[1]

Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy. Proof verification and hardness of approximation problems. In *Proceedings of the Thirty Third Annual Symposium on Foundations of Computer Science*, pages 14–23, 1992.

[2]

Sanjeev Arora and Shmuel Safra. Probabilistic checking of proofs. In *Proceedings of the Thirty Third Annual Symposium on Foundations of Computer Science*, pages 2–13, 1992.

[3]

Mihir Bellare and Shafi Goldwasser. New paradigms for digital signatures and message authentication based on non-interactive zero knowledge proofs. In G. Brassard, editor,

*Advances in Cryptology—CRYPTO’ 89*, volume 435 of

*Lecture Notes in Computer Science*, pages 194–211. Springer-Verlag, 1990, 20–24 August 1989.

CrossRefGoogle Scholar[4]

Mihir Bellare, Silvio Micali, and Rafail Ostrovsky. Perfect zero-knowledge in constant rounds. In *Proceedings of the Twenty Second Annual ACM Symposium on Theory of Computing*, pages 482–493, 1990.

[5]

Mihir Bellare and Phillip Rogaway. Non-interactive perfect zero-knowledge. Unpublished manuscript, June 1990.

[6]

Manuel Blum, Alfredo De Santis, Silvio Micali, and Giuseppe Persiano. Noninteractive zero-knowledge.

*SIAM Journal on Computing*, 20(6):1084–1118, December 1991.

MATHCrossRefMathSciNetGoogle Scholar[7]

Manuel Blum, Paul Feldman, and Silvio Micali. Non-interactive zero-knowledge and its applications (extended abstract). In *Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing*, pages 103–112, Chicago, Illinois, 2–4 May 1988.

[8]

Ivan Damgård. Interactive hashing can simplify zero-knowledge protocol design. In

*Proceedings of Crypto’ 95*, Lecture Notes in Computer Science, volume 403, pages 100–109. Springer-Verlag, 1994.

Google Scholar[9]

Ivan Damgård, Oded Goldreich, Tatsuaki Okamoto, and Avi Wigderson. Honest verifier vs. dishonest verifier in public coin zero-knowledge proofs. In

*Proceedings of Crypto’ 95*, Lecture Notes in Computer Science, volume 403. Springer-Verlag, 1995.

Google Scholar[10]

Ivan Damgård, Oded Goldreich, and Avi Wigderson. Hashing functions can simplify zero-knowledge protocol design (too). Technical Report RS-94-39, BRICS, November 1994. See Part 1 of [9].

[11]

Alfredo De Santis, Giovanni Di Crescenzo, and Giuseppe Persiano. Randomness-efficient non-interactive zero-knowledge (extended abstract). In Pierpaolo Degano, Robert Gorrieri, and Alberto Marchetti-Spaccamela, editors,

*Automata, Languages and Programming*, 24th International Colloquium, volume 1256 of

*Lecture Notes in Computer Science*, pages 716–726, Bologna, Italy, 7–11 July 1997. Springer-Verlag.

Google Scholar[12]

Alfredo De Santis, Giovanni Di Crescenzo, Giuseppe Persiano, and Moti Yung. Image Density is complete for non-interactive-SZK. In *Automata, Languages and Programming, 25th International Colloquium*, Lectures Notes in Computer Science, pages 784–795, Aalborg, Denmark, 13–17 July 1998. Springer-Verlag. See [13].

[13]

Alfredo De Santis, Giovanni Di Crescenzo, Giuseppe Persiano, and Moti Yung. Image Density is complete for non-interactive-SZK, May 1999. Preliminary draft of full version.

[14]

Alfredo De Santis, Giovanni Di Crescenzo, and Guiseppe Persiano. The knowledge complexity of quadratic residuosity languages.

*Theoretical Computer Science*, 132(1–2):291–317, 26 September 1994.

MATHCrossRefMathSciNetGoogle Scholar[15]

Alfredo De Santis, Silvio Micali, and Giuseppe Persiano. Non-interactive zero-knowledge proof systems. In Carl Pomerance, editor,

*Advances in Cryptology — CRYPTO’ 87*, volume 293 of

*Lecture Notes in Computer Science*, pages 52–72. Springer-Verlag, 1988, 16–20 August 1987.

Google Scholar[16]

Alfredo De Santis, Silvio Micali, and Giuseppe Persiano. Non-interactive zero-knowledge with preprocessing. In S. Goldwasser, editor,

*Advances in Cryptology — CRYPTO’ 88*, volume 403 of

*Lecture Notes in Computer Science*, pages 269–282. Springer-Verlag, 1990, 21–25 August 1988.

Google Scholar[17]

Giovanni Di Crescenzo, Tatsuaki Okamoto, and Moti Yung. Keeping the SZK-verifier honest unconditionally. In *Advances in Cryptology — CRYPTO’ 97*, pages 31–45, 1997.

[18]

Danny Dolev, Cynthia Dwork, and Moni Naor. Non-malleable cryptography (extended abstract). In *Proceedings of the Twenty Third Annual ACM Symposium on Theory of Computing*, pages 542–552, New Orleans, Louisiana, 6–8 May 1991.

