https://github.com/nccgroup/pasta-curves

Provides the Pasta curves: Pallas, Vesta and their field elements Fp and Fq.
https://github.com/nccgroup/pasta-curves

cryptography elliptic-curve-cryptography elliptic-curves

Last synced: 6 days ago
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Provides the Pasta curves: Pallas, Vesta and their field elements Fp and Fq.

• Host: GitHub
• URL: https://github.com/nccgroup/pasta-curves
• Owner: nccgroup
• License: mit
• Created: 2022-05-19T17:50:07.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2023-12-29T20:42:42.000Z (11 months ago)
• Last Synced: 2024-04-14T07:57:56.687Z (7 months ago)
• Topics: cryptography, elliptic-curve-cryptography, elliptic-curves
• Language: Haskell
• Homepage:
• Size: 63.5 KB
• Stars: 3
• Watchers: 9
• Forks: 4
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • Changelog: CHANGELOG.md
  • License: LICENSE

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README

        
# pasta-curves

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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"](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/).

The reference Rust implementation (which inspired this implementation) 

can be found at: .

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}

~~~

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Copyright 2022 Eric Schorn; Licensed under the MIT License.