The Finite Lab-Transform (FLT) for Invertible Functions in Cryptography

Abstract

This article introduces a novel number theoretical transformation: the Finite Lab-Transform or FLT, which preserves meta-properties of transformed functionality of 2-operand computer functions described over ℤn. Existing machine cryptography applies functions described as addition over Finite Field GF(n=2^k) applied in encryption such as AES-GCM and ChaCha20 and hashing as SHA-256, which are part of standard TLS 3.1. Usually as bitwise XOR of words of k bits. This functionality is modified by the FLT.  Properties like involution, associativity and invertibility are preserved by the FLT. The FLT allows secret customization of existing and novel cryptographic primitives while maintaining proven data-flow. Improvement of security against brute force attacks with a factor greater than 10^400 can be achieved.