Continuously Non-malleable Secret Sharing for General Access Structures.

We study leakage-resilient continuously non-malleable secret sharing, as recently introduced by Faonio and Venturi (CRYPTO 2019). In this setting, an attacker can continuously tamper and leak from a target secret sharing of some message, with the goal of producing a modified set of shares that reconstructs to a message related to the originally shared value. Our contributions are two fold. In the plain model, assuming one-to-one one-way functions, we show how to obtain noisy-leakage-resilient continuous non-malleability for arbitrary access structures, in case the attacker can continuously leak from and tamper with all of the shares independently. In the common reference string model, we show how to obtain a new flavor of security which we dub bounded-leakage-resilient continuous non-malleability under selective k-partitioning. In this model, the attacker is allowed to partition the target n shares into any number of non-overlapping blocks of maximal size k, and then can continuously leak from and tamper with the shares within each block jointly. Our construction works for arbitrary access structures, and assuming (doubly enhanced) trapdoor permutations and collision-resistant hash functions, we achieve a concrete instantiation for k is an element of O(log n). Prior to our work, there was no secret sharing scheme achieving continuous non-malleability against joint tampering, and the only known scheme for independent tampering was tailored to threshold access structures.