Non-Interactive Forward-Secure Threshold Signature without Random Oracles

Forward-secure threshold signature is one kind of important distributed signatures. In a (t, n) forward-secure threshold signature, if an adversary attacks fewer than t players, she cannot forge any valid signature; even if an adversary attacks t or more players in some time period, she cannot forge the signatures of previous time periods. At present, all forward-secure threshold schemes are at most proven to be secure in the random oracle model. However, security in the random oracle model does not imply security in the real world. In this work, we proposed the first forward-secure threshold signature scheme that can be proven secure without random oracles. In this scheme, the complexity of any performance parameter is at most log-squared in terms of the total number of time periods T. Another important point that differentiates our scheme from previous schemes is that our scheme does not need any interaction among the players in key update and signing algorithms. Therefore, the players can update their shares and sign the message, possibly in a completely decentralized fashion, which is very valuable in ad-hoc circumstances.