# jubjub [](https://crates.io/crates/jubjub) #
<img
width="15%"
align="right"
src="https://raw.githubusercontent.com/zcash/zips/master/protocol/jubjub.png"/>
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 `1.36` or later.
* All operations are constant time unless explicitly noted.
* This implementation does not require the Rust standard library.
## [Documentation](https://docs.rs/jubjub)
## Curve Description
Jubjub is the [twisted Edwards curve](https://en.wikipedia.org/wiki/Twisted_Edwards_curve) `-u^2 + v^2 = 1 + d.u^2.v^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 construction.
Jubjub is birationally equivalent to a [Montgomery curve](https://en.wikipedia.org/wiki/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/](./doc/evidence/) for supporting evidence that Jubjub meets the [SafeCurves](https://safecurves.cr.yp.to/index.html) criteria. The tool in [./doc/derive/](./doc/derive/) will derive the curve parameters via the above criteria to demonstrate rigidity.
## Acknowledgements
Jubjub was designed by Sean Bowe. Daira Hopwood is responsible for its name and specification. The security evidence in [./doc/evidence/](./doc/evidence/) is the product of Daira Hopwood and based on SafeCurves by Daniel J. Bernstein and Tanja Lange. Peter Newell and Daira Hopwood are responsible for the Jubjub bird image.
Please see `Cargo.toml` for a list of primary authors of this codebase.
## License
Licensed under either of
* Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
* MIT license ([LICENSE-MIT](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.