Orthogonal Matrix in Cryptography

TL;DR

This paper proposes a cryptographic method leveraging the properties of orthogonal matrices and their exponentials to create complex encryption and decryption processes.

Contribution

It introduces a novel encryption technique based on the exponential of orthogonal matrices, exploiting their diagonalizability for secure message transformation.

Findings

Orthogonal matrix exponentials enable complex encryption.

The method simplifies encryption using diagonalization properties.

Potential for efficient and secure cryptographic schemes.

Abstract

In this work is proposed a method using orthogonal matrix transform properties to encrypt and decrypt a message. It will be showed how to use matrix functions to create complex encryptions. Because orthogonal matrix are always diagonalizable on R, and the exponential of a diagonal matrix is easy to compute, the exponential of orthogonal matrix will be used to encrypt text messages.