A special purpose integer factorization algorithm

Abstract

Factorization of large integers is a significant mathematical problem with practical applications to public key cryptography. It is considered to be a part of cryptanalysis. The progress in factoring tends to weaken the existing efficient public key cryptosystems. Several algorithms such as trial division, Pollard rho, Pollard p-1, Quadratic sieve, Lenstra's elliptic curve and Number field sieve are available to solve the integer factorization problem. In this paper a special purpose factorization algorithm is proposed to find the factors of a composite number which is the product of two primes. The running time complexity of the proposed scheme is discussed. The efficiency of the scheme is proved theoretically.