# pasta-curves

This Haskell library provides the Pasta Curves consisting of: the `Pallas`

curve and its `Fp`

field element, the `Vesta`

curve and its `Fq`

field
element, and a variety of supporting functionality such as point/element
arithmetic, serialization, and hash-to-curve. The algorithms are NOT constant
time.

Pallas is y2 = x3 + 5 over Fp(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001).
The order of the Pallas curve is 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001.

Vesta is y2 = x3 + 5 over Fq(0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001).
The order of the Vesta curve is 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001.

The curves are designed such that the order of one matches the field
characteristic of the other. For a brief introduction, see the Zcash blog
titled “The Pasta Curves for Halo 2 and Beyond”.
The reference Rust implementation (which inspired this implementation)
can be found at: https://github.com/zcash/pasta_curves.

Example usage of this library implementation:

```
$ cabal repl
ghci> a = 9 :: Fp
ghci> a*a
0x0000000000000000000000000000000000000000000000000000000000000051
ghci> pointMul a base :: Vesta
Projective {_px = 0x3CDC6A090F2BB3B52714C083929B620FE24ADBCBBD420752108CD7C29E543E5E,
_py = 0x08795CD330B3CE5AA63BD2B18DE155AE3C96E8AF9DA2CC742C6BA1464E490161,
_pz = 0x1FA26F58F3A641ADFE81775D3D53378D6178B6CCBF14F9BD4AB5F10DEE28D878}
```

Copyright 2022 Eric Schorn; Licensed under the MIT License.