ON USING THE SYMMETRIC GROUP IN A CRYPTOSYSTEM

Abstract

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 ( ) from converting to a permutation
(as it is in there suggestion) to converting the permutation (which used to
encrypt the plaintext to an integer and then the cipher text ( . ) will
be an integer and not a permutation which can be decrypted by multiply it with the
number .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.