Symmetric Key Encryption for Arbitrary Block Sizes from Affine Spaces

TL;DR

This paper introduces a symmetric key encryption method for arbitrary block sizes based on affine spaces over finite fields, enabling a vast key space and flexible message sizes.

Contribution

It presents a novel encryption scheme that leverages affine space transformations over finite fields for arbitrary block sizes, expanding the possibilities beyond traditional fixed-size block ciphers.

Findings

Supports block sizes less than 2^128.

Provides over 2^5478 keys for certain block sizes.

Utilizes algebro-geometric transformations for encryption.

Abstract

A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine spaces over various finite fields. Then algebro-geometric transformations on those affine spaces is transported back to provide encryption. For a specific block size${}<2^{128}$ we get more than $2^{5478}$ keys.