IJARCCE ISSN (Online) 2278-1021 ISSN (Print) 2319 5940 International Journal of Advanced Research in Computer and Communication Engineering ISO 3297:2007 Certified Vol. 6, Issue 5, May 2017 Copyright to IJARCCE DOI10.17148/IJARCCE.2017.6571 377 A Review: Solving ECDLP Problem using Pollard‟s Rho Algorithm Santosh P. Lokhande 1 , Dr. Indivar Gupta 2 , Dr. Dinesh B. Kulkarni 3 Student, M.Tech, Computer Science and Engineering (Specialization in Information Technology) Walchand College of Engineering, Sangli, Maharashtra, India 1 Scientist, Scientific Analysis Group (SAG), Defence Research and Development Organization, New Delhi, Delhi 2 Professor, Department of Information Technology Walchand College of Engineering, Sangli, Maharashtra, India 3 Abstract: In Public Key Cryptography system, separate keys are used to encode and decode the data. Public key being distributed publicly, the strength of security depends on large key size. The discrete logarithm for mathematical base in Public Key Cryptography systems. Unlike the finite field Discrete Logarithm Problem; there are no general purpose sub exponential algorithms to solve the Elliptic Curve Discrete Logarithm Problem. Though good algorithms are known for certain specific types of elliptic curves, all known algorithms that apply to general curves take fully exponential time. As a result, elliptic curves are gaining popularity for building cryptosystems. The absence of sub exponential algorithms implies that smaller fields can be chosen compared to those needed for cryptosystems. Elliptic curve based cryptosystems are popular because they provide good security at key sizes much smaller than number theoretical Public Key Schemes like RSA cryptosystem. Solving Elliptic Curve Discrete Logarithm Problem using Pollard‟s Rho algorithm provide efficiency in terms of time and storage. Using various parallel architectures like MPI, GP-GPU and FPGA increase accessing precision and efficiency of solving ECDLP.This article covers Elliptic Curve Cryptography, Elliptic Curve Discrete Logarithm Problem and Pollard's Rho algorithms to solve ECDLP. Keywords: Elliptic curve, ECC, DLP, ECDLP, Pollard‟s Rho Algorithm, Parallel Architectures. I. INTRODUCTION The first practical realization followed in 1977 when Ron Rivest, Adi Shamir and Len Adleman proposed their now well-known RSA cryptosystem, in which security is based on the intractability of the integer factorization problem. Elliptic curve cryptography (ECC) was discovered in 1985 by Neal Koblitz and Victor Miller [2]. Elliptic curve cryptographic schemes are public-key mechanisms that provide the same functionality as RSA schemes. However, their security is based on the hardness of Elliptic Curve Discrete Logarithm Problem (ECDLP). For example, it is generally accepted that a 160-bit elliptic curve key provides the same level of security as a 1024-bit RSA key [3]. The advantages that can be gained from smaller key sizes include speed and efficient use of power, bandwidth, and storage. Due to smaller key size, implementation of elliptic curve based cryptosystems requires less memory. Therefore elliptic curve based cryptosystems have become popular in small devices such as Smart cards, PDA providing good amount of security. The strength of elliptic curve cryptosystem is directly proportional to the order of the underlying finite field. As the field order increases the hardness of the cryptography system increases. Traditional methods are not capable to solve the ECDLP in polynomial amount of time. Pollards Rho Algorithm, proposed by J.M Pollard [4], gives good results in terms of time and space to solve ECDLP problem. The growing parallel architectures enable us to make the use of parallelized versions of algorithm for time optimization. The paper is organized as follows. The second section covers the related work done in solving the ECDLP problem. Third section covers the background of elliptic curve cryptography, Discrete Logarithm Problem (DLP), ECDLP problem. Fourth section covers Pollard‟s Rho algorithm. Fifth section covers parallel version of Pollard‟s Rho algorithm. II. RELATED WORK To check the strength of cryptographic systems a lot of attacks have been attempted on the systems. Large amount of work has been carried out in solving the integer factorization problem (IFP), discrete logarithm problem in multiplicative group of finite field (DLP) and in the group points on an elliptic curve (ECDLP). The concept of elliptic curve cryptography was put forward by V. Miller in 1986 [2], after that N. Koblitz, A. Menezes and S. Vanstone in