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给出了有限乘法群 F p 与有限域Fp上奇异椭圆曲线y2 - 2xy =x3之间的一个同构 ,证明了假如能够求解关于该奇异曲线的离散对数问题 ,那么就可求解Fp 上的离散对数问题 .说明了基于椭圆曲线离散对数问题的密码体制比基于有限域Fp 上离散对数问题的密码体制具有更好的密码学特性
A isomorphism between the finite multiplicative group F p and the singular elliptic curve y2 - 2xy = x3 on the finite field Fp is proved, which proves that if the discrete logarithm problem on the singular curve can be solved, Discrete logarithm problem.It is shown that the cryptosystem based on the elliptic curve discrete logarithm problem has better cryptographic properties than the cryptosystem based on the discrete logarithm problem on the finite field Fp