Post-Quantum Cryptography: Breaking Xifrat

In recent years, the National Institute of Standards and Technology (NIST) has been calling for a transition to post-quantum cryptography. With the rapid advancement of quantum computers, established cryptographic methods are at risk of being compromised, meaning that traditional public-key cryptosystems can no longer ensure the confidentiality and integrity of digital communications. As a potential solution, Xifrat1-Sign, a digital signature scheme based on quasigroups, has been proposed to NIST. By leveraging the special properties of the algebraic structure of quasigroups, and particularly, the restricted-commutativity, this cryptographic scheme aims to provide quantum-resistant security. To assess its robustness, we conducted a comprehensive cryptanalysis of the Xifrat cryptosystem using computational group theory and differential statistical analyses. As a result, we identified multiple vulnerabilities in its design, enabling us to compromise the system in seconds.This study significantly advances our understanding of the Xifrat cryptosystem and other quasigroup-based schemes, contributing to the

development of more secure cryptographic frameworks in the era of emerging quantum technologies.