Abstract
Damgård, Fazio and Nicolosi (TCC 2006) gave a transformation of Sigma-protocols, 3-move honest verifier zero-knowledge proofs, into efficient non-interactive zero-knowledge arguments for a designated verifier. Their transformation uses additively homomorphic encryption to encrypt the verifier’s challenge, which the prover uses to compute an encrypted answer. The transformation does not rely on the random oracle model but proving soundness requires a complexity leveraging assumption.
We propose an alternative instantiation of their transformation and show that it achieves culpable soundness without complexity leveraging. This improves upon an earlier result by Ventre and Visconti (Africacrypt 2009), who used a different construction which achieved weak culpable soundness.
We demonstrate how our construction can be used to prove validity of encrypted votes in a referendum. This yields a voting system with homomorphic tallying that does not rely on the Fiat-Shamir heuristic.
Pyrros Chaidos—This author was supported by an EPSRC scholarship (EP/G037264/1 – Security Science DTC).
Jens Groth—This research was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 307937.
Chapter PDF
Similar content being viewed by others
Keywords
References
Adida, B.: Helios: web-based open-audit voting. In: Security Symposium, SS 2008, pp. 335–348. USENIX Association (2008)
Barak, B., Canetti, R., Nielsen, J.B., Pass, R.: Universally composable protocols with relaxed set-up assumptions. In: Foundations of Computer Science, FOCS 2004, pp. 186–195. IEEE (2004)
Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Computer and Communications Security, pp. 62–73. ACM (1993)
Bernhard, D., Cortier, V., Pereira, O., Smyth, B., Warinschi, B.: Adapting helios for provable ballot privacy. In: Atluri, V., Diaz, C. (eds.) ESORICS 2011. LNCS, vol. 6879, pp. 335–354. Springer, Heidelberg (2011)
Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: Theory of Computing, STOC 1988, pp. 103–112. ACM (1988)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. Journal of the ACM (JACM) 51(4), 557–594 (2004)
Cortier, V., Galindo, D., Glondu, S., Izabachène, M.: Distributed ElGamal á la Pedersen: application to Helios. In: Privacy in the Electronic Society, WPES 2013, pp. 131–142. ACM (2013)
Cramer, R., Shoup, V.: A practical public-key encryption schemes secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO ’98. LNCS, vol. 1462. Springer, Heidelberg (1998)
Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, p. 45. Springer, Heidelberg (2002)
Damgård, I.B.: 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)
Damgård, I.B., Fazio, N., Nicolosi, A.: Non-interactive zero-knowledge from homomorphic encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 41–59. Springer, Heidelberg (2006)
Damgård, I., Jurik, M., Nielsen, J.B.: A generalization of Paillier’s public-key system with applications to electronic voting. International Journal of Information Security 9(6), 371–385 (2010)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Gennaro, R., Gentry, C., Parno, B., Raykova, M.: Quadratic span programs and succinct NIZKs without PCPs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 626–645. Springer, Heidelberg (2013)
Gentry, C., Groth, J., Ishai, Y., Peikert, C., Sahai, A., Smith, A.: Using fully homomorphic hybrid encryption to minimize non-interative zero-knowledge proofs. Journal of Cryptology, 1–24 (2014)
Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: Foundations of Computer Science, FOCS 2003, pp. 102–113. IEEE (2003)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM Journal on 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.: Short non-interactive zero-knowledge proofs. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 341–358. Springer, Heidelberg (2010)
Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)
Groth, J., Ostrovsky, R., Sahai, A.: New techniques for noninteractive zero-knowledge. Journal of the ACM 59(3), 11:1–11:35 (2012)
Groth, J., Sahai, A.: Efficient noninteractive proof systems for bilinear groups. SIAM Journal on Computing 41(5), 1193–1232 (2012)
Jakobsson, M., Sako, K., Impagliazzo, R.: Designated verifier proofs and their applications. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 143–154. Springer, Heidelberg (1996)
Kilian, J., Petrank, E.: An efficient noninteractive zero-knowledge proof system for NP with general assumptions. Journal of Cryptology 11(1), 1–27 (1998)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Theory of Computing, STOC 2013, pp. 427–437. ACM (1990)
Okamoto, T., Uchiyama, S.: A new public-key cryptosystem as secure as factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: Security and Privacy, pp. 238–252. IEEE (2013)
Ventre, C., Visconti, I.: Co-sound zero-knowledge with public keys. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 287–304. Springer, Heidelberg (2009)
Wikström, D.: Simplified submission of inputs to protocols. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 293–308. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 International Association for Cryptologic Research
About this paper
Cite this paper
Chaidos, P., Groth, J. (2015). Making Sigma-Protocols Non-interactive Without Random Oracles. In: Katz, J. (eds) Public-Key Cryptography -- PKC 2015. PKC 2015. Lecture Notes in Computer Science(), vol 9020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46447-2_29
Download citation
DOI: https://doi.org/10.1007/978-3-662-46447-2_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-46446-5
Online ISBN: 978-3-662-46447-2
eBook Packages: Computer ScienceComputer Science (R0)