54 lines
2.7 KiB
Markdown
54 lines
2.7 KiB
Markdown
# jubjub [](https://crates.io/crates/jubjub) #
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<img
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width="15%"
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align="right"
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src="https://raw.githubusercontent.com/zcash/zips/master/protocol/jubjub.png"/>
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This is a pure Rust implementation of the Jubjub elliptic curve group and its associated fields.
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* **This implementation has not been reviewed or audited. Use at your own risk.**
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* This implementation targets Rust `1.36` or later.
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* All operations are constant time unless explicitly noted.
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* This implementation does not require the Rust standard library.
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## [Documentation](https://docs.rs/jubjub)
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## Curve Description
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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`.
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```
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q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
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r = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
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d = -(10240/10241)
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```
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The choice of `GF(q)` is made to be the scalar field of the BLS12-381 elliptic curve construction.
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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.
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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.
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## Acknowledgements
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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.
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Please see `Cargo.toml` for a list of primary authors of this codebase.
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## License
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Licensed under either of
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* Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
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* MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
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at your option.
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### Contribution
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Unless you explicitly state otherwise, any contribution intentionally
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submitted for inclusion in the work by you, as defined in the Apache-2.0
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license, shall be dual licensed as above, without any additional terms or
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conditions.
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