Paper 2024/377

Connecting Leakage-Resilient Secret Sharing to Practice: Scaling Trends and Physical Dependencies of Prime Field Masking

Sebastian Faust, Technical University of Darmstadt
Loïc Masure, LIRMM, Univ. Montpellier, CNRS
Elena Micheli, Technical University of Darmstadt
Maximilian Orlt, Technical University of Darmstadt
François-Xavier Standaert, Université Catholique de Louvain

Symmetric ciphers operating in (small or mid-size) prime fields have been shown to be promising candidates to maintain security against low-noise (or even noise-free) side-channel leakage. In order to design prime ciphers that best trade physical security and implementation efficiency, it is essential to understand how side-channel security evolves with the field size (i.e., scaling trends). Unfortunately, it has also been shown that such a scaling trend depends on the leakage functions and cannot be explained by the standard metrics used to analyze Boolean masking with noise. In this work, we therefore initiate a formal study of prime field masking for two canonical leakage functions: bit leakages and Hamming weight leakages. By leveraging theoretical results from the leakage-resilient secret sharing literature, we explain formally why (1) bit leakages correspond to a worst-case and do not encourage operating in larger fields, and (2) an opposite conclusion holds for Hamming weight leakages, where increasing the prime field modulus p can contribute to a security amplification that is exponential in the number of shares,with log(p) seen as security parameter like the noise variance in Boolean masking. We combine these theoretical results with experimental ones and show that the interest masking in larger prime fields can degrade gracefully when leakage functions slightly deviate from the Hamming weight abstraction, motivating further research towards characterizing (ideally wide) classes of leakage functions offering such guarantees.

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Published by the IACR in EUROCRYPT 2024
side-channel analysismaskingprime fieldleakage-resilient cryptographysecret-sharing
Contact author(s)
sebastian faust @ tu-darmstadt de
loic masure @ lirmm fr
elena micheli @ tu-darmstadt de
maximilian orlt @ tu-darmstadt de
fstandae @ uclouvain be
2024-03-01: approved
2024-02-29: received
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      author = {Sebastian Faust and Loïc Masure and Elena Micheli and Maximilian Orlt and François-Xavier Standaert},
      title = {Connecting Leakage-Resilient Secret Sharing to Practice: Scaling Trends and Physical Dependencies of Prime Field Masking},
      howpublished = {Cryptology ePrint Archive, Paper 2024/377},
      year = {2024},
      note = {\url{}},
      url = {}
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