International Association for Cryptologic Research

International Association
for Cryptologic Research


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

Loïc Masure , Université Catholique de Louvain (UCLouvain)
Pierrick Méaux , University of Luxembourg
Thorben Moos , Université Catholique de Louvain (UCLouvain)
François-Xavier Standaert , Université Catholique de Louvain (UCLouvain)
DOI: 10.1007/978-3-031-30634-1_20 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2023
Abstract: Embedded devices used in security applications are natural targets for physical attacks. Thus, enhancing their side-channel resistance is an important research 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 bitslice 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 small to medium 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 illustrate 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 despite the same amount of information being leaked per share.
  title={Effective and Efficient Masking with Low Noise using Small-Mersenne-Prime Ciphers},
  author={Loïc Masure and Pierrick Méaux and Thorben Moos and François-Xavier Standaert},