Leakage-resilient Linear Secret-sharing Against Arbitrary Bounded-size Leakage Family

Hemanta K. Maji, Hai H. Nguyen, Anat Paskin-Cherniavsky, Tom Suad, Mingyuan Wang, Xiuyu Ye, Albert Yu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Motivated by leakage-resilient secure computation of circuits with addition and multiplication gates, this work studies the leakage-resilience of linear secret-sharing schemes with a small reconstruction threshold against any bounded-size family of joint leakage attacks, i.e., the leakage function can leak global information from all secret shares. We first prove that, with high probability, the Massey secret-sharing scheme corresponding to a random linear code over a finite field F is leakage-resilient against any ℓ -bit joint leakage family of size at most | F| k-2.01/ 8 , where k is the reconstruction threshold. Our result (1) bypasses the bottleneck due to the existing Fourier-analytic approach, (2) enables secure multiplication of secrets, and (3) is near-optimal. We use combinatorial and second-moment techniques to prove the result. Next, we show that the Shamir secret-sharing scheme over a prime-order field F with randomly chosen evaluation places and with threshold k is leakage-resilient to any ℓ -bit joint leakage family of size at most | F| 2k-n-2.01/ (k! · 8 ) with high probability. We prove this result by marrying our proof techniques for the first result with the existing Fourier analytical approach. Moreover, it is unlikely that one can extend this result beyond k/ n⩽ 0.5 due to the technical hurdle for the Fourier-analytic approach.

Original languageEnglish
Title of host publicationTheory of Cryptography - 20th International Conference, TCC 2022, Proceedings
EditorsEike Kiltz, Vinod Vaikuntanathan
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages29
ISBN (Print)9783031223174
StatePublished - 2022
Event20th Theory of Cryptography Conference, TCC 2022 - Chicago, United States
Duration: 7 Nov 202210 Nov 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13747 LNCS


Conference20th Theory of Cryptography Conference, TCC 2022
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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