چکیده (انگلیسی):

Elliptic Curve cryptosystems appear to be more secure and efficient when requiring small key size to
implement than other public 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 Rho for finding ECDLP using cycle detection with stack and a mixture of cycle detection and
random walks. The Pollard’s Rho using cycle detection with stack requires less iterations than 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 and speed up the
computation of discrete logarithm problem on elliptic curves.