Over the last few decades, coding theory has closely associated and interplayed with cryptography in many aspects. An interesting example is the secret-sharing scheme in which the underlying idea can be characterized from both coding-theoretic and cryptographic perspectives. This chapter presents a new formalization and characterization of masking schemes and shows how to enhance their security through a coding-theoretic approach. We first present a coding-theoretic formalization of various masking schemes, by the so-called code-based masking (CBM) paradigm. We then propose a framework for quantifying the information leakage of CBM using mutual information and signal-to-noise (SNR) as the leakage metrics. We derive an interesting formal connection between these two metrics and coding-theoretic properties of the underlying linear codes in CBM. At last, we define the optimal linear code for CBM and show some interesting properties to enhance inner product masking and Shamir’s secret sharing (SSS)-based polynomial masking schemes and more generally any CBM scheme.

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Coding-Theoretic Formalization and Evaluation

  • Wei Cheng,
  • Sylvain Guilley,
  • Olivier Rioul

摘要

Over the last few decades, coding theory has closely associated and interplayed with cryptography in many aspects. An interesting example is the secret-sharing scheme in which the underlying idea can be characterized from both coding-theoretic and cryptographic perspectives. This chapter presents a new formalization and characterization of masking schemes and shows how to enhance their security through a coding-theoretic approach. We first present a coding-theoretic formalization of various masking schemes, by the so-called code-based masking (CBM) paradigm. We then propose a framework for quantifying the information leakage of CBM using mutual information and signal-to-noise (SNR) as the leakage metrics. We derive an interesting formal connection between these two metrics and coding-theoretic properties of the underlying linear codes in CBM. At last, we define the optimal linear code for CBM and show some interesting properties to enhance inner product masking and Shamir’s secret sharing (SSS)-based polynomial masking schemes and more generally any CBM scheme.