DSA_44
       7 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth6
       8 ms: build/test/test.out ML_DSA.PolynomialEncodingDecodingWithSignificantBitWidth4
      15 ms: build/test/test.out ML_DSA.Power2Round
      40 ms: build/test/test.out ML_DSA.MakingAndUsingOfHintBits
     185 ms: build/test/test.out ML_DSA.ML_DSA_44_KnownAnswerTests
     285 ms: build/test/test.out ML_DSA.ML_DSA_65_KnownAnswerTests
     353 ms: build/test/test.out ML_DSA.ML_DSA_87_KnownAnswerTests
     904 ms: build/test/test.out ML_DSA.ArithmeticOverZq
   15794 ms: build/test/test.out ML_DSA.ML_DSA_44_KeygenSignVerifyFlow
   24303 ms: build/test/test.out ML_DSA.ML_DSA_65_KeygenSignVerifyFlow
   32317 ms: build/test/test.out ML_DSA.ML_DSA_87_KeygenSignVerifyFlow

Note

There is a help menu, which introduces you to all available commands; just run make from the root directory of this project.

Benchmarking

Warning

Relying only on average timing measurement for understanding performance characteristics of ML-DSA sign algorithm may not be a good idea, given that it's a post-quantum digital signature scheme of "Fiat-Shamir with Aborts" paradigm - simply put, during signing procedure it may need to abort and restart again, multiple times, based on what message is being signed or what random seed is being used for default hedged signing. So it's a better idea to also compute other statistics such as minimum, maximum and median ( pretty useful ) when timing execution of sign procedure. In following benchmark results, you'll see such statistics demonstrating broader performance characteristics of ML-DSA sign procedure for various parameter sets.

Benchmarking key generation, signing and verification algorithms for various instantiations of ML-DSA can be done, by issuing

make benchmark -j  # If you haven't built google-benchmark library with libPFM support.
make perf -j       # If you have built google-benchmark library with libPFM support.

Caution

Ensure you've put all CPU cores on performance mode, before running benchmarks, follow guide @ https://github.com/google/benchmark/blob/main/docs/reducing_variance.md.

On 12th Gen Intel(R) Core(TM) i7-1260P

Benchmark result in JSON format @ bench_result_on_Linux_6.11.0-9-generic_x86_64_with_g++_14.json.

On Raspberry Pi 4B

Benchmark result in JSON format @ bench_result_on_Linux_6.6.51+rpt-rpi-v8_aarch64_with_g++_12.json.

On AWS EC2 Instance c8g.large i.e. AWS Graviton4

Benchmark result in JSON format @ bench_result_on_Linux_6.8.0-1016-aws_aarch64_with_g++_13.json.

More about this EC2 instance @ https://aws.amazon.com/ec2/instance-types/c8g.

Usage

ml-dsa is a header-only C++20 constexpr library, mainly targeting 64 -bit desktop/ server grade platforms, which is also pretty easy to use. Let's see how to get started with it.

• Clone ml-dsa repository.

cd

# Single step cloning and importing of submodules
git clone https://github.com/itzmeanjan/ml-dsa.git --recurse-submodules
# Or clone and then run tests, which will automatically bring in dependencies
git clone https://github.com/itzmeanjan/ml-dsa.git && pushd ml-dsa && make test -j && popd

• Write a program which makes use of ML-DSA-{44, 65, 87} key generation, signing and verification API ( all of these functions and constants, representing how many bytes of memory to allocate for holding seeds, public/ secret key and signature, live under ml_dsa_{44,65,87}:: namespace ), while importing proper header files.

// main.cpp

// In case interested in using ML-DSA-65 or ML-DSA-87 API, import "ml_dsa_65.hpp" or "ml_dsa_87.hpp"
// and use keygen/ sign/ verify functions living either under `ml_dsa_65::` or `ml_dsa_87::` namespace.
#include "ml_dsa/ml_dsa_44.hpp"
#include "randomshake/randomshake.hpp"

int main() {
    // --- --- --- Key Generation --- --- ---

    std::array<uint8_t, ml_dsa_44::KeygenSeedByteLen> seed{};
    std::array<uint8_t, ml_dsa_44::PubKeyByteLen> pubkey{};
    std::array<uint8_t, ml_dsa_44::SecKeyByteLen> seckey{};

    randomshake::randomshake_t<128> csprng;
    csprng.generate(seed);

    ml_dsa_44::keygen(seed, pubkey, seckey);

    // --- --- --- Message Signing --- --- ---

    std::array<uint8_t, ml_dsa_44::SigningSeedByteLen> rnd{};
    std::array<uint8_t, ml_dsa_44::SigByteLen> sig{};

    // 32 -bytes randomness, for default and recommended *hedged* message signing.
    csprng.generate(rnd);
    // For deterministic message signing, uncomment following statement, while commenting above statement.
    // std::fill(rnd.begin(), rnd.end(), 0);

    constexpr size_t msg_byte_len = 32; // message byte length can be >= 0
    std::array<uint8_t, msg_byte_len> msg{};

    // Sample a psuedo-random message, to be signed.
    csprng.generate(msg);

    // Note, we're passing an empty context.
    const bool has_signed = ml_dsa_44::sign(rnd, seckey, msg, {}, sig);
    assert(has_signed);

    // --- --- --- Signature Verification --- --- ---

    const bool is_valid = ml_dsa_44::verify(pubkey, msg, {}, sig);
    assert(is_valid);

    return 0;
}

• Finally compile your program, while letting your compiler know where it can find ml-dsa and its dependency headers.

