Multi-Key Homomorphic Signatures Unforgeable under Insider Corruption presented at Asiacrypt2018 2018

by Sherman Chow, Russell Lai, Raymond Tai, Harry Wong,

Summary : Homomorphic signatures (HS) allows the derivation of the signature of the message-function pair (m, g), where m=g(m1,…,mK) , given the signatures of each of the input messages mk signed under the same key. Multi-key HS (M-HS) introduced by Fiore et al. (ASIACRYPT’16) further enhances the utility by allowing evaluation of signatures under different keys. The unforgeability of existing M-HS notions assumes that all signers are honest. We consider a setting where an arbitrary number of signers can be corrupted, called unforgeability under corruption, which is typical for natural applications (e.g., verifiable multi-party computation) of M-HS. Surprisingly, there is a huge gap between M-HS (for arbitrary circuits) with and without unforgeability under corruption: While the latter can be constructed from standard lattice assumptions (ASIACRYPT’16), we show that the former likely relies on non-falsifiable assumptions. Specifically, we propose a generic construction of M-HS with unforgeability under corruption from zero-knowledge succinct non-interactive argument of knowledge (ZK-SNARK) (and other standard assumptions), and then show that such M-HS implies zero-knowledge succinct non-interactive arguments (ZK-SNARG). Our results leave open the pressing question of what level of authenticity and utility can be achieved in the presence of corrupt signers under standard assumptions.