Abstract
In this work, we present a zero knowledge argument for general arithmetic circuits that is public-coin and constant rounds, so it can be made non-interactive and publicly verifiable with the Fiat-Shamir heuristic. The construction is based on the MPC-in-the-head paradigm, in which the prover jointly emulates all MPC protocol participants and can provide advice in the form of Beaver triples whose accuracy must be checked by the verifier. Our construction follows the Beaver triple sacrificing approach used by Baum and Nof [PKC 2020]. Our improvements reduce the communication per multiplication gate from 4 to 2 field elements, matching the performance of the cut-and-choose approach taken by Katz, Kolesnikov, and Wang [CCS 2018] and with lower additive overhead for some parameter settings. We implement our protocol and analyze its cost on Picnic-style post-quantum digital signatures based on the AES family of circuits.
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References
Alagic, G., et al.: Status report on the second round of the NIST post-quantum cryptography standardization process (2020). https://csrc.nist.gov/publications/detail/nistir/8309/final
Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part I. LNCS, vol. 9056, pp. 430–454. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_17
Ames, S., Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Ligero: lightweight sublinear arguments without a trusted setup. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 2087–2104. ACM Press, October/November 2017
Araki, T., Furukawa, J., Lindell, Y., Nof, A., Ohara, K.: High-throughput semi-honest secure three-party computation with an honest majority. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 2016, pp. 805–817. ACM Press, October 2016
Baum, C., Malozemoff, A.J., Rosen, M., Scholl, P.: Mac’n’cheese: zero-knowledge proofs for arithmetic circuits with nested disjunctions. Cryptology ePrint Archive, Report 2020/1410 (2020). https://eprint.iacr.org/2020/1410
Baum, C., Nof, A.: Concretely-efficient zero-knowledge arguments for arithmetic circuits and their application to lattice-based cryptography. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part I. LNCS, vol. 12110, pp. 495–526. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_17
Baum, C., de Saint Guilhem, C.D., Kales, D., Orsini, E., Scholl, P., Zaverucha, G.: Banquet: short and Fast Signatures from AES. In: Garay, J.A. (ed.) PKC 2021. LNCS, vol. 12710, pp. 266–297. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-75245-3_11
Bellare, M., Goldwasser, S.: New paradigms for digital signatures and message authentication based on non-interactive zero knowledge proofs. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 194–211. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_19
Ben-Efraim, A., Nielsen, M., Omri, E.: Turbospeedz: double your online SPDZ! Improving SPDZ using function dependent preprocessing. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 530–549. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_26
Ben-Sasson, E., et al.: Zerocash: decentralized anonymous payments from bitcoin. In: 2014 IEEE Symposium on Security and Privacy, pp. 459–474. IEEE Computer Society Press, May 2014
Ben-Sasson, E., Chiesa, A., Genkin, D., Tromer, E., Virza, M.: SNARKs for C: verifying program executions succinctly and in zero knowledge. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 90–108. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_6
Ben-Sasson, E., Chiesa, A., Riabzev, M., Spooner, N., Virza, M., Ward, N.P.: Aurora: transparent succinct arguments for R1CS. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part I. LNCS, vol. 11476, pp. 103–128. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_4
Ben-Sasson, E., Chiesa, A., Spooner, N.: Interactive oracle proofs. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part II. LNCS, vol. 9986, pp. 31–60. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_2
Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M.: Succinct non-interactive zero knowledge for a von neumann architecture. In: Fu, K., Jung, J. (eds.) USENIX Security 2014, pp. 781–796. USENIX Association, August 2014
Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_11
Beullens, W., Delpech de Saint Guilhem, C.: LegRoast: efficient post-quantum signatures from the legendre PRF. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 130–150. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_8
Bhadauria, R., Fang, Z., Hazay, C., Venkitasubramaniam, M., Xie, T., Zhang, Y.: Ligero++: a new optimized sublinear IOP. In: Ligatti, J., Ou, X., Katz, J., Vigna, G. (eds.) ACM CCS 2020, pp. 2025–2038. ACM Press, November 2020
Bitansky, N., Chiesa, A., Ishai, Y., Paneth, O., Ostrovsky, R.: Succinct non-interactive arguments via linear interactive proofs. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 315–333. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_18
Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: 20th ACM STOC, pp. 103–112. ACM Press, May 1988
