Kim, K.H., Kim, S.I. and Choe, J.S. (2007) New Fast Algorithms for Arithmetic on Elliptic Curves over Fields of Characteristic Three. Cryptology ePrint Archive: Report 2007/179. http://eprint.iacr.org/2007/179
GF(3n)椭圆曲线密码体制中标量乘快速算法研究Research on Fast Algorithms for Scalar Multiplication of Elliptic Curve Cryptography over GF (3n)
椭圆曲线密码体制, 标量乘, 递推归纳, 滑动窗口Elliptic Curve Cryptography (ECC), Scalar Multiplication, Recursion, Sliding Window
《Advances in Applied Mathematics》, Vol.4 No.4, 2015-11-30
In this paper we investigate the fast algorithm of scalar multiplication based on Elliptic Curve Cryptography (ECC) over fields of characteristic three, and make improvements both in underlying operations and upper operations respectively. In the underlying operations, we deduce a formula of calculating 3kP directly under the affine coordinates based upon the idea of recursion, trading inversion for multiplication and trading multiplication for cube, which reduces the inversion to once; in the upper operations, we adopt the sliding window scalar multiplication method, which reduces the length of the non-zero windows and the total computations of 3P effectively.