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Multiplicative non-abelian sharing schemes and their application to threshold cryptography

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Advances in Cryptology — ASIACRYPT'94 (ASIACRYPT 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 917))

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Abstract

We show how to construct a perfect zero-knowledge threshold proof of knowledge of an isomorphism between two graphs, and extend this result to general access structures. The provers work sequentially and are not allowed to interact among themselves, so the number of message communications each prover sends is the same as with the Goldreich-Micali-Wigderson [12] scheme. Our construction is based on multiplicative sharing schemes in which the secret belongs to a group which is not necessarily Abelian.

A part of this work has been supported by NSF Grant NCR-9106327. Partly carried out while visiting Royal Holloway, University of London and the Università di Salerno, Italy, respectively, and supported in part by NSF Grant INT-9123464 and in part by CNR AI n.94.00011.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee, WI 53201-0784, USA

    Yvo Desmedt

  2. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi (SA), Italy

    Giovanni Di Crescenzo

  3. Department of Mathematics, RH-University of London, TW20 OEX, Egham, Surrey, UK

    Mike Burmester

Authors
  1. Yvo Desmedt
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  2. Giovanni Di Crescenzo
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  3. Mike Burmester
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Josef Pieprzyk Reihanah Safavi-Naini

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© 1995 Springer-Verlag Berlin Heidelberg

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Desmedt, Y., Di Crescenzo, G., Burmester, M. (1995). Multiplicative non-abelian sharing schemes and their application to threshold cryptography. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000421

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  • DOI: https://doi.org/10.1007/BFb0000421

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  • Print ISBN: 978-3-540-59339-3

  • Online ISBN: 978-3-540-49236-8

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