[Resource Topic] 2022/863: Effective and Efficient Masking with Low Noise using Small-Mersenne-Prime Ciphers

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Title:
Effective and Efficient Masking with Low Noise using Small-Mersenne-Prime Ciphers

Authors: Loïc Masure, Pierrick Méaux, Thorben Moos, and François-Xavier Standaert

Abstract:

Embedded devices with built-in security features are natural targets for physical attacks. Thus, enhancing their side-channel resistance is an important practical challenge. A standard solution for this purpose is the use of Boolean masking schemes, as they are well adapted to current block ciphers with efficient bit-slice representations. Boolean masking guarantees that the security of an implementation grows exponentially in the number of shares under the assumption that leakages are sufficiently noisy (and independent). Unfortunately, it has been shown that this noise assumption is hardly met on low-end devices. In this paper, we therefore investigate techniques to mask cryptographic algorithms in such a way that their resistance can survive an almost complete lack of noise. Building on seed theoretical results of Dziembowski et al., we put forward that arithmetic encodings in prime fields can reach this goal. We first exhibit the gains that such encodings lead to thanks to a simulated information theoretic analysis of their leakage (with up to six shares). We then provide figures showing that on platforms where optimized arithmetic adders and multipliers are readily available (i.e., most MCUs and FPGAs), performing masked operations in Mersenne-prime fields as opposed to binary extension fields will not lead to notable implementation overheads. We compile these observations into a new AES-like block cipher, called AES-prime, which is well-suited to leverage the remarkable advantages of masking in prime fields. We also confirm the practical relevance of our findings by evaluating concrete software (ARM Cortex-M3) and hardware (Xilinx Spartan-6) implementations. Our experimental results show that security gains over Boolean masking (and, more generally, binary encodings) can reach orders of magnitude.

ePrint: https://eprint.iacr.org/2022/863

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