Modified Reversible Radix-n Machine Computations with Novel N-state Carry Functions

Applications in Cryptography

Abstract

            Machine Cryptography uses digital circuitry that performs operations described as modulo-n additions (as in SHA-256 and ChaCha20) and additions over GF(2^k) (as in AES-GCM and many other protocols). These additions are well documented and are used to ‘mix’ data. By themselves these operations provide no additional security. The security is provided by unknown or secret data “a key” that is mixed with what is called “cleartext” to generate “ciphertext.”
             Sets of data, like multiple bytes, are treated in this article as a radix-n words of n-state elements.  A key-word of k n-state elements and a “cleartext” word of k n-state elements are added radix-n resulting in a “ciphertext” word of k n-state elements. Canonical forms of n-state carry functions for reversible modulo-n additions and additions over GF(n) are provided. This modified and preferably secret radix-n addition increases security in an unpredictable way. 
            The radix-n modifications are applied in known cryptography such as AES-GCM, ChaCha20 and SHA-256. This improves the security and appears to be resistant against quantum computer (QC) attacks.