A New Variant of Subset-sum Cryptosystem over Rsa

RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard, who first publicly described it in 1978. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept secret. 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): An instance of the Subset Sum problem is a pair (S, t), where S = {x1 , x2 , ..., xn} is a set of positive integers and t (the target) is a positive integer. The decision problem asks for a subset of S whose sum is as large as possible, but not larger than t. This problem is NP-complete. However, if the set of numbers (called the knapsack) is super increasing, 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 we present a new algorithm (Modified Subset-Sum cryptosystem over RSA) which is secure against Mathematical attack, Brute-force attack, Factorization attack and Chosen-cipher-text attack on RSA as well as Shamir attacks. This paper also presents comparison between Modified Subset Sum Cryptosystem and RSA cryptosystems in respect of security and performance.