A Class of Non Invertible Matrices in GF (2) for Practical One Way Hash Algorithm

TL;DR

This paper introduces a class of non-invertible permutation matrices in GF(2) that can be used in a one-way hash algorithm, offering a simple and efficient alternative to invertible matrices for cryptographic purposes.

Contribution

The paper proposes a new class of non-invertible permutation matrices in GF(2) suitable for one-way hash functions, which are easy to generate and do not require inversion.

Findings

Matrices are permutation matrices with one '1' per row and column.

These matrices are non-invertible and easy to generate.

Potential application in practical one-way hash algorithms.

Abstract

In this paper, we describe non invertible matrix in GF(2)which can be used as multiplication matrix in Hill Cipher technique for one way hash algorithm. The matrices proposed are permutation matrices with exactly one entry 1 in each row and each column and 0 elsewhere. Such matrices represent a permutation of m elements. Since the invention, Hill cipher algorithm was used for symmetric encryption, where the multiplication matrix is the key. The Hill cipher requires the inverse of the matrix to recover the plaintext from cipher text. We propose a class of matrices in GF(2) which are non invertible and easy to generate.