[19]

Cynthia Dwork, Moni Naor, and Amit Sahai. Concurrent zero-knowledge. In *Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing*, pages 409–418, 1998.

[20]

Uriel Feige, Dror Lapidot, and Adi Shamir. Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In *31st Annual Symposium on Foundations of Computer Science*, volume I, pages 308–317, St. Louis, Missouri, 22-24 October 1990. IEEE.

[21]

Lance Fortnow. The complexity of perfect zero-knowledge. In Silvio Micali, editor, *Advances in Computing Research*, volume 5, pages 327–343. JAC Press, Inc., 1989.

[22]

Oded Goldreich and Eyal Kushilevitz. A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm.

*Journal of Cryptology*, 6:97–116, 1993.

MATHCrossRefMathSciNetGoogle Scholar[23]

Oded Goldreich, Silvio Micali, and Avi Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems.

*Journal of the Association for Computing Machinery*, 38(1):691–729, 1991.

MATHMathSciNetGoogle Scholar[24]

Oded Goldreich and Yair Oren. Definitions and properties of zero-knowledge proof systems.

*Journal of Cryptology*, 7(1):1–32, Winter 1994.

MATHCrossRefMathSciNetGoogle Scholar[25]

Oded Goldreich, Amit Sahai, and Salil Vadhan. Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge. In *Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing*, pages 399–408, 1998.

[26]

Oded Goldreich, Amit Sahai, and Salil Vadhan. Can statistical zero knowledge be made non-interactive? or On the relationship of SZK and NISZK. Submitted to

*ECCC*, May 1999.

http://www.eccc.uni-trier.de/eccc/.

[27]

Oded Goldreich and Salil Vadhan. Comparing entropies in statistical zero-knowledge with applications to the structure of SZK. In *Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity*, pages 54–73, Atlanta, GA, May 1999. IEEE Computer Society Press.

[28]

Shafi Goldwasser and Silvio Micali. Probabilistic encryption.

*Journal of Computer and System Sciences*, 28(2):270–299, 1984.

MATHCrossRefMathSciNetGoogle Scholar[29]

Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof systems.

*SIAM Journal on Computing*, 18(1):186–208, February 1989.

MATHCrossRefMathSciNetGoogle Scholar[30]

Russell Impagliazzo, Leonid A. Levin, and Michael Luby. Pseudo-random generation from one-way functions (extended abstracts). In *Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing*, pages 12–24, Seattle, Washington, 15-17 May 1989.

[31]

Joe Kilian and Erez Petrank. An efficient noninteractive zero-knowledge proof system for NP with general assumptions.

*Journal of Cryptology*, 11(1):1–27, Winter 1998.

MATHCrossRefMathSciNetGoogle Scholar[32]

R. E. Ladner, N. A. Lynch, and A. L. Selman. A comparison of polynomial time reducibilities.

*Theoretical Computer Science*, 1(2):103–123, December 1975.

MATHCrossRefMathSciNetGoogle Scholar[33]

Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan. Algebraic methods for interactive proofs. In *Proceedings of the Thirty First Annual Symposium on Foundations of Computer Science*, pages 1–10, 1990.

[34]

Moni Naor and Moti Yung. Public-key cryptosystems provably secure against chosen ciphertext attacks. In *Proceedings of the Twenty Second Annual ACM Symposium on Theory of Computing*, pages 427–437, Baltimore, Maryland, 14–16 May 1990.

[35]

Tatsuaki Okamoto. On relationships between statistical zero-knowledge proofs. In *Proceedings of the Twenty Eighth Annual ACM Symposium on the Theory of Computing*, 1996. See also preprint of full version, Oct. 1997.

[36]

Rafail Ostrovsky. One-way functions, hard on average problems, and statistical zero-knowledge proofs. In *Proceedings of the Thirty Second Annual Symposium on Foundations of Computer Science*, pages 133–138, 1991.

[37]

Rafail Ostrovsky and Avi Wigderson. One-way functions are essential for nontrivial zero-knowledge. In *Proceedings of the Second Israel Symposium on Theory of Computing and Systems*, 1993.

[38]

Amit Sahai and Salil Vadhan. A complete promise problem for statistical zero-knowledge. In *Proceedings of the Thirty Eighth Annual Symposium on Foundations of Computer Science*, pages 448–457, 1997.

[39]

Amit Sahai and Salil Vadhan. Manipulating statistical difference. In Panos Pardalos, Sanguthevar Rajasekaran, and José Rolim, editors, *Randomization Methods in Algorithm Design (DIMACS Workshop, December 1997)*, volume 43 of *DIMACS Series in Discrete Mathematics and Theoretical Computer Science*, pages 251–270. American Mathematical Society, 1999.

[40]

Adi Shamir. IP=PSPACE. In *Proceedings of the Thirty First Annual Symposium on Foundations of Computer Science*, pages 11–15, 1990.

[41]

Andrew C. Yao. Theory and application of trapdoor functions. In *Proceedings of the Twenty Third Annual Symposium on Foundations of Computer Science*, pages 80–91, 1982.