rajeshrk18 / cheetah

A STARK-friendly elliptic curve defined over a sextic extension of a small prime field.

Cheetah 🐆

This crate provides an implementation of the Cheetah curve over a sextic extension of the prime field Fp, with p = 2⁶⁴ - 2³² + 1.

• This implementation can be made no_std by relying on the alloc crate instead.
• Arithmetic operations are all constant time unless "_vartime" is explicited mentioned

WARNING: This is an ongoing, prototype implementation subject to changes. In particular, it has not been audited and may contain bugs and security flaws. This implementation is NOT ready for production use.

Features

• std (on by default): Enables use of the Rust standard library.
• serialize (on by default): Enables Serde serialization.

Description

Cheetah is a STARK-friendly elliptic curve defined over a sextic extension of Fp, p = 2⁶⁴ - 2³² + 1 defined by E: y^2 = x^3 + x + B with B = u + 395 where

• u^6 - 7 = 0 is the polynomial defining Fp6 / Fp

Cheetah defines a subgroup G of prime order

q = 55610362957290864006699123731285679659474893560816383126640993521607086746831

of 255-bits.

The extension Fp6 has been specifically constructed with a sparse polynomial of the form X^6 - A, where A is a small quadratic and cubic non-residue. The current implementation may however not be fully optimal with respect to the number of multiplications in the base field.

The Cheetah curve has been generated with the Sagemath utility script sextic_search.sage available here.

Curve security

Elliptic curves based on extension fields may suffer from specific attacks that do not apply to common elliptic curves constructed over large prime fields and may outperform regular Pollard-Rho attacks, and hence require more scrutiny when evaluating their estimated security level. To verify the security level of Cheetah against generic attacks as well as cover and decomposition attacks, please use the Sagemath utility script verify.sage available here.

License

Licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.