#curve #elliptic-curve #cycle #field #pasta #pallas #vesta

no-std pasta_curves

Implementation of the Pallas and Vesta (Pasta) curve cycle

12 releases

0.5.1 Mar 2, 2023
0.5.0 Dec 6, 2022
0.4.1 Oct 13, 2022
0.4.0 May 4, 2022
0.0.0 Mar 3, 2021

#1411 in Magic Beans

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86,571 downloads per month
Used in 92 crates (27 directly)


3.5K SLoC


This crate provides an implementation of the Pasta elliptic curve constructions, Pallas and Vesta. More details about the Pasta curves can be found in this blog post.


Minimum Supported Rust Version

Requires Rust 1.56 or higher.

Minimum supported Rust version can be changed in the future, but it will be done with a minor version bump.

Curve Descriptions

  • Pallas: y2 = x3 + 5 over GF(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001).

  • Vesta: y2 = x3 + 5 over GF(0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001).

The Pasta curves form a cycle with one another: the order of each curve is exactly the base field of the other. This property is critical to the efficiency of recursive proof systems. They are designed to be highly 2-adic, meaning that a large power-of-two multiplicative subgroup exists in each field. This is important for the performance of polynomial arithmetic over their scalar fields and is essential for protocols similar to PLONK.

These curves can be reproducibly obtained using a curve search utility we’ve published.


Licensed under either of

at your option.


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.


~16K SLoC