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2020 | OriginalPaper | Chapter

Signatures from Sequential-OR Proofs

Authors : Marc Fischlin, Patrick Harasser, Christian Janson

Published in: Advances in Cryptology – EUROCRYPT 2020

Publisher: Springer International Publishing

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Abstract

OR-proofs enable a prover to show that it knows the witness for one of many statements, or that one out of many statements is true. OR-proofs are a remarkably versatile tool, used to strengthen security properties, design group and ring signature schemes, and achieve tight security. The common technique to build OR-proofs is based on an approach introduced by Cramer, Damgård, and Schoenmakers (CRYPTO’94), where the prover splits the verifier’s challenge into random shares and computes proofs for each statement in parallel.

In this work we study a different, less investigated OR-proof technique, highlighted by Abe, Ohkubo, and Suzuki (ASIACRYPT’02). The difference is that the prover now computes the individual proofs sequentially. We show that such sequential OR-proofs yield signature schemes which can be proved secure in the non-programmable random oracle model. We complement this positive result with a black-box impossibility proof, showing that the same is unlikely to be the case for signatures derived from traditional OR-proofs. We finally argue that sequential-OR signature schemes can be proved secure in the quantum random oracle model, albeit with very loose bounds and by programming the random oracle.

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previous chapter Sigma Protocols for MQ, PKP and SIS, and Fishy Signature Schemes

next chapter Compact Adaptively Secure ABE from k-Lin: Beyond and Towards

One can think of this as a very lossy mode.

One could indeed argue why we are here allowed to program the random oracle in light of the discussion about non-programmability. One may think of this here as a restriction of the reduction, that it needs to be able to cope with such external oracles. Technically, it gives the required advantage over the reduction to make the meta-reduction argument work.

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Title: Signatures from Sequential-OR Proofs
Authors: Marc Fischlin
Patrick Harasser
Christian Janson
Publisher: Springer International Publishing
Book: Advances in Cryptology – EUROCRYPT 2020
Print ISBN: 978-3-030-45726-6

Electronic ISBN: 978-3-030-45727-3

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-45727-3_8

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