Leakage-Resilient Secret Sharing
February 27, 2019 (GHC 8102)

A secret sharing scheme allows a dealer to share a secret among a set of n parties such that any authorized subset of the parties can recover the secret, while any unauthorized subset learns no information about the secret. A leakage-resilient secret sharing scheme (introduced in independent works by Goyal and Kumar, STOC ’18 and Benhamouda, Degwekar, Ishai and Rabin, CRYPTO ’18) additionally requires the secrecy to hold against every unauthorized set of parties even if they obtain some bounded leakage from every other share. The leakage is said to be local if it is computed independently for each share. So far, the only known constructions of local leakage resilient secret sharing schemes are for threshold access structures for very low (O(1)) or very high (n-o(log n)) thresholds.

In this work, we give a compiler that takes a secret sharing scheme for any monotone access structure and produces a local leakage resilient secret sharing scheme for the same access structure, with only a constant factor asymptotic blow-up in the sizes of the shares. Furthermore, the resultant secret sharing scheme has optimal leakage-resilience rate, i.e., the ratio between the leakage tolerated and the size of each share can be made arbitrarily close to 1.

Based on joint work with Prasanth Vasudevan.