Taming Adaptive Security and New Access Structures in Evolving Secret Sharing

Evolving secret sharing (Komargodski, Naor, and Yogev, TCC 2016) allows a dealer to share a secret value in an online manner, without knowing the access structure or the maximum number of parties in advance, and without ever updating the shares of older players. In this paper, we continue the study of evolving secret sharing schemes in the computational setting, as first considered by Francati and Venturi (ASIACRYPT 2024), where the number of parties is upper bounded by an unknown polynomial and the privacy property only holds against computationally-bounded adversaries. Our main results are outlined below:We construct secret sharing schemes for new evolving access structures. In particular, we design secret sharing schemes for the so-called dynamic weighted threshold evolving access structure and for all evolving monotone functions in NP.We initiate the study of adaptive security for evolving secret sharing, where the attacker can corrupt shareholders in an adaptive manner. In particular, we design adaptively-secure secret sharing schemes for the dynamic weighted threshold evolving access structure and for evolving monotone circuits. We construct secret sharing schemes for new evolving access structures. In particular, we design secret sharing schemes for the so-called dynamic weighted threshold evolving access structure and for all evolving monotone functions in NP. We initiate the study of adaptive security for evolving secret sharing, where the attacker can corrupt shareholders in an adaptive manner. In particular, we design adaptively-secure secret sharing schemes for the dynamic weighted threshold evolving access structure and for evolving monotone circuits.