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. Conventionally, security is provided by unknown or secret data (a “key stream”) that is mixed with often ‘known’ data (“clear text’). Security is generally created by the unknown or secret keystream and not by a secrecy of a function.

This article describes ways to create large numbers of (secret) reversible n-state carry functions for radix-n additions known as ripple carry additions. Canonical forms of n-state carry functions for reversible modulo-n additions and additions over GF(n) are provided. Novel reversible n-state carry functions are provided that keep the n-state machine additions reversible but now unpredictable.

The modifications are applied in known cryptography such as AES-GCM, ChaCha20 and SHA-256. These improve the security and appear to be resistant against quantum computer (QC) attacks. Irreversible n-state carry functions are applied in one-way machine cryptography