Abstract
New practical zero-knowledge proofs are given for some number-theoretic problems. All of the problems are in NP, but the proofs given here are much more efficient than the previously known proofs. In addition, these proofs do not require the prover to be super-polynomial in power. A BPP prover with the appropriate trap-door knowledge is sufficient. The proofs are perfect or statistical zero-knowledge in all cases except one.
This research was supported in part by NSA Grant No. MDA904-88-H-2006.
Chapter PDF
References
Adleman, L., and M.-D. Huang, Recognizing primes in random polynomial time, Proc. 19th ACM Symp. on Theory of Computing, 1987, pp. 462–469.
Adleman, L., K. Manders, and G. Miller, On taking roots in finite fields, Proc. 18th IEEE Symp. on Foundations of Computer Science, 1977, pp. 175–178.
Bach, E., How to generate factored random numbers, SIAM Journal on Computing, vol. 17, No. 2, April 1988, pp. 179–193.
Bellare, M., S. Micali and R. Ostrovsky, personal communication.
Benaloh, J., Cryptographic capsules: a disjunctive primitive for interactive protocols, Advances in Cryptology-Crypto’ 86 Proceedings, 1987, pp. 213–222.
Berlekamp, E. Factoring polynomials over large finite fields, Mathematics of Computations, vol. 24, 1970, pp. 713–735.
Brassard, G., and C. Crépeau, Non-transitive transfer of confidence: a perfect zero-knowledge interactive protocol for SAT and beyond, Proc. 27th IEEE Symp. on Foundations of Computer Science, 1986, pp. 188–195.
Brassard, G., C. Crépeau, and J.M. Robert, All-or-nothing disclosure of secrets, Advances in Cryptology-Crypto’ 86 Proceedings, 1987, pp. 234–238.
Chaum, D., Demonstrating that a public predicate can be satisfied without revealing any information about how, Advances in Cryptology-Crypto’ 86 Proceedings, 1987, pp. 195–199.
Chaum, D. J.-H. Evertse, J. van de Graaf, An improved protocol for demonstrating possession of discrete logarithms and some generalizations, Advances in Cryptology — EUROCRYPT’ 87 Proceedings, 1988, pp. 127–141.
Chaum, D., J.-H. Evertse, J. van de Graaf, and R. Peralta, Demonstrating possession of a discrete logarithm without revealing it, Advances in Cryptology-Crypto’ 86 Proceedings, 1987, pp. 200–212.
Davenport, H., Multiplicative Number Theory, Markham Publishing Company, 1967.
Feige, U., A. Fiat, and A. Shamir, Zero-knowledge proofs of identity, Journal of Cryptology, 1(2), 1988, pp. 77–94.
Goldreich, O., S. Micali, and A,. Wigderson, Proofs that yield nothing but their validity and a methodology of cryptographic protocol design, Proc. 27th IEEE Symp. on Foundations of Computer Science, 1986, pp. 174–187.
Goldreich, O., S. Micali, and A,. Wigderson, Proofs that yield nothing but their validity and a methodology of cryptographic protocol design, To appear.
Goldwasser, S., and S. Micali, Probabilistic encryption, Journal of Computer and System Sciences, vol. 28, 1984, pp. 270–299.
Goldwasser, S., S. Micali, and C. Rackoff, The knowledge complexity of interactive proof systems, SIAM Journal on Computing, vol. 18, 1989, pp. 186–208.
Van de Graaf, J., and R. Peralta, A simple and secure way to show the validity of your public key, Advances in Cryptology-Crypto’ 87 Proceedings, 1988, pp. 128–134.
Knuth, D. E. The Art of Computer Programming Vol 2, Addison-Wesley, 1969.
Oren, Y. On the Cunning Power of Cheating Verifiers: some Observations About Zero Knowledge Proofs, Proc. 28th IEEE Symp. on Foundations of Computer Science, 1987, pp. 462–471.
Rabin, M.O., Digitalized signatures and public-key functions as intractable as factorization, Technical Report MIT/LCS/TR-212, M.I.T., January 1979.
Rabin, M.O., Probabilistic algorithms in finite fields, SIAM Journal on Computing, vol. 9, 1980, pp. 273–280.
Rosser, J. B., and Schoenfeld, L., Approximate Formulas for some Functions of Prime Numbers, Illinois Journal of Math. vol. 6, 1962, pp. 64–94.
Schwarz, W., in American Math. Monthly, vol. 73, 1966, pp. 426–427.
Tompa, M., and H. Woll, Random self-reducibility and zero knowledge interactive proofs of possession of information, Proc. 28th IEEE Symp. on Foundations of Computer Science, 1987, pp. 472–482.
Wagstaff, S. S., Greatest of the Least Primes in Arithmetic Progressions Having a Given Modulus, Mathematics of Computation, vol. 33 no. 147, July 1979, pp. 1073–1080.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boyar, J., Friedl, K., Lund, C. (1990). Practical Zero-Knowledge Proofs: Giving Hints and Using Deficiencies. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_18
Download citation
DOI: https://doi.org/10.1007/3-540-46885-4_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53433-4
Online ISBN: 978-3-540-46885-1
eBook Packages: Springer Book Archive