关键词: 椭圆曲线密码体制, 有限域, 点运算, 混合坐标系

Abstract: Elliptic Curve Cryptosystem (ECC) is a kind of public-key cryptosystem based on algebraic curve. Point algorithms on elliptic curve are essential operations in ECC and its speed are decided by selected coordinate. On the basis of analyzing existing coordinates such as affine coordinate, Standard projective coordinate, Jacobian projective coordinate and Lopez & Dahab projective coordinate, an extension of Lopez & Dahab projective coordinate was proposed and a mixed projective coordinate was given to improve the speed of scalar multiplication. The result of analysis indicates that the operation time complexity of scalar multiplication under the mixed projective coordinate is more reduced than under any other coordinates.

Key words: Elliptic Curve Cryptosystem (ECC), finite field, point algorithms, mixed coordinates