Continuously Non-malleable Secret Sharing: Joint Tampering, Plain Model and Capacity

We study non-malleable secret sharing against joint leakage and joint tampering attacks. Our main result is the first threshold secret sharing scheme in the plain model achieving resilience to noisy-leakage and continuous tampering. The above holds under (necessary) minimal computational assumptions (i.e., the existence of one-to-one one-way functions), and in a model where the adversary commits to a fixed partition of all the shares into non-overlapping subsets of at most t- 1 shares (where t is the reconstruction threshold), and subsequently jointly leaks from and tampers with the shares within each partition. We also study the capacity (i.e., the maximum achievable asymptotic information rate) of continuously non-malleable secret sharing against joint continuous tampering attacks. In particular, we prove that whenever the attacker can tamper jointly with k> t/ 2 shares, the capacity is at most t- k. The rate of our construction matches this upper bound. An important corollary of our results is the first non-malleable secret sharing scheme against independent tampering attacks breaking the rate-one barrier (under the same computational assumptions as above).