Improving Single-Trace Attacks on the Number-Theoretic Transform for Cortex-M4

The Number-Theoretic Transform (NTT) is a key feature for the efficiency of numerous lattice-based cryptographic schemes. The arithmetic structure of that operation makes it an important target for soft-analytical side-channel attacks, that are powerful single-trace side-channel attacks exploiting known arithmetic structure to improve noise tolerance. Among others, Pessl et al. used the belief-propagation technique to attack a software implementation of the Kyber key encapsulation mechanism for Arm Cortex-M4 microcontrollers. However, that implementation has since been thoroughly optimized, in particular through the use of an improved version of Plantard modular arithmetic. In this paper, we describe how we successfully attack the latest available version of this implementation. We show that precise knowledge of the implementation at hand allows for better performance of the belief-propagation technique. By modeling each individual arithmetic operation performed by the microcontroller, we are able to recover the secret values processed during the NTT, even with very noisy side-channel leakage. We also study some strategies for the attacker to either maximize the success rate, or minimize the runtime of the attack.