Efficient Algorithms for Elliptic Curve Cryptosystems

摘要: This contribution describes three algorithms for efficient implementations of elliptic curve cryptosystems. The first algorithm is an entirely new approach which accelerates the multiplications points core operation in public-key systems. works conjunction with k-ary or sliding window method. explores computational advantages by computing repeated point doublings directly through closed formulae rather than from individual doublings. reduces number inversions underlying finite field at cost extra multiplications. For many practical implementations, where inversion least four times as costly multiplication, proofs to be faster traditional multiplication methods. second deals composite Galois fields form GF((2n)n). Based on idea Itoh and Tsujii, we optimize software implementation curves. reduced subfield GF(2n). third application Karatsuba-Ofman Algorithm We provide a detailed complexity analysis case that arithmetic performed table look-up. apply all system over GF((216)11). absolute performance measures operations entire multiplication.