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
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
Both instantiations, i.e. the one minimizing the public key size and the one
minimizing the signature size, are provided.
The scalar field is
Fr = GF(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001), encoded on 32 bytes in little endian.
For G1, the base field is
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 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
lexicographically larger than
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.
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.
To get the coverage:
dune runtest --instrument-with bisect_ppx --force bisect-ppx-report html
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
>= "0.6.0" & < "0.7.0" & with-test
with-test & >= "2.5"
>= "1.10" & < "2.0"
>= "0.6.1" & < "0.7.0"