Single Bit Randomness Leakage: The Vulnerability in Post-Quantum Cryptography Standard CRYSTALS-Dilithium

As advancements in quantum computing continue, post-quantum cryptography has become essential for ensuring the security of sensitive information, and side-channel resistance is one of the significant concerns. In this paper, we investigate the side-channel resistance of CRYSTALS-Dilithium, which has been selected by NIST as a standard post-quantum signature scheme. We propose a novel single-bit leakage attack that leverages signatures transmitted during communication to recover a target bit of large randomness used in the CRYSTALS-Dilithium algorithm. Notably, this recovered bit directly aids in reconstructing of the private key within the algorithm. To validate our methodology, we adopt the officially released source code of the CRYSTALS-Dilithium algorithm provided by NIST and deploy it on a Cortex M4 architecture. The power consumption leakages during the execution of the CRYSTALS-Dilithium algorithm are recorded, and the leakages are leveraged to execute the proposed attack alongside state-of-the-art attacks. Experimental results demonstrate that, when applying our proposed method, the success rate of single-bit recovery can be improved by approximately 20\% compared to existing state-of-the-art attacks, with an attack efficiency gain of approximately three times.