Subgroup Presentations of Symmetric Group in Crypto-analysis

This paper is aimed at improving the shift cipher by providing more keys which guarantee the security of information being sent across a communication channel. The more radical solution to the problem of key sharing developed by Diffie-Hellman is adopted, merged with group theoretic approach. The result is demonstrated using Romeo and Juliet scenario, where the key exchange was done thrice; single key followed by two different keys, a total of three. Finally, the result was modeled mathematically using group presentations, as set of bijections on finite sets.