RSA algorithm using modified subset sum cryptosystem

Abstract

RSA is the asymmetric cryptography system. The security of RSA public key cryptosystem is based on the assumption that factoring of a large number (modulus) is difficult. In RSA if one can factor modulus into its prime numbers then the private key is also detected and hence the security of the cryptosystem is broken. The Subset-Sum cryptosystem (Knapsack Cryptosystem) is also an asymmetric cryptographic technique. The Merkle-Hellman system is based on the subset sum problem (a special case of the knapsack problem): given a list of numbers and a third number, which is the sum of a subset of these numbers, determine the subset. In general, this problem is known to be NP-complete. However, if the set of numbers (called the knapsack) is superincreasing, that is, each element of the set is greater than the sum of all the numbers before it, the problem is ‘easy’ and solvable in polynomial time with a simple greedy algorithm. So in this paper a Modified Subset-Sum over RSA Public key cryptosystem (MSSRPKC) is presented which is secure against Mathematical and brute-force attacks on RSA as well as Shamir attacks. This paper also presents comparison between MSSRPKC and RSA cryptosystems in respect of security and performance.