A VARIANT OF POLLARD�S RHO ATTACK ON ELLIPTIC CURVE CRYPTOSYSTEMS | Science Publications

Journal of Computer Science

Mohammed Elamrani¹  Siham Ezzouak¹  Abdelmalek Azizi¹ 

关键词: Cycle Detection;    Discrete Logarithm Problem;    Elliptic Curve;    Pollard Rho Method;    Random Walk;   

DOI  :  10.3844/jcssp.2014.1575.1581

学科分类：计算机科学（综合）

来源: Science Publications

【 摘 要 】

Elliptic Curve cryptosystems appear to be more secure andefficient when requiring smallkey size to implement than otherpublic key cryptosystems. Its security is based upon the difficulty of solving Elliptic Curve Discrete Logarithm Problem (ECDLP). This study proposes a variant of generic algorithm Pollard’s Rhofor finding ECDLP using cycle detection with stackand a mixture of cycle detection and random walks. The Pollard’s Rho using cycle detection with stack requires lessiterationsthan Pollard’s Rho original in reaching collision. Random walks allow the iteration function to act randomly than the original iteration function, thus, the Pollard rho method performs more efficiently. In practice, the experiment results show that the proposed methods decreases the number of iterations andspeed up the computation of discrete logarithm problem on elliptic curves.

【 授权许可】

Unknown