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
See below how to use in your project.
dune runtest dune build @test/js/browser/serve # Check _build/default/test/js/browser and run `npm run serve`
To get the coverage (only ok for bls12-381-unix and bls12-381-gen)
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
here, version >=
0.8.1, and suppose this module is loaded before in the global namespace under
test/js/browser/for an example. You need
to use the appropriate package depending on the platform you target (Node or a
bundler for the browser). For instance, if you target Node (resp. a bundler
like webpack for a browser usage), you must use
bls12-381-js-gen: if the module is loaded somewhere else than in the global
namespace like the previous package supposes, you can use this third library
that provides functors. The functors are expecting a module of the signature:
sig val rust_module : unit -> Jsoo_lib.ESModule.t val get_wasm_memory_buffer : unit -> Jsoo_lib.Memory.Buffer.t end
For more examples, see the test directories.
Run the benchmarks
opam install core_bench dune exec benchmark/bench_ec.exe dune exec benchmark/bench_ff.exe dune exec benchmark/bench_pairing.exe
opam install odoc dune build @doc
>= "1.10" & < "1.12"
>= "0.6.1" & < "0.7.0"