Performance Analysis of Parallel Pollard's Rho Factoring Algorithm

Abstract

Integer factorization is one of the vital algorithms discussed as a part of analysis of any black-box cipher suites where the cipher algorithm is based on number theory. The origin of the problem is from Discrete Logarithmic Problem which appears under the analysis of the cryptographic algorithms as seen by a cryptanalyst. The integer factorization algorithm poses a potential in computational science too, obtaining the factors of a very large number is challenging with a limited computing infrastructure. This paper analyses the Pollard’s Rho heuristic with a varying input size to evaluate the performance under a multi-core environment and also to estimate the threshold for each computing infrastructure

Accelerating the Wheel Factoring Techniques

“…There are more factoring techniques, but they require more knowledge of cryptosystems or specific requirements for the prime factors (see [1,3,4,19]). Utilizing highperformance-Computing systems such as multicore systems [6,7,13,15], cloud computing systems [28], and graphics processing units [2,8] is one method for accelerating factoring algorithms.…”

“…The special-purpose factoring algorithms [16] find tiny prime factors rapidly regardless of the value of n. If n has no tiny factors, employing one of the special-purpose factoring algorithms will almost surely fail, which is the primary issue with them. Examples of such factoring algorithms include the Fermat technique [5] with time complexity of O( √ n), Pollard's elliptic curve method, Pollard's wheel factoring method, Pollard's p-method with time complexity of O( √ n log n), and Pollard's p − 1 method [15]. The general-purpose factorization techniques factor n regardless of the size of the prime factors, albeit they require exponential or subexponential time.…”