What is proactive secret sharing scheme?

In some papers, they just wrote that proactive secret sharing scheme is a secret sharing scheme which its shares are periodically updated. Does it have formal definition ?

• Can you link some of these papers? – nope Aug 19 '17 at 3:21

Proactive secret sharing schemes are typically used for multi-party computation variously referred to as "Secure computation" or simply MPC that arose from the work of Yao and Goldreich, Micali and Wigderson (GMW) in the 80s. MPC's require secrets to be shared among multiple parties, and some of these parties may be controlled by an adversary that is in the most general setting able to deviate from the specified protocol in a "byzantine" manner. As a concrete case, in the GMW protocol with $$n$$ parties, in order for the $$i$$th party to share its bit $$b_{i} \in \{0,1\}$$ with the other $$n - 1$$ parties, she generates $$n - 1$$ i.i.d uniformly random bits and sends one of the generated bits to each of the parties. She then sets her share of $$b_{i}$$ such that the sum of her share and the other $$n - 1$$ bits mod 2 gives back the original bit $$b_{i}$$. This sharing scheme is "perfectly" secure since there is no complexity assumption. In the classic MPC model, it is assumed that the parties controlled by the adversary are determined beforehand and remain fixed during the course. This is sometimes called static corruption.