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2020 | OriginalPaper | Buchkapitel

Non-interactive Composition of Sigma-Protocols via Share-then-Hash

verfasst von : Masayuki Abe, Miguel Ambrona, Andrej Bogdanov, Miyako Ohkubo, Alon Rosen

Erschienen in: Advances in Cryptology – ASIACRYPT 2020

Verlag: Springer International Publishing

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Abstract

Proofs of partial knowledge demonstrate the possession of certain subsets of witnesses for a given collection of statements \(x_1,\dots ,x_n\). Cramer, Damgård, and Schoenmakers (CDS), built proofs of partial knowledge, given “atomic” protocols for individual statements \(x_i\), by having the prover randomly secret share the verifier’s challenge and using the shares as challenges for the atomic protocols. This simple and highly-influential transformation has been used in numerous applications, ranging from anonymous credentials to ring signatures.

We consider what happens if, instead of using the shares directly as challenges, the prover first hashes them. We show that this elementary enhancement can result in significant benefits:

the proof contains a single atomic transcript per statement \(x_i\),
it suffices that the atomic protocols are \({\kappa }\)-special sound for \({\kappa }\ge 2\),
when compiled to a signature scheme using the Fiat-Shamir heuristic, its unforgeability can be proved in the non-programmable random oracle model.

None of the above features is satisfied by the CDS transformation.

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Vorheriges Kapitel Crowd Verifiable Zero-Knowledge and End-to-End Verifiable Multiparty Computation

Nächstes Kapitel Succinct Diophantine-Satisfiability Arguments

Although the total length of secrets \((s_1,\dots ,s_n)\) is \(\mu N\), as above it is enough to store the \(\ell \) disjunction values \((d_1,\dots ,d_\ell )\) sampled by \(\mathsf {Share}\).

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Titel: Non-interactive Composition of Sigma-Protocols via Share-then-Hash
verfasst von: Masayuki Abe
Miguel Ambrona
Andrej Bogdanov
Miyako Ohkubo
Alon Rosen
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2020
Print ISBN: 978-3-030-64839-8

Electronic ISBN: 978-3-030-64840-4

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-64840-4_25

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