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Groth-Sahai proofs revisited

Smart, Nigel P.; Ghadafi, Essam; Warinschi, Bogdan


Nigel P. Smart

Essam Ghadafi
Senior Lecturer in Computer Science

Bogdan Warinschi


P.Q Nguyen

D Pointcheval


Since their introduction in 2008, the non-interactive zero-knowledge (NIZK) and non-interactive witness indistinguishable (NIWI) proofs designed by Groth and Sahai have been used in numerous applications. In this paper, we offer two contributions to the study of these proof systems. First, we identify and correct some errors, present in the oringal online manuscript, that occur in two of the three instantiations of the Groth-Sahai NIWI proofs for which the equation checked by the verifier is not valid for honest executions of the protocol. In particular, implementations of these proofs would not work correctly. We explain why, perhaps surprisingly, the NIZK proofs that are built from these NIWI proofs do not suffer from a similar problem. Secondly, we study the efficiency of existing instantiations and note that only one of the three instantiations has the potential of being practical. We therefore propose a natural extension of an existing assumption from symmetric pairings to asymmetric ones which in turn enables Groth-Sahai proofs based on new classes of efficient pairings. © 2010 Springer-Verlag Berlin Heidelberg.


Smart, N. P., Ghadafi, E., Smart, N. P., & Warinschi, B. (2010). Groth-Sahai proofs revisited. Lecture Notes in Artificial Intelligence, 6056 LNCS, 177-192.

Journal Article Type Conference Paper
Acceptance Date May 26, 2010
Publication Date Dec 1, 2010
Journal Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Print ISSN 0302-9743
Electronic ISSN 1611-3349
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 6056 LNCS
Pages 177-192
Keywords Groth-Sahai, proofs, revisited
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