The implementation of the Pollard factorization method in the cryptanalysis of the Rabin public key algorithm

Abstract

Rabin algorithm is an asymmetric cryptography algorithm that is used to obfuscate messages by using two different keys that are used in encryption and decryption process. Rabin algorithm is considered secure since its protection depends on the hardness of factoring a very large odd number into two very large prime numbers. Various factorization methods that exist are Fermat, Kraitchik, Euler, and variants of Pollard method. In this research, we test the security of the Rabin algorithm by cryptanalyzing its public key into its two private keys using the Pollard factorization algorithm. In order to check that a very large number is prime or composite, we use the Lehmann algorithm. Our research shows that Pollard is able to factorize some Rabin public keys and the size of the public key is not directly proportional to the processing time.