Abstract
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 Pollardâs Rho for finding ECDLP using cycle detection with stack and a mixture of cycle detection and random walks. The Pollardâs Rho using cycle detection with stack requires less iterations than Pollardâs 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.
Highlights
Elliptic curves over finite fields have been proposed by Diffie-Hellman to implement key passing scheme and elliptic curves variants for digital signature
Its security is based upon the difficulty of solving Elliptic Curve Discrete Logarithm Problem (ECDLP)
There are several attacks against this cryptosystem such as Baby-Step Giant-Step (Shanks, 1971), Pollard’s Rho method and its parallelized variant, their complexity is the square root of the prime order of new cycle detection proposed by (Nivasch, 2004) and the random walks proposed by Teske
Summary
Elliptic curves over finite fields have been proposed by Diffie-Hellman to implement key passing scheme and elliptic curves variants for digital signature. The security of this cryptosystem is linked to the difficulty to solve elliptic curve discrete logarithm problem and if this problem is resolved the cryptosystem is broken. The remainder of this study is proceded as follow: Section 2 introduces some basic definitions for the elliptic curves, Floyd’s algorithm and Pollard’s Rho algorithm. Pollard’s Rho method is known as the best method to
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.