Abstract
We construct non-interactive zero-knowledge arguments for circuit satisfiability with perfect completeness, perfect zero-knowledge and computational soundness. The non-interactive zero-knowledge arguments have sub-linear size and very efficient public verification. The size of the non-interactive zero-knowledge arguments can even be reduced to a constant number of group elements if we allow the common reference string to be large. Our constructions rely on groups with pairings and security is based on two new cryptographic assumptions; we do not use the Fiat-Shamir heuristic or random oracles.
Chapter PDF
Similar content being viewed by others
Keywords
References
Abe, M., Fehr, S.: Perfect NIZK with adaptive soundness. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 118–136. Springer, Heidelberg (2007)
Barak, B., Canetti, R., Nielsen, J.B., Pass, R.: Universally composable protocols with relaxed set-up assumptions. In: FOCS, pp. 186–195 (2004)
Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid encryption problem. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004)
Bellare, M., Palacio, A.: Towards plaintext-aware public-key encryption without random oracles. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 48–62. Springer, Heidelberg (2004)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM CCS, pp. 62–73 (1993)
Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: STOC, pp. 103–112 (1988)
Boyen, X., Waters, B.: Compact group signatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 427–444. Springer, Heidelberg (2006)
Boyen, X., Waters, B.: Full-domain subgroup hiding and constant-size group signatures. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 1–15. Springer, Heidelberg (2007)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. In: STOC, pp. 209–218 (1998)
Canetti, R., Goldreich, O., Halevi, S.: On the random-oracle methodology as applied to length-restricted signature schemes. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 40–57. Springer, Heidelberg (2004)
Chandran, N., Groth, J., Sahai, A.: Ring signatures of sub-linear size without random oracles. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 423–434. Springer, Heidelberg (2007)
Clos, C.: A study of non-blocking switching networks. Bell System Technical Journal 32(2), 406–424 (1953)
Damgård, I.: Non-interactive circuit based proofs and non-interactive perfect zero-knowledge with preprocessing. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 341–355. Springer, Heidelberg (1993)
De Santis, A., Di Crescenzo, G., Ostrovsky, R., Persiano, G., Sahai, A.: Robust non-interactive zero knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 566–598. Springer, Heidelberg (2001)
De Santis, A., Di Crescenzo, G., Persiano, G.: Randomness-optimal characterization of two NP proof systems. In: Rolim, J.D.P., Vadhan, S.P. (eds.) RANDOM 2002. LNCS, vol. 2483, pp. 179–193. Springer, Heidelberg (2002)
De Santis, A., Persiano, G.: Zero-knowledge proofs of knowledge without interaction. In: FOCS, pp. 427–436 (1992)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. SIAM Journal of Computing 30(2), 391–437 (2000)
Dwork, C., Naor, M.: Zaps and their applications. In: FOCS, pp. 283–293 (2000)
Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs under general assumptions. SIAM Journal of Computing 29(1), 1–28 (1999)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)
Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM Journal of Computing 25(1), 169–192 (1996)
Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. Journal of Cryptology 7(1), 1–32 (1994)
Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: FOCS, pp. 102–113 (2003)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proofs. SIAM Journal of Computing 18(1), 186–208 (1989)
Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006)
Groth, J.: Linear algebra with sub-linear zero-knowledge arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192–208. Springer, Heidelberg (2009)
Groth, J.: Short non-interactive zero-knowledge proofs. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)
Groth, J., Ostrovsky, R.: Cryptography in the multi-string model. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 323–341. Springer, Heidelberg (2007)
Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006)
Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero-knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006)
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)
Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: STOC, pp. 723–732 (1992)
Kilian, J., Petrank, E.: An efficient noninteractive zero-knowledge proof system for NP with general assumptions. Journal of Cryptology 11(1), 1–27 (1998)
Maurer, U.M., Renner, R., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)
Micali, S.: Computationally sound proofs. SIAM Journal of Computing 30(4), 1253–1298 (2000)
Naor, M.: On cryptographic assumptions and challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg (2003)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: The non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
Sahai, A.: Non-malleable non-interactive zero-knowledge and adaptive chosen-ciphertext security. In: FOCS, pp. 543–553 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 International Association for Cryptologic Research
About this paper
Cite this paper
Groth, J. (2010). Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17373-8_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-17373-8_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17372-1
Online ISBN: 978-3-642-17373-8
eBook Packages: Computer ScienceComputer Science (R0)