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Necessary and Sufficient Assumptions for Non-interactive Zero-Knowledge Proofs of Knowledge for All NP Relations

Extended Abstract
  • Alfredo De Santis
  • Giovanni Di Crescenzo
  • Giuseppe Persiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1853)

Abstract

Establishing relationships between primitives is an important area in the foundations of Cryptography. In this paper we consider the primitive of non-interactive zero-knowledge proofs of knowledge, namely, methods for writing a proof that on input x the prover knows y such that relation R(x, y) holds. These proofs have important applications for the construction of cryptographic protocols, as cryptosystems and signatures that are secure under strong types of attacks. They were first defined in [10], where a sufficient condition for the existence of such proofs for all NP relations was given. In this paper we show, perhaps unexpectedly, that such condition, based on a variant of public-key cryptosystems, is also necessary. Moreover, we present an alternative and natural condition, based on a variant of commitment schemes, which we show to be necessary and sufficient as well for the construction of such proofs. Such equivalence also allows us to improve known results on the construction of such proofs under the hardness of specific computational problems. Specifically, we show that assuming the hardness of factoring Blum integers is sufficient for such constructions.

Keywords

Random String Commitment Scheme Reference String Trapdoor Permutation Chosen Ciphertext Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Alfredo De Santis
    • 1
  • Giovanni Di Crescenzo
    • 2
  • Giuseppe Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversitá di SalernoBaronissi (SA)Italy
  2. 2.Telcordia Technologies Inc.MorristownUSA

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