# GF(3n)椭圆曲线快速算法研究Research on Fast Algorithms of Elliptic Curve over GF(3n)

Abstract: GF(3n) , as a more special type field of GF(3n) , the elliptic curve cryptosystem based on which has their own advantages. As we know, reducing the operation of inverse is an important method in elliptic curve cryptography fast calculation. It requires 2k times inversions on elliptic curves over GF(3n) to compute scalar multiplication 3kp by individual computation. This paper deduces a formula of calculating 3kp directly based upon the idea of recursive induction and trading inversions for multiplication, which reduces the inversion to once. The proposed algorithm is prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication is high. And the bigger the ratio is, the more the efficiency improves.

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