Published: 15 Feb 2022
OCaml implementation of BLS12-381
The scalar field is
Fr = GF(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001), encoded on 32 bytes in little endian.
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
y encoded in big endian.
The « compressed » form uses the first 3 most significant (and unused) bits of the coordinate
the first most significant bit is always set to
1to carry the information it is the compressed encoding of a point.
the second most significant bit is set to
1if the element is the identity of the curve.
the third most significant bit is the sign of
y. It is set to
yis lexicographically larger than
# if you implement a library and you don't need an actual implementation opam install bls12-381 # to target UNIX opam install bls12-381-unix
By default, if the architecture supports ADX,
bls12-381-unix 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-unix
will instruct to build bls12-381-unix 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-unix will be compiled without ADX opcodes.
To get the coverage:
dune runtest --instrument-with bisect_ppx --force bisect-ppx-report html
How to use in my project
If you are developing a library using
bls12-381, you only need to add
bls12-381 in the dependency list. However, if you are writing a binary, three packages are relevant:
bls12-381-unix: to be used for UNIX
Run the benchmarks
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
opam install odoc dune build @doc