Polyadic encryption

TL;DR

The paper addresses secure information transfer in signal processing by encoding plaintext into polyadic arities within $(m,n)$-rings and introducing polyadic discretization of amplitudes in $\mathbb{Z}_{(m,n)}^{[a,b]}$. Plaintext elements $y_j$ are mapped to arities $(a,b,m)$ and transmitted as sums of $\ell_f(m-1)+1$ polyadic-sourced signals, producing total amplitudes $A_{tot}^{(\ell_f)}$ that encode the arities. The receiver reconstructs $(a,b,m)$ by solving a small system of quadratic equations across multiple polyadic powers, thereby recovering $y_j$. This approach offers a novel, key-optional cryptographic mechanism rooted in polyadic algebraic structures and their arity-shape mapping, with potential implications for secure communications in signal processing.

Abstract

A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then we use polyadic techniques to transfer the plaintext into series of special integers. The receiver restores the plaintext using special rules and systems of equations.