We show a robust secret sharing scheme for a maximal threshold t < n/2 that features an optimal overhead in share size, offers security against a rushing adversary, and runs in polynomial time. Previous robust secret sharing schemes for t < n/2 either suffered from a suboptimal overhead, offered no (provable) security against a rushing adversary, or ran in superpolynomial time.

Lecture Notes in Computer Science
Theory of Cryptography Conference
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Fehr, S, & Yuan, C. (2020). Robust secret sharing with almost optimal share size and security against rushing adversaries. In TCC 2020: Theory of Cryptography (pp. 470–498). doi:10.1007/978-3-030-64381-2_17