# Assuming `ml-dsa` was cloned just under $HOME

ML_DSA_HEADERS=~/ml-dsa/include
SHA3_HEADERS=~/ml-dsa/sha3/include
RANDOMSHAKE_HEADERS=~/ml-dsa/RandomShake/include

g++ -std=c++20 -Wall -Wextra -pedantic -O3 -march=native -I $ML_DSA_HEADERS -I $SHA3_HEADERS -I $RANDOMSHAKE_HEADERS main.cpp

ML-DSA Variant	Namespace	Header
ML-DSA-44 Routines	ml_dsa_44::	include/ml_dsa/ml_dsa_44.hpp
ML-DSA-65 Routines	ml_dsa_65::	include/ml_dsa/ml_dsa_65.hpp
ML-DSA-87 Routines	ml_dsa_87::	include/ml_dsa/ml_dsa_87.hpp

---

✨

All the functions, in this ML-DSA header-only library, are implemented as constexpr functions. Hence you should be able to evaluate ML-DSA key generation, signing and verification at compile-time itself, given that all inputs are known at compile-time, of course.

I present you with following demonstration program, which generates a ML-DSA-44 keypair, signs a message, producing a ML-DSA-44 signature and finally verifies the signature - all at program compile-time. Notice, the static assertion.

// compile_time_ml_dsa_44.cpp
//
// Compile and run this program with
// $ g++ -std=c++20 -Wall -Wextra -pedantic -fconstexpr-ops-limit=175000000 -I include -I sha3/include -I RandomShake/include compile_time_ml_dsa_44.cpp && ./a.out
// or
// $ clang++ -std=c++20 -Wall -Wextra -pedantic -fconstexpr-steps=30000000 -I include -I sha3/include -I RandomShake/include compile_time_ml_dsa_44.cpp && ./a.out

#include "ml_dsa/ml_dsa_44.hpp"

// Compile-time
//
// - Generation of a new keypair, given seed
// - Signing of a known message
// - Verification of signature
//
// for ML-DSA-44, using KAT no. (1). See kats/ml_dsa_44.kat.
constexpr auto
ml_dsa_44_keygen_sign_verify() -> auto
{
  // 7c9935a0b07694aa0c6d10e4db6b1add2fd81a25ccb148032dcd739936737f2d
  constexpr std::array<uint8_t, ml_dsa_44::KeygenSeedByteLen> ξ = { 124, 153, 53, 160, 176, 118, 148, 170, 12, 109, 16,  228, 219, 107, 26,  221, 47,  216, 26, 37,  204, 177, 72,  3,   45, 205, 115, 153, 54,  115, 127, 45 };
  // 0000000000000000000000000000000000000000000000000000000000000000
  constexpr std::array<uint8_t, ml_dsa_44::SigningSeedByteLen> rnd{};
  // d81c4d8d734fcbfbeade3d3f8a039faa2a2c9957e835ad55b22e75bf57bb556ac8
  constexpr std::array<uint8_t, 33> msg = { 216, 28,  77, 141, 115, 79,  203, 251, 234, 222, 61,  63, 138, 3,  159, 170, 42, 44,  153, 87, 232, 53,  173, 85,  178, 46,  117, 191, 87, 187, 85, 106, 200 };

  std::array<uint8_t, ml_dsa_44::PubKeyByteLen> pkey{};
  std::array<uint8_t, ml_dsa_44::SecKeyByteLen> skey{};
  std::array<uint8_t, ml_dsa_44::SigByteLen> sig{};

  ml_dsa_44::keygen(ξ, pkey, skey);
  ml_dsa_44::sign(rnd, skey, msg, {}, sig);
  return ml_dsa_44::verify(pkey, msg, {}, sig);
}

int
main()
{
  // Notice static_assert, yay !
  static_assert(ml_dsa_44_keygen_sign_verify() == true, "Must be able to generate a new keypair, sign a message and verify the signature at program compile-time !");
  return 0;
}

---

See example program, which demonstrates how to use ML-DSA-44 API, similarly you can use ML-DSA-{65, 87} API. Run the example by issuing

make example -j

ML-DSA-44 @ NIST security level 2
Seed      : afc6c351c70775e04b4ece579e72400afbb31fe8bad3d1d8ed0ba40526b0d528
Pubkey    : 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
Seckey    : 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Message   : 8a556fe4a5e29a37e80f2ad8f3f8679f1cd3f22b1532bd171373f76aa1402158
Signature : 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
Verified   : true

Note

Looking at the API documentation, in header files i.e. include/ml_dsa/ml_dsa_{44,65,87}.hpp, can give you a good idea of how to use ML-DSA API. Note, this library doesn't expose any raw pointer -based interface, rather almost everything is wrapped under statically defined std::span - which one can easily create from std::{array, vector}. I opt for using statically defined std::span -based function interfaces, because we always know, at compile-time, how many bytes the seeds/ keys/ signatures are, for various different ML-DSA instantiations. This gives much better type safety and compile-time error reporting.