Complexity analysis of a top down algorithm motivated by power product expansions

Abstract

This paper introduces the Binomial Expansion Cryptosystem, a prototype for a crpytosytem which could also be of interest to small elite organizations. Let be a set of positive integers. The Binomial Expansion Cryptosystem exploits the one to one correspondence between a finite integer power product expansion, , and its associated power series representation , by taking the product representation, converting it into series format, and transmitting a set of N coefficients, namely . The crux of our decryption amounts to solving a finite number of Diophantine equations. It is accomplished through a so called Generalized Top-Down Algorithm and transforms into . Algebraic and complexity properties of the Generalized Top-Down Algorithm are analyzed. Preliminary security issues are discussed. Numerous detailed examples are provided.