Investigation of Hill Cipher Modifications Based on Permutation and Iteration

TL;DR

This paper analyzes recent Hill cipher modifications that incorporate permutation and iteration, demonstrating how they enhance security through non-linear transformations and proposing new, computationally efficient variants that maintain strong cryptographic properties.

Contribution

It introduces two novel Hill cipher modifications using column swapping and permutation, reducing complexity while preserving the cipher's strength.

Findings

Proposed modifications achieve significant avalanche effect.

Reduced iterations lead to lower encryption time.

Maintained cryptographic strength with fewer computational resources.

Abstract

Two recent Hill cipher modifications which iteratively use interweaving and interlacing are considered. We show that strength of these ciphers is due to non-linear transformation used in them (bit-level permutations). Impact of number of iterations on the avalanche effect is investigated. We propose two Hill cipher modifications using column swapping and arbitrary permutation with significantly less computational complexity (2 iterations are used versus 16). The proposed modifications decrease encryption time while keeping the strength of the ciphers. Numerical experiments for two proposed ciphers indicate that they can provide a substantial avalanche effect.