MulLeak: Exploiting Multiply Instruction Leakage to Attack the Stack-optimized Kyber Implementation on Cortex-M4

CRYSTALS-Kyber, one of the NIST PQC standardization schemes, has garnered considerable attention from researchers in recent years for its side-channel security. Various targets have been explored in previous studies; however, research on extracting secret information from stack-optimized implementations targeting the Cortex-M4 remains scarce, primarily due to the lack of memory access operations, which increases the difficulty of attacks.This paper shifts the focus to the leakage of multiply instructions and present a novel cycle-level regression-based leakage model for the following attacks. We target the polynomial multiplications in decryption process of the stack-optimized implementation targeting the Cortex-M4, and propose two regression-based profiled attacks leveraging known ciphertext and chosen ciphertext methodologies to recover the secret coefficients individually. The later one can also be extended to the protected implementation.Our practical evaluation, conducted on the stack-optimized Kyber-768 implementation from the pqm4 repository, demonstrates the effectiveness of the proposed attacks. Focusing on the leakage from the pair-pointwise multiplication, specifically the macro doublebasemul_frombytes_asm, we successfully recover all secret coefficients with a success rate exceeding 95% using a modest number of traces for each attack. This research underscores the potential vulnerabilities in PQC implementations against side-channel attacks and contributes to the ongoing discourse on the physical security of cryptographic algorithms.