International Association
for Cryptologic Research

Number Theoretic Transform (NTT) has been widely used in accelerating computations in lattice-based cryptography. However, attackers can potentially launch power analysis targeting the NTT because it is one of the most time-consuming parts of the implementation. This extended time frame provides a natural window of opportunity for attackers. In this paper, we investigate the first CPU frequency leakage (Hertzbleed-like) attacks against NTT in lattice-based KEMs. Our key observation is that different inputs to NTT incur different Hamming weights in its output and intermediate layers. By measuring the CPU frequency during the execution of NTT, we propose a simple yet effective attack idea to find the input to NTT that triggers NTT processing data with significantly low Hamming weight. We further apply our attack idea to real-world applications that are built upon NTT: CPAsecure Kyber without Compression and Decompression functions, and CCA-secure NTTRU. This leads us to extract information or frequency hints about the secret key. Integrating these hints into the LWE-estimator framework, we estimate a minimum of 35% security loss caused by the leakage. The frequency and timing measurements on the Reference and AVX2 implementations of NTT in both Kyber and NTTRU align well with our theoretical analysis, confirming the existence of frequency side-channel leakage in NTT. It is important to emphasize that our observation is not limited to a specific implementation but rather the algorithm on which NTT is based. Therefore, our results call for more attention to the analysis of power leakage against NTT in lattice-based cryptography.

The recent Hertzbleed disclosure demonstrates how remote-timing analysis can reveal secret information previously only accessible to local-power analysis. At worst, this constitutes a fundamental break in the constant-time programming principles and the many deployed programs that rely on them. But all hope is not lost. Hertzbleed relies on a coarse-grained, noisy channel that is difficult to exploit. Indeed, the Hertzbleed paper required a bespoke cryptanalysis to attack a specific cryptosystem (SIKE). Thus, it remains unclear if Hertzbleed represents a threat to the broader security ecosystem. In this paper, we demonstrate that Hertzbleed's effects affect cryptosystems beyond SIKE. We demonstrate how latent gadgets in other cryptosystem implementations---specifically ``constant-time'' ECDSA and Classic McEliece---can be combined with existing cryptanalysis to bootstrap Hertzbleed attacks on those cryptosystems.

Microarchitectural side-channel attacks have shaken the foundations of modern processor design. This talk will discuss the latest research on this topic.