A Review on Solving ECDLP over Large Finite Field Using Parallel Pollard’s Rho (ρ) Method
Journal Title: IOSR Journals (IOSR Journal of Computer Engineering) - Year 2016, Vol 18, Issue 2
Abstract
Abstract: Elliptic Curve Discrete Log Problem (ECDLP) is the underlying basis of many popular Public Key Scheme like Diffie-Hellman and ElGamal. The strength of such public key schemes is based on the difficulty ofsolving the ECDLP. The best method for solving the ECDLP has time complexity exponential in the size of the underlying field. ECDLP based cryptosystems are popular because they provide good security at key sizes much smaller than number theoretical Public Key Schemes like RSA cryptosystem. Elliptic curve cryptosystem based on ECDLP are also present in the list of recommended algorithms for use by NIST and NSA. Since ECDLP based cryptosystems are in wide-spread use, continuous efforts on monitoring the effectiveness of new attacks or improvements to existing attacks on ECDLP over large field is important. Using the parallel Pollard’s method to solve the ECDLP efficiently is one of the prime concerns. Use of different parallel architectures like cluster computing (MPI), GPGPU, FPGA cluster increases the effectiveness of attack. This article covers various aspects of finite field, Elliptic Curve Cryptography (ECC), ECDLP, methods for solving ECDLP along with emphasis on parallel Pollard’s methods using CPU cluster.
Authors and Affiliations
Kaushal A. Chavan , Dr. Indivar Gupta , Dr. Dinesh B. Kulkarni
Keywords
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