Documentation available here.
This library provides a fast implementation of:
- operations over the scalar field
- operations over the groups G1 and G2, 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
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 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 to1
ify
is lexicographically larger than-y
.
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.
dune runtest
To get the coverage:
dune runtest --instrument-with bisect_ppx --force
bisect-ppx-report html
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
opam install odoc
dune build @doc