Stronger lower bounds for leakage-resilient secret sharing

Hoffmann C, Simkin M. 2023. Stronger lower bounds for leakage-resilient secret sharing. 8th International Conference on Cryptology and Information Security in Latin America. LATINCRYPT: Conference on Cryptology and Information Security in Latin America, LNCS, vol. 14168, 215–228.

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Author
Hoffmann, CharlotteISTA ; Simkin, Mark
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
Volume
14168
Page
215-228
Conference
LATINCRYPT: Conference on Cryptology and Information Security in Latin America
Conference Location
Quito, Ecuador
Conference Date
2023-10-03 – 2023-10-06
ISSN
eISSN
IST-REx-ID

Cite this

Hoffmann C, Simkin M. Stronger lower bounds for leakage-resilient secret sharing. In: 8th International Conference on Cryptology and Information Security in Latin America. Vol 14168. Springer Nature; 2023:215-228. doi:10.1007/978-3-031-44469-2_11
Hoffmann, C., & Simkin, M. (2023). Stronger lower bounds for leakage-resilient secret sharing. In 8th International Conference on Cryptology and Information Security in Latin America (Vol. 14168, pp. 215–228). Quito, Ecuador: Springer Nature. https://doi.org/10.1007/978-3-031-44469-2_11
Hoffmann, Charlotte, and Mark Simkin. “Stronger Lower Bounds for Leakage-Resilient Secret Sharing.” In 8th International Conference on Cryptology and Information Security in Latin America, 14168:215–28. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-44469-2_11.
C. Hoffmann and M. Simkin, “Stronger lower bounds for leakage-resilient secret sharing,” in 8th International Conference on Cryptology and Information Security in Latin America, Quito, Ecuador, 2023, vol. 14168, pp. 215–228.
Hoffmann C, Simkin M. 2023. Stronger lower bounds for leakage-resilient secret sharing. 8th International Conference on Cryptology and Information Security in Latin America. LATINCRYPT: Conference on Cryptology and Information Security in Latin America, LNCS, vol. 14168, 215–228.
Hoffmann, Charlotte, and Mark Simkin. “Stronger Lower Bounds for Leakage-Resilient Secret Sharing.” 8th International Conference on Cryptology and Information Security in Latin America, vol. 14168, Springer Nature, 2023, pp. 215–28, doi:10.1007/978-3-031-44469-2_11.
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