A Vector Space Approach to Generate Dynamic Keys for Hill Cipher

TL;DR

This paper introduces a novel variant of the Hill cipher that uses dynamically generated invertible matrices based on vector spaces, enhancing security against known-plaintext attacks.

Contribution

It proposes a method to generate dynamic key matrices using vector spaces, improving Hill cipher security against known-plaintext attacks.

Findings

Enhanced security against known-plaintext attack

Use of vector space-based matrix generation

Dynamic key matrices for each plaintext block

Abstract

In this paper, a variant of the Hill cipher is proposed. In the classical Hill cipher, an invertible matrix is used for encryption but the scheme is vulnerable to the known-plaintext attack which can reveal the matrix. In our proposed cryptosystem, each plaintext block is encrypted by a new invertible key matrix that thwarts the known-plaintext attack. To generate the invertible matrices which serve as the dynamic keys we make use of the vector spaces, randomly generated basis and non-singular linear transformation. Resulting cipher is secure against the known-plaintext attack.