Comparative study on Integer Factorization algorithm-Pollard's RHO and Pollard's P-1

The difficulty of solving any cryptographic algorithm is often based on Integer Factorization or Discrete Logarithm or both at a same time. Most secure public key cryptographic algorithm is base on Integer Factorization have gained their security level because of the fact that there exist no known deterministic polynomial time algorithm for finding the factors of given composite number. This paper is focused to Integer Factorization problem. Here we have outlined Pollard's rho algorithm and Pollard's p-1 algorithm. The two algorithms are implemented in MuPad and have been executed on some set of numbers to arrive at comparative conclusion.