I am working on Cryptographic protocols. While I was doing a survey, I required some "Non-Interactive Zero Knowledge Proofs" (NIZK) which I can use.

I can only find transformations between different models of NIZK in the abstract sense, like the Hidden Bits Model (J.Katz) and non-malleable NIZK (A.Sahai)

Is there any credible material like Thesis/Papers where I can find example constructions of Non-Interactive Zero Knowledge Proofs which I can make use for my protocols.


  • 2
    $\begingroup$ Can you modify the title so that it matches your question more clearly? You are specifically asking about NIZK, not general ZK. $\endgroup$ Sep 8, 2011 at 16:39
  • $\begingroup$ @Tsuyoshi I edited it as per your suggestion. $\endgroup$ Sep 8, 2011 at 16:55

2 Answers 2


I'm not sure what exactly you are looking for.

Goldreich's book ("Foundations of Cryptography, volume 1") contains an extensive discussion of non-interactive ZK proofs. So do these lecture notes of Katz (lectures 11-13): http://www.cs.umd.edu/~jkatz/gradcrypto2/scribes.html.

You could also look at this paper: Uriel Feige, Dror Lapidot, Adi Shamir: Multiple NonInteractive Zero Knowledge Proofs Under General Assumptions. SIAM J. Comput. 29(1): 1-28 (1999) and references therein.


The most famous "efficient" NIZK is by Groth and Sahai:

Jens Groth, Amit Sahai Efficient Non-interactive Proof Systems for Bilinear Groups, Eurocrypt 2008

If you are willing to use stronger security assumptions, you can get even better efficiency. See the following paper of Groth (and subsequent improvements by other people), for example:

Jens Groth Short Pairing-Based Non-interactive Zero-Knowledge Arguments, Asiacrypt 2010


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