Paper 2025/1248 Original: eprint.iacr.org/2025/1248 ↗

Beyond Side-Channels: Evaluating Inner Product Masking Against SIFA

Abstract

Statistical Ineffective Fault Attack (SIFA) presents a critical threat to cryptographic implementations by circumventing conventional detection-based countermeasures effective against traditional fault attacks. Particularly, SIFA operates via two mechanisms: SIFA-1 exploits fault effectiveness dependency on target values, while SIFA-2 leverages conditional propagation of faulted values based on sensitive intermediates. Recent studies suggest that, masking, mainly a side-channel protection, also exhibits promising resistance to SIFA-1, such as prime masking. In this paper, we systematically evaluate the resilience of Inner Product Masking (IPM) against SIFA, which has been established in prior works as a powerful side-channel-resistant alternative to Boolean masking. Specifically, with regard to SIFA-1, our theoretical analysis demonstrates that Inner Product (IP) encoding provides stronger SIFA-1 resistance than both Boolean and prime masking under generic multi-bit fault models using various fault types. More interestingly, an equivalence between Side-channel and SIFA-1 security has been theoretically established for IP encoding, indicating that optimal IP encoding exists that simultaneously provides the highest side-channel resistance and maximizes the complexity of effective SIFA-1 attacks. For SIFA-2, our analysis reveals that IPM’s protection remains fundamentally bounded by the computational field size, consistent with previous results in this regard, e.g., for prime field masking. However, some vulnerabilities to persistent faults are anticipated for the most recently proposed IPM multiplication gadget. Given the compatibility with existing ciphers and demonstrated superior resistance against SIFA-1, IPM emerges as a more promising fault-resistant encoding technique compared to prime masking.