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Randomness-efficient non-interactive zero knowledge

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  • Session 18: Cryptography
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

The model of Non-Interactive Zero-Knowledge allows to obtain minimal interaction between prover and verifier in a zero-knowledge proof if a public random string is available to both parties. In this paper we investigate upper bounds for the length of the random string for proving one and many statements, obtaining the following results:

  • We show how to prove in non-interactive perfect zero-knowledge any polynomial number of statements using a random string of fixed length, that is, not depending on the number of statements. Previously, such a result was known only in the case of computational zero-knowledge.

  • Under the quadratic residuosity assumption, we show how to prove any NP statement in non-interactive zero-knowledge on a random string of length ⊝(nk), where n is the size of the statement and k is the security parameter, which improves the previous best construction by a factor of ⊝(k).

Part of this work was done while at Università di Salerno, Italy

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi, SA, Italy

    Alfredo De Santis & Pino Persiano

  2. Computer Science and Engineering Department, University of California at San Diego, 92093, La Jolla, CA, USA

    Giovanni Di Crescenzo

Authors
  1. Alfredo De Santis
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  2. Giovanni Di Crescenzo
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  3. Pino Persiano
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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De Santis, A., Di Crescenzo, G., Persiano, P. (1997). Randomness-efficient non-interactive zero knowledge. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_225

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  • DOI: https://doi.org/10.1007/3-540-63165-8_225

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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