ON USING THE SYMMETRIC GROUP IN A CRYPTOSYSTEM

This paper propose to overcome the negative point of the cryptosystem based on the symmetric group that had been suggested by (Doliskani,Ehsan and Zakerolhosseini)[1], which is the relatively large memory and bandwidth requirements for storing and transmitting permutations (symmetric group elements), our suggestion is to get benefit from the bijection between permutations and integers and modify the way we encrypt plaintext (m ) from converting m to a permutation (as it is in there suggestion) to converting the permutation (g^a)^k (which used to encrypt the plaintext (m) to an integer and then the cipher text (m . (g^a)^k ) will be an integer and not a permutation which can be decrypted by multiply it with the number ((g^a)^k)^-1 .By such modification we get the benefits of using the symmetric group elements in our public key such as non commutative, high computational speed and high flexibility in selecting keys which make the Discrete Logarithm Problem (DLP) resistant to attacks by algorithms such as Pohlig- Hellman.