From Golden to Unimodular Cryptography
This work addresses security vulnerabilities in cryptography for secure communication, though it appears incremental as it builds directly on golden cryptography.
The authors generalized golden cryptography to unimodular cryptography using general unimodular matrices instead of Q-matrices, preserving error correction properties while adding resilience to chosen plaintext attacks. They also identified a limitation in golden cryptography regarding double errors in ciphertext rows and proposed an additional check number to enable correction.
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.