# From Golden to Unimodular Cryptography

## TL;DR

This paper generalizes golden cryptography using unimodular matrices, enhancing error correction and security against certain attacks, while also addressing double error correction with an additional check number.

## Contribution

It introduces a unimodular matrix-based cryptography that maintains error correction and improves resistance to chosen plaintext attacks.

## Key findings

- Preserves original error correction properties.
- Resilient to chosen plaintext attacks.
- Provides a method for correcting double errors.

## Abstract

We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q-matrices, and prove that it preserves the original error correction properties of the encryption. Moreover, the additional parameters involved in generating the coding matrices make this unimodular cryptography resilient to the chosen plaintext attacks that worked against the golden cryptography. Finally, we show that even the golden cryptography is generally unable to correct double errors in the same row of the ciphertext matrix, and offer an additional check number which, if transmitted, allows for the correction.