bls12-381

Implementation of BLS12-381 and some cryptographic primitives built on top of it
README

This library provides a fast implementation of:

  • operations over the scalar field, including (i)FFT.

  • operations over the groups G1 and G2, including EC-FFT, hash_to_curve as
    described in this
    specification

    and the pippenger algorithm for fast multi scalar exponentiation.

  • operations over the target group of the pairing (GT), written additively.

  • pairing from G1 x G2 to GT

  • BLS signatures described in this
    specification
    .
    Both instantiations, i.e. the one minimizing the public key size and the one
    minimizing the signature size, are provided.

  • an instantiation of
    Poseidon providing a security of
    128 bits. See the
    documentation

    for more information on the used parameters.

  • an instantiation of
    Rescue providing a security of
    128 bits. See the
    documentation

    for more information on the used parameters.

Encoding

Scalar

The scalar field is Fr = GF(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001), encoded on 32 bytes in little endian.

Groups

For G1, the base field is Fq: GF(0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab)
and E(Fq) := y^2 = x^3 + 4. An element of the base field can be encoded on 48 bytes (using only
381 bits, leaving 3 bits unused).

For G2, the base field is Fq2 := Fq[Z]/(X^2 + 1) and E(Fq2) := y^2 = x^3 + 4 (Z + 1). An element of the base field can be encoded on 2 * 48 bytes
representing each coefficient of the polynomial. 3 bits of each coefficient
encoding are unused.

The « uncompressed » form (x, y) of G1 and G2 is the concatenation of the elements x and y encoded in big endian.

The « compressed » form uses the first 3 most significant (and unused) bits of
the coordinate x.

  • the first most significant bit is always set to 1 to carry the information it
    is the compressed encoding of a point.

  • the second most significant bit is set to 1 if the element is the identity of the curve.

  • the third most significant bit is the sign of y. It is set to 1 if y is
    lexicographically larger than -y.

Install

opam install bls12-381

By default, if the architecture supports ADX, bls12-381 with be compiled using ADX
opcodes (giving optimisations up to 20% for some arithmetic operations). If you
don't want to build using ADX, you can add the environment variable
BLST_PORTABLE and set it to any value.
For instance,

BLST_PORTABLE=y opam install bls12-381

will instruct to build bls12-381 without ADX. This might be useful if you
build docker images on ADX machines but you need the image to be portable on
architecture not supporting ADX.

If the architecture does not support ADX, bls12-381 will be compiled without ADX opcodes.

Run tests

dune runtest

To get the coverage:

dune runtest --instrument-with bisect_ppx --force
bisect-ppx-report html

Run the benchmarks

Install core_bench:

opam install core_bench

See files listed in the directory benchmark and execute it with dune exec. For instance:

dune exec ./benchmark/bench_fr.exe

Documentation

opam install odoc
dune build @doc
Install
Sources
ocaml-bls12-381-3.0.3.tar.bz2
md5=367dcf0ed22d785fd521b838082fa60d
sha512=dd801c6c642f61191762df0619a9e4a05524b7b85b2cd1bd8ddcfebfe78fca39be571c8b6552d91d3ae149683948a577d08e3f896d688ca6aad0ed5dd15e5799
Dependencies
ff-pbt
>= "0.6.0" & < "0.7.0" & with-test
bisect_ppx
with-test & >= "2.5"
alcotest
with-test
hex
>= "1.3.0"
zarith
>= "1.10" & < "2.0"
ff-sig
>= "0.6.1" & < "0.7.0"
dune
>= "2.8.4"
ocaml
>= "4.08"
Reverse Dependencies