New identities for the Shannon function and applications

TL;DR

This paper introduces new identities for the Shannon entropy function expressed as linear combinations of other entropy functions involving polynomial quotients, with applications demonstrated in cryptography.

Contribution

It presents novel identities for Shannon entropy involving polynomial quotients and applies these to cryptographic key analysis.

Findings

New identities for Shannon entropy expressed as linear combinations.

Application of identities to cryptographic key analysis.

Potential for improved entropy-based cryptographic methods.

Abstract

We show how the Shannon entropy function H(p,q)is expressible as a linear combination of other Shannon entropy functions involving quotients of polynomials in p,q of degree n for any given positive integer n. An application to cryptographic keys is presented.