Stronger lower bounds for leakage-resilient secret sharing

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Conference Paper | Published | English

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Author
Hoffmann, CharlotteISTA ; Simkin, Mark

Corresponding author has ISTA affiliation

Department
Series Title
LNCS
Abstract
Threshold secret sharing allows a dealer to split a secret s into n shares, such that any t shares allow for reconstructing s, but no t-1 shares reveal any information about s. Leakage-resilient secret sharing requires that the secret remains hidden, even when an adversary additionally obtains a limited amount of leakage from every share. Benhamouda et al. (CRYPTO’18) proved that Shamir’s secret sharing scheme is one bit leakage-resilient for reconstruction threshold t≥0.85n and conjectured that the same holds for t = c.n for any constant 0≤c≤1. Nielsen and Simkin (EUROCRYPT’20) showed that this is the best one can hope for by proving that Shamir’s scheme is not secure against one-bit leakage when t0c.n/log(n). In this work, we strengthen the lower bound of Nielsen and Simkin. We consider noisy leakage-resilience, where a random subset of leakages is replaced by uniformly random noise. We prove a lower bound for Shamir’s secret sharing, similar to that of Nielsen and Simkin, which holds even when a constant fraction of leakages is replaced by random noise. To this end, we first prove a lower bound on the share size of any noisy-leakage-resilient sharing scheme. We then use this lower bound to show that there exist universal constants c1, c2, such that for sufficiently large n it holds that Shamir’s secret sharing scheme is not noisy-leakage-resilient for t≤c1.n/log(n), even when a c2 fraction of leakages are replaced by random noise.
Publishing Year
Date Published
2023-10-01
Proceedings Title
8th International Conference on Cryptology and Information Security in Latin America
Publisher
Springer Nature
Volume
14168
Page
215-228
Conference
LATINCRYPT: Cryptology and Information Security in Latin America
Conference Location
Quito, Ecuador
Conference Date
2023-10-03 – 2023-10-06
ISSN
eISSN
IST-REx-ID
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