Theoretical Approach to Backdoor Attacks on the Template of CRYSTALS-Dilithium

Anticipating the potential of quantum processors to compromise the security of widely employed cryptographic algorithms, there is a current need for extensive research in post-quantum cryptography across all communication technologies, including 6G. Therefore, post-quantum cryptography has recently witnessed the emergence of new and prominent representatives, such as the new standard for quantum-safe digital signatures, called CRYSTALS-Dilithium. This work presents a theoretical approach to two backdoor attacks on that algorithm, in which the objective is to extract the message through the signature. Although the hypotheses of this work are very theoretical, since they assume that the message is encrypted and that the attacker possesses the private key, given the enormous relevance of the new standard post-quantum encryption, this study is of great interest. In particular, it relies on installing a backdoor in the signing process to later be able to extract the message through the signature. This document provides several details of the attacks, thus demonstrating the feasibility of leaking the original message during the signing phase.