jubjub/README.md

jubjub

This is a pure Rust implementation of the Jubjub elliptic curve group and its associated fields.

• This implementation has not been reviewed or audited. Use at your own risk.
• This implementation targets Rust 1.28 or later.
• This crate is #![no_std] and so does not require the standard library.
• All operations are constant-time unless explicitly noted.

Documentation

Curve Description

Jubjub is the twisted Edwards curve -x^2 + y^2 = 1 + d.x^2.y^2 of rational points over GF(q) with a subgroup of prime order r and cofactor 8.

q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
r = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
d = -(10240/10241)

The choice of GF(q) is made to be the scalar field of the BLS12-381 elliptic curve group.

Jubjub is birationally equivalent to a Montgomery curve y^2 = x^3 + Ax^2 + x over the same field with A = 40962. This value of A is the smallest integer such that (A - 2) / 4 is a small integer, A^2 - 4 is nonsquare in GF(q), and the Montgomery curve and its quadratic twist have small cofactors 8 and 4, respectively. This is identical to the relationship between Curve25519 and ed25519.

Please see ./doc/evidence/ for supporting evidence that Jubjub meets the SafeCurves criteria. The tool in ./doc/derive/ will derive the curve parameters via the above criteria to demonstrate rigidity.

License

Licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.