Warning This implementation is not yet audited. If you consider using it in production, be careful !

sphincs

SPHINCS+: Stateless Hash-based Digital Signature Algorithm

Introduction

SPHINCS+ is one of those post-quantum digital signature algorithms ( DSA ), which is selected by NIST for standardization. Quoting directly from SPHINCS+ specification

SPHINCS+ is probably the most conservative design of a post-quantum signature scheme, on the other hand, it is rather inefficient in terms of signature size and speed.

SPHINCS+ builds on SPHINCS with various improvements. I suggest you read section 1.1 of the specification.

SPHINCS+ DSA offers following three APIs

keygen: Computes random keypair where secret key is 4n -bytes and public key is 2n -bytes | n = security parameter ( in bytes )

Note

SPHINCS+ secret key holds a copy of public key, which is used when signing messages.

sign: Given M ( > 0 ) -bytes message, SPHINCS+ secret key ( of 4n -bytes ) is used for signing message, by default deterministically. Though one might specifically ask for randomized signing, which will produce random signatures for same message.
verify: Given M ( > 0 ) -bytes message and SPHINCS+ signature, it uses SPHINCS+ public key ( of 2n -bytes ) for verifying signature, returning boolean result. Truth value is returned if signature is successfully verified.

Here I'm maintaining SPHINCS+ as zero-dependency, header-only and easy-to-use C++ library, which implements SPHINCS+-SHAKE key generation/ signing/ verification algorithms, for all parameter sets ( encompassing NIST security levels {1, 3, 5} ), as suggested in section 7.2 and table 3 of the specification.

Find the SPHINCS+ specification here, which was followed during this work.

sha3 is the only dependency of this project, which itself is a zero-dependency, header-only C++ library, implementing SHA3 specification of NIST ( i.e. FIPS PUB 202 ). This is done in order to modularize commonly seen symmetric key dependency in post-quantum cryptographic constructions.

sha3 is pinned to specific commit, using git submodule. See usage below in order to understand how to use SPHINCS+ in your project.

Follow progress of NIST PQC standardization effort here.

Prerequisites

A C++ compiler with C++20 standard library support such as g++ or clang++

$ clang++ --version
Ubuntu clang version 14.0.0-1ubuntu1
Target: aarch64-unknown-linux-gnu
Thread model: posix
InstalledDir: /usr/bin

$ g++ --version
g++ (Ubuntu 11.2.0-19ubuntu1) 11.2.0

System development utilities such as make, cmake & git

$ make --version
GNU Make 4.3

$ cmake --version
cmake version 3.22.1

$ git --version
git version 2.34.1

For benchmark you'll need to have google-benchmark installed. I found this installation guide helpful.
sha3: a zero-dependency, header-only C++ library, is the only dependency of this project, which is pinned to specific git commit, using git submodule. Import Sha3 after cloning SPHINCS+ repository.

git clone https://github.com/itzmeanjan/sphincs.git
cd sphincs
git submodule update --init

# now you can {test, benchmark, use} SPHINCS+

Testing

For ensuring that SPHINCS+ implementation is functionally correct and compliant with specification, you may issue

Note

This implementation of SPHINCS+ specification is tested to be compatible and conformant with latest version of the specification. That's ensured by generating known answer tests ( KATs ) following https://gist.github.com/itzmeanjan/d483872509b8a1a7c4d6614ec9d43e6c and testing this implementation using those test vectors.

make

[test] WOTS+ one-time signature
[test] Fixed Input-Length XMSS signature
[test] HyperTree signature
[test] FORS signature
[test] SPHINCS+ signature
bash test_kat.sh
clang++ -std=c++20 -Wall -Wextra -pedantic -O3 -march=native -I ./include -I ./sha3/include -fPIC --shared wrapper/sphincs+-shake.cpp -o wrapper/libsphincs+-shake.so
~/Documents/work/sphincs/wrapper/python ~/Documents/work/sphincs
=========================================================================================== test session starts ============================================================================================
platform darwin -- Python 3.10.8, pytest-7.1.3, pluggy-1.0.0 -- /usr/local/opt/python@3.10/bin/python3.10
cachedir: .pytest_cache
benchmark: 3.4.1 (defaults: timer=time.perf_counter disable_gc=False min_rounds=5 min_time=0.000005 max_time=1.0 calibration_precision=10 warmup=False warmup_iterations=100000)
rootdir: /Users/anjan/Documents/work/sphincs/wrapper/python
plugins: benchmark-3.4.1
collected 12 items

test_sphincs_shake.py::test_sphincs_shake_128s_robust PASSED                                                                                                                                         [  8%]
test_sphincs_shake.py::test_sphincs_shake_128s_simple PASSED                                                                                                                                         [ 16%]
test_sphincs_shake.py::test_sphincs_shake_128f_robust PASSED                                                                                                                                         [ 25%]
test_sphincs_shake.py::test_sphincs_shake_128f_simple PASSED                                                                                                                                         [ 33%]
test_sphincs_shake.py::test_sphincs_shake_192s_robust PASSED                                                                                                                                         [ 41%]
test_sphincs_shake.py::test_sphincs_shake_192s_simple PASSED                                                                                                                                         [ 50%]
test_sphincs_shake.py::test_sphincs_shake_192f_robust PASSED                                                                                                                                         [ 58%]
test_sphincs_shake.py::test_sphincs_shake_192f_simple PASSED                                                                                                                                         [ 66%]
test_sphincs_shake.py::test_sphincs_shake_256s_robust PASSED                                                                                                                                         [ 75%]
test_sphincs_shake.py::test_sphincs_shake_256s_simple PASSED                                                                                                                                         [ 83%]
test_sphincs_shake.py::test_sphincs_shake_256f_robust PASSED                                                                                                                                         [ 91%]
test_sphincs_shake.py::test_sphincs_shake_256f_simple PASSED                                                                                                                                         [100%]

===================================================================================== 12 passed in 1275.34s (0:21:15) ======================================================================================
~/Documents/work/sphincs

Benchmarking

Find micro-benchmarking ( using google-benchmark ) results here.

Usage

sphincs is a zero-dependency, header-only C++ library which is pretty easy to use. To get started

Clone SPHINCS+ repository
Fetch sha3 dependency, by enabling git submodule

pushd sphincs
git submodule update --init
popd

Write program which makes use of SPHINCS+ {keygen, signing, verification} API ( all of these routines live under sphincs:: namespace ), while importing include/sphincs.hpp and correctly parameterizing invoked functions so that you use desired SPHINCS+ instance, among recommended variants.

Note

C++ compile-time checks are in-place to ensure that you only use SPHINCS+ parameter sets which are suggested in the specification ( it's linked below ). See utils.hpp to understand how it's done using constexpr requirements.

Finally compile your program, while letting your compiler know where it can find SPHINCS+ and Sha3 headers.

Note

For recommended parameter sets, find table 3 of SPHINCS+ specification.

SPHINCS+-SHAKE API Usage Flow

Generate new keypair
Sign non-empty message using secret key
Verify signature using message and public key

Step	Header	Namespace	Routine	Input(s)	Output(s)
Key Generation	sphincs.hpp	`sphincs::`	`keygen<n, h, d, w, v>(skey, pkey)`	-	4n -bytes secret key, 2n -bytes public key
Signing	sphincs.hpp	`sphincs::`	`sign<n, h, d, a, k, w, v, randomize = false>(msg, mlen, skey, sig)`	mlen -bytes message and 4n -bytes secret key	(1 + k * (a + 1) + h + d * len) * n -bytes signature
Verification	sphincs.hpp	`sphincs::`	`verify<n, h, d, a, k, w, v>(msg, mlen, sig, pkey)`	mlen -bytes message, (1 + k * (a + 1) + h + d * len) * n -bytes signature and 2n -bytes public key	Boolean value, denoting successful verification by returning truth value

Here's an example program which demonstrates how to

Compute ( at compile-time ) how much memory to allocate for public key, secret key and signature, based on chosen parameter set

Note

Utility routines live under namespace sphincs_utils::, in header utils.hpp. You won't probably need to import it seperately, it becomes available with inclusion of sphincs.hpp.

Generate new keypair, using system randomness
Sign random 32 -bytes message, using secret key
Verify signature using message and public key

for SPHINCS+-SHAKE-128s-robust parameter set. It can be adapted for other parameter sets fairly easily.

pushd example; g++ -std=c++20 -Wall -O3 -I ../include -I ../sha3/include sphincs+-shake.cpp && ./a.out; popd

SPHINCS+-SHAKE-128s-robust @ NIST Security Level 1
Secret Key   : 49a5ca3d5f151f2c9c0f197d324724c9c2313bdb69720a1bc615434b4874ba41949e000ab275dd6da569ff32757c021586eb2036e1ba14483e809ffa0c5505f5
Public Key   : 949e000ab275dd6da569ff32757c021586eb2036e1ba14483e809ffa0c5505f5
Message      : 80bce832fab336eefdceef28ab89838667d164d255298fe888344760199a8c3c
Signature    : 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
Verified      : true

Find the example program here, demonstrating keygen/ sign/ verify API usage.

itzmeanjan / sphincs

sphincs

Introduction

Prerequisites

Testing

Benchmarking

Usage

SPHINCS+-SHAKE API Usage Flow

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