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DOI: 10.4230/LIPIcs.ITC.2026.9

Resilience of Inner-Product Masking Scheme Against Hamming Weight Leakage

Authors: Aniruddha Biswas, Jihun Hwang, Hemanta K. Maji, and Xiuyu Ye

Published in: LIPIcs, Volume 385, 7th Conference on Information-Theoretic Cryptography (ITC 2026)

Abstract

Additive masking is a widely used countermeasure against side-channel attacks in which a secret is additively split into multiple random shares. However, over binary fields, the number of 1’s in the binary representation (i.e., the Hamming weight) of the shares reveals information about the original secret. Inner-product masking scheme has been proposed as a promising alternative that is secure against such information leakage. In this work, we establish that inner-product masking over a binary extension field is provably secure against Hamming weight leakage, and it translates into security against arbitrary symmetric function leakage from the shares. In addition, we present an efficiently computable score function that quantifies its security against leakages, enabling users to test and certify its security. Finally, we derive a relationship between the leakage resilience of inner-product masking and additive masking over arbitrary fields; roughly speaking, they are at least as secure as additive masking. Our approach is Fourier-analytic and involves estimating spectral norms of the Hamming slice by studying Krawtchouk polynomials.

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Aniruddha Biswas, Jihun Hwang, Hemanta K. Maji, and Xiuyu Ye. Resilience of Inner-Product Masking Scheme Against Hamming Weight Leakage. In 7th Conference on Information-Theoretic Cryptography (ITC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 385, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{biswas_et_al:LIPIcs.ITC.2026.9,
  author =	{Biswas, Aniruddha and Hwang, Jihun and Maji, Hemanta K. and Ye, Xiuyu},
  title =	{{Resilience of Inner-Product Masking Scheme Against Hamming Weight Leakage}},
  booktitle =	{7th Conference on Information-Theoretic Cryptography (ITC 2026)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-426-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{385},
  editor =	{Dodis, Yevgeniy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2026.9},
  URN =		{urn:nbn:de:0030-drops-271023},
  doi =		{10.4230/LIPIcs.ITC.2026.9},
  annote =	{Keywords: Local leakage resilience, additive masking, inner product masking, Hamming weight leakage, Fourier analysis, Krawtchouk polynomials}
}

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DOI: 10.4230/LIPIcs.ITC.2025.3

Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places

Authors: Jihun Hwang, Hemanta K. Maji, Hai H. Nguyen, and Xiuyu Ye

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract

Can Shamir’s secret-sharing protect its secret even when all shares are partially compromised? For instance, repairing Reed-Solomon codewords, when possible, recovers the entire secret in the corresponding Shamir’s secret sharing. Yet, Shamir’s secret sharing mitigates various side-channel threats, depending on where its "secret-sharing polynomial" is evaluated. Although most evaluation places yield secure schemes, none are known explicitly; even techniques to identify them are unknown. Our work initiates research into such classifier constructions and derandomization objectives. In this work, we focus on Shamir’s scheme over prime fields, where every share is required to reconstruct the secret. We investigate the security of these schemes against single-bit probes into shares stored in their native binary representation. Technical analysis is particularly challenging when dealing with Reed-Solomon codewords over prime fields, as observed recently in the code repair literature. Furthermore, ensuring the statistical independence of the leakage from the secret necessitates the elimination of any subtle correlations between them. In this context, we present: 1) An efficient algorithm to classify evaluation places as secure or vulnerable against the least-significant-bit leakage. 2) Modulus choices where the classifier above extends to any single-bit probe per share. 3) Explicit modulus choices and secure evaluation places for them. On the way, we discover new bit-probing attacks on Shamir’s scheme, revealing surprising correlations between the leakage and the secret, leading to vulnerabilities when choosing evaluation places naïvely. Our results rely on new techniques to analyze the security of secret-sharing schemes against side-channel threats. We connect their leakage resilience to the orthogonality of square wave functions, which, in turn, depends on the 2-adic valuation of rational approximations. These techniques, novel to the security analysis of secret sharings, can potentially be of broader interest.

Cite as

Jihun Hwang, Hemanta K. Maji, Hai H. Nguyen, and Xiuyu Ye. Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hwang_et_al:LIPIcs.ITC.2025.3,
  author =	{Hwang, Jihun and Maji, Hemanta K. and Nguyen, Hai H. and Ye, Xiuyu},
  title =	{{Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.3},
  URN =		{urn:nbn:de:0030-drops-243531},
  doi =		{10.4230/LIPIcs.ITC.2025.3},
  annote =	{Keywords: Shamir’s secret sharing, leakage resilience, physical bit probing, secure evaluation places, secure modulus choice, square wave families, LLL algorithm, Fourier analysis}
}

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Documents authored by Hwang, Jihun

Resilience of Inner-Product Masking Scheme Against Hamming Weight Leakage

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Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places

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