Boneh, D., Boyle, E., Corrigan-Gibbs, H., Gilboa, N., Ishai, Y.: Zero-knowledge proofs on secret-shared data via fully linear PCPs. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 67–97. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_3
Bootle, J., Cerulli, A., Chaidos, P., Groth, J., Petit, C.: Efficient zero-knowledge arguments for arithmetic circuits in the discrete log setting. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 327–357. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_12
Bootle, J., Cerulli, A., Ghadafi, E., Groth, J., Hajiabadi, M., Jakobsen, S.K.: Linear-time zero-knowledge proofs for arithmetic circuit satisfiability. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 336–365. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_12
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y.: Compressing vector OLE. In: Lie, D., Mannan, M., Backes, M., Wang, X. (eds.) ACM CCS 2018, pp. 896–912. ACM Press, October 2018
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 489–518. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_16
Bünz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy, pp. 315–334. IEEE Computer Society Press, May 2018
Bünz, B., Fisch, B., Szepieniec, A.: Transparent SNARKs from DARK compilers. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 677–706. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_24
Camenisch, J., Lysyanskaya, A.: An efficient system for non-transferable anonymous credentials with optional anonymity revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93–118. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_7
Chase, M., et al.: Post-quantum zero-knowledge and signatures from symmetric-key primitives. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 1825–1842. ACM Press, October/November 2017
Chiesa, A., Forbes, M.A., Spooner, N.: A zero knowledge sumcheck and its applications. Cryptology ePrint Archive, Report 2017/305 (2017). http://eprint.iacr.org/2017/305
Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.: Marlin: preprocessing zkSNARKs with universal and updatable SRS. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 738–768. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_26
Corrigan-Gibbs, H., Boneh, D.: Prio: private, robust, and scalable computation of aggregate statistics. In: NSDI, pp. 259–282. USENIX Association (2017)
Costello, C., et al.: Geppetto: versatile verifiable computation. In: 2015 IEEE Symposium on Security and Privacy, pp. 253–270. IEEE Computer Society Press, May 2015
Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38
de Saint Guilhem, C.D., De Meyer, L., Orsini, E., Smart, N.P.: BBQ: using AES in picnic signatures. In: Paterson, K.G., Stebila, D. (eds.) SAC 2019. LNCS, vol. 11959, pp. 669–692. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-38471-5_27
De Santis, A., Persiano, G.: Zero-knowledge proofs of knowledge without interaction (extended abstract). In: 33rd FOCS, pp. 427–436. IEEE Computer Society Press, October 1992
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). https://doi.org/10.1007/3-540-47721-7_12
Frederiksen, T.K., Nielsen, J.B., Orlandi, C.: Privacy-free garbled circuits with applications to efficient zero-knowledge. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 191–219. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_7
Gabizon, A.: AuroraLight: improved prover efficiency and SRS size in a sonic-like system. Cryptology ePrint Archive, Report 2019/601 (2019). https://eprint.iacr.org/2019/601
Gabizon, A., Williamson, Z.J., Ciobotaru, O.: PLONK: permutations over lagrange-bases for oecumenical noninteractive arguments of knowledge. Cryptology ePrint Archive, Report 2019/953 (2019). https://eprint.iacr.org/2019/953
Ganesh, C., Kondi, Y., Patra, A., Sarkar, P.: Efficient adaptively secure zero-knowledge from garbled circuits. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part II. LNCS, vol. 10770, pp. 499–529. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_17
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). https://doi.org/10.1007/978-3-642-38348-9_37
Giacomelli, I., Madsen, J., Orlandi, C.: ZKBoo: faster zero-knowledge for Boolean circuits. In: Holz, T., Savage, S. (eds.) USENIX Security 2016, pp. 1069–1083. USENIX Association, August 2016
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press, May 1987
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(3), 691–729 (1991)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)
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). https://doi.org/10.1007/978-3-642-17373-8_19
Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_11
Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to zk-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 698–728. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_24
Gvili, Y., Ha, J., Varia, S.S.M., Yang, Z., Zhang, X.: TurboIKOS (2021). https://github.com/sarahscheffler/TurboIKOS
Heath, D., Kolesnikov, V.: Stacked garbling for disjunctive zero-knowledge proofs. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part III. LNCS, vol. 12107, pp. 569–598. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45727-3_19
Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: Johnson, D.S., Feige, U. (eds.