On Proactive Verifiable Secret Sharing Schemes

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004

This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player's shares and we present two types of attacks in the information theoretic case. Then we prove the conditions for the security of such a proactive scheme. Proactivity can be added also using re-sharing instead of commitment to 0. We investigate this alternative approach too and describe two protocols. We also show that both techniques are not secure against a mobile adversary. To summarize we generalize the existing threshold protocols to protocols for general access structure. Besides this, we propose attacks against the existing proactive verifiable secret sharing schemes, and give modifications of the schemes that resist these attacks.