Paper improves Shamir leakage-resilience bound below one half
Original title: An Explicit Below Half Threshold Bound for the Local Leakage Resilience of Shamir's Secret Sharing Scheme
For large n and prime p greater than n, resilience holds whenever t/n is at least 0.489.
A cs.CR paper studies how much local leakage Shamir's secret sharing over prime fields can tolerate before reconstruction fails. Against arbitrary 1-bit leakage from each share, the authors show that for all sufficiently large n and every prime p greater than n, the (n,t)-Shamir scheme is exp(-Ω(n))-resilient whenever t/n is at least 0.489, for any distinct nonzero evaluation points. The proof refines dual-code list recovery and combines Fourier estimates based on leakage-function support sizes and biases. No implementation or attack is described.
Unconfirmed: The bound is asymptotic for all sufficiently large n; a concrete n is not given.
- The bound applies to arbitrary 1-bit local leakage.
- Resilience is exponential in n under the stated threshold.
- The result holds for any distinct nonzero evaluation points.
From the original article
1 min read at arxiv.orgAs a fundamental cryptographic primitive, secret sharing distributes a secret among multiple parties and allows certain authorized parties to recover the secret while preventing unauthorized parties from knowing the secret. However, local leakage from each party member allows an adversary to learn partial information from each share, which is not guaranteed by traditional security.
By Cheng Zhang · arxiv.org
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