Implementation of Integer Factorization Algorithm with Pisano Period

Abstract

AbstractThe problem of factorization of large integers into the prime factors has always been of mathematical interest for centuries. In this paper, starting with a historical overview of integer factorization algorithms, the study is extended to some recent developments in the prime factorization with Pisano period. To reduce the computational complexity of Fibonacci number modulo operation, the fast Fibonacci modulo algorithm has been used. To find the Pisano periods of large integers, a stochastic algorithm is adopted. The Pisano period factorization method has been proved slightly better than the recently developed algorithms such as quadratic sieve method and the elliptic curve method. This paper ideates new insights in the area of integer factorization problems.KeywordsCryptographyNetwork securityInteger factorization algorithmPisano period