Welcome to the resource topic for 2024/838
Title:
Verifiable Secret Sharing from Symmetric Key Cryptography with Improved Optimistic Complexity
Authors: Ignacio Cascudo, Daniele Cozzo, Emanuele Giunta
Abstract:In this paper we propose verifiable secret sharing (VSS) schemes
secure for any honest majority in the synchronous model, and that only use symmetric-key cryptographic tools, therefore having plausibly post-quantum security. Compared to the state-of-the-art scheme with these features (Atapoor et al., Asiacrypt `23), our main improvement lies on the complexity of the optimistic'' scenario where the dealer and all but a small number of receivers behave honestly in the sharing phase: in this case, the running time and download complexity (amount of information read) of each honest verifier is polylogarithmic and the total amount of broadcast information by the dealer is logarithmic; all these complexities were linear in the aforementioned work by Atapoor et al. At the same time, we preserve these complexities with respect to the previous work for the pessimistic’’ case where the dealer or O(n) receivers cheat actively.
The new VSS protocol is of interest in multiparty computations where each party runs one VSS as a dealer, such as distributed key generation protocols.
Our main technical handle is a distributed zero-knowledge proof of low degreeness of a polynomial, in the model of Boneh et al. (Crypto 19) where the statement (in this case the evaluations of the witness polynomial) is distributed among several verifiers, each knowing one evaluation. Using folding techniques similar to FRI (Ben-Sasson et al., ICALP 18) we construct such a proof where each verifier receives polylogarithmic information and runs in polylogarithmic time.
ePrint: https://eprint.iacr.org/2024/838
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