Encryption based on Ballot, Stack permutations and Balanced Parentheses using Catalan-keys

Abstract

This paper examines the possibilities of applying Catalan numbers in cryptography. It also offers the application of appropriate combinatorial problems (Ballot Problem, Stack permutations and Balanced Parentheses) in encryption and decryption of files and plaintext. The paper analyzes the properties of Catalan numbers and their relation to these combined problems. Applied copyright method is related to the decomposition of Catalan numbers in the process of efficient keys generating. Java software solution which enables key generating with the properties of the Catalan numbers is presented at the end of the paper. Java application allows encryption and decryption of plaintext based on the generated key and combinatorial problems.