SQISign: compact post-quantum signatures from quaternions and isogenies

This code implements the original version of the isogeny-based signature scheme SQISign. For details see this paper.

An updated and optimized version can be found here.

(C) 2020, The SQISign team. MIT license.

Dependencies

The code depends on the latest stable version of the PARI/GP library, 2.11.4.

The code has an optional dependency on GMP, which is also an optional dependency of PARI/GP and is typically installed along with it.

Supported platforms

The code compiles and runs on Linux and MacOS.

It contains two implementations of the low-level arithmetic functions:

• One based on handwritten assembly for the x86-64 platform, starting from Broadwell architectures.

• One based on GMP.

By default, both versions are compiled and tested.

Compile

To compile and test the code, run

make
make check

The tests typically take 2-3 minutes.

To only compile and test the assembly version:

make asm
make check_asm

To only compile and test the GMP version:

make gmp
make check_gmp

Tuning

The algorithms have already been tuned on a modern processors, and the default values should be fine. However, should you wish to fine-tune for your machine, run:

make tune
make

Be patient, tuning takes several minutes.

Run benchmarks

To run benchmarks type

make benchmark

Allow a few minutes for the benchmarks to complete. This produces files named bench_xxx.tsv containing timing information on the various parts of the signature.

By default, only benchmarks for the assembly version are produced. If you want benchmarks for the GMP version, run

make benchmark_gmp

Timings

The following are timings (medians) obtained running the benchmarks above on an Intel Core i7-6700 CPU @ 3.40GHz with Turbo Boost disabled.

	Mcycles	ms
keygen	1,959	575
sign	7,767	2,279
verify	142	42