In-depth Correlation Power Analysis Attacks on a Hardware Implementation of CRYSTALS-Dilithium

During the standardisation process of post-quantum cryptography, NIST encourages research on side-channel analysis for candidate schemes. As the recommended lattice signature scheme, CRYSTALS-Dilithium, when implemented on hardware, has only been subjected to the side-channel attack presented by Steffen et al. in IACR ePrint 2022. This attack is not complete and requires excessive traces. Therefore, we investigate the leakage of an FPGA (Kintex7) implementation of CRYSTALS-Dilithium using the CPA method, where with a minimum of 70000 traces partial private key coefficients can be recovered. As far as we know, this is the first work that applies power leakage to sidechannel attacks on FPGA implementations of CRYSTALS-Dilithium. Furthermore, we optimise the attack by extracting Point-of-Interests using known information due to parallelism (named CPA-PoI) and by iteratively utilising parallel leakages (named CPA-ITR). We experimentally demonstrate that when recovering the same number of key coefficients, the CPA-PoI and CPA-ITR reduce the number of traces used by up to 16.67 percent and 25 percent, respectively, compared to the CPA method. When attacking with the same number of traces, the CPA-PoI method and the CPA-ITR method increase the number of recovered key coefficients by up to 55.17 percent and 93.10 percent, respectively, compared to the CPA method. Our experiments confirm that the FPGA implementation of CRYSTALS-Dilithium is also very vulnerable to side-channel analysis