[Resource Topic] 2016/834: Multi-Key Homomorphic Signatures Unforgeable under Insider Corruption

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Title:
Multi-Key Homomorphic Signatures Unforgeable under Insider Corruption

Authors: Russell W. F. Lai, Raymond K. H. Tai, Harry W. H. Wong, Sherman S. M. Chow

Abstract:

Homomorphic signatures (HS) allows the derivation of the signature of the message-function pair (m, g), where m = g(m_1, \ldots, m_K), given the signatures of each of the input messages m_k 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. While the unforgeability of existing M-HS notions unrealistically assumes that all signers are honest, we consider the setting where an arbitrary number of signers can be corrupted, which is typical in natural applications (e.g., verifiable multi-party computation) of M-HS. Surprisingly, there is a huge gap between M-HS with and without unforgeability under corruption: While the latter can be constructed from standard lattice assumptions (ASIACRYPT’16), we show that the former must rely on non-falsifiable assumptions. Specifically, we propose a generic construction of M-HS with unforgeability under corruption from adaptive zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARK) (and other standard assumptions), and then show that such M-HS implies adaptive zero-knowledge succinct non-interactive arguments (ZK-SNARG). Our results leave open the pressing question of what level of authenticity can be guaranteed in the multi-key setting under standard assumptions.

ePrint: https://eprint.iacr.org/2016/834

Slides: https://asiacrypt.iacr.org/2018/files/SLIDES/WEDNESDAY/P514/0850-1030/MKHS_Russell.pdf

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