In the rapid development of contemporary information technology, security has become important technique in many applications including Virtual Private Network (VPN), electronic commerce ,secure internet access etc. The security of public key encryption such as RSA scheme relied on the integer factorization problem. The security of RSA algorithm is based on a positive integer n, because each transmitting node generates pair of keys such as public and private. Encryption and decryption of any message depends on positive integer n. Where, the positive integer n is the product of two prime numbers and pair of key generation is depend on these prime numbers. In the paper [11], an algorithm for modular multiplication for public key cryptosystem is presented. This method is based on the following two ideas: (i) The remainder in regard to n can be constructed from the remainder with modulus (2n+1) and the remainder with modulus (2n+2). (ii) It often happens that 2n+1can easily be factorized, even if n is a prime number or n is difficult to be factorized into prime factors. The changed modulus value will be stated, which might be the one of the modulus factor i. e. , (2n+1). Even if the hacker factorizes this new modulus value, they can't be searched out the original decryption key (d). Incapability to find the original decryption key, the factorization is insignificant. This proposed method helps to overcome the weakness of factorization found in RSA.

Pubic key cryptosystem modular multiplication RSA Cryptosystem modulus factor