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Cheetah curve:STARK友好的椭圆曲线

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2023-12-01

1. 引言

Toposware团队2022年论文《Security Analysis of Elliptic Curves over Sextic Extension of Small Prime Fields》,开源代码见:

Cheetah定位为STARK友好的椭圆曲线 y 2 = x 3 + x + B y^2=x^3+x+B y2=x3+x+B,其基域为:Goldilocks素数域( p = 2 64 − 2 32 + 1 p=2^{64}-2^{32}+1 p=264232+1)的sextic extension,其中:【该基域具有large two-adicity,适于FFT相关运算 以及 基于椭圆曲线的签名】

  • B = u + 395 B=u+395 B=u+395 u 6 − 7 = 0 u^6-7=0 u67=0为the polynomial defining Fp6/Fp

Cheetah定义了一个subgroup G G G,其prime order为:

  • q = 55610362957290864006699123731285679659474893560816383126640993521607086746831 q=55610362957290864006699123731285679659474893560816383126640993521607086746831 q=55610362957290864006699123731285679659474893560816383126640993521607086746831

参考资料

[1] Cheetah: A STARK-friendly elliptic curve for fast native and in-circuit computations

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