Abstract:
Fast scalar multiplication on two family of supersingular elliptic curves in characteristic 2 and 3 is discussed. Provable secure cryptographic scheme can be obtained on these curves. With the complex multiplication property of these curves, a fast algorithm without precomputation is derived from Frobenius endomorphism and another fast endomorphism, which is 4 times and 3 times faster than IEEE1363 standard method.
Key words:
Cryptography,
Elliptic curve,
Scalar multiplication
摘要: 研究了特征为2和3的域上的超奇异椭圆曲线的快速标量乘法。该两类曲线适合建立可证明安全的密码体制,利用这两类曲线的复乘性质,结合Frobenius自同态和可以简单计算的自同态,给出了一种不用预计算的快速算法,相较IEEE1363标准算法,计算效率分别提高了4倍和3倍。
关键词:
密码学,
椭圆曲线,
标量乘法
ZHANG Ning; CHEN Zhixiong; XIAO Guozhen. Fast Scalar Multiplication on Two Family of Supersingular Elliptic Curve[J]. Computer Engineering, 2006, 32(23): 143-144,.
张 宁;陈志雄;肖国镇. 两类超奇异椭圆曲线的快速标量乘法[J]. 计算机工程, 2006, 32(23): 143-144,.