Leakage Resilient Cheating Detectable Secret Sharing Schemes

Abstract

A secret sharing scheme generates shares of a secret that will be distributed among a set of participants such that the shares of qualified subsets of participants can reconstruct the secret, and shares of non-qualified subsets leak no information about the secret. Secret sharing is a fundamental cryptographic primitive in multiparty computation, threshold cryptography, and secure distributed systems. Leakage resilient secret sharing models side channel leakages from all the shares to the adversary, rendering the adversary more powerful. In CRYPTO’19 Srinivasan and Vasudevan (SV) proposed compilers that convert a secret sharing for a general access structure to a leakage resilient secret sharing for the same access structure in two leakage models: local leakage and strong local leakage. In this paper we consider cheater detectable secret sharing that provides security against active (cheating) attackers that modify their controlled shares with the goal of modifying the reconstructed secret. We extend the SV compilers to convert a linear secret sharing for a general access structure to a cheater detectable secret sharing for the same access structure when the adversary has access to the shares of a non-qualified subset and the leaked information from all other shares. Our extensions add a precoding step to the SV compilers that use Algebraic Manipulation Detection (AMD) codes, and work for both well established models of cheater detection known as \(\textsf {OKS}\) and \(\textsf {CDV}\) models, using weak and strong AMD codes, respectively. To prove our results we formalize two security notions for leakage resilient cheating detectable secret sharing, and prove relation between them, which can be of independent interest. We discuss directions for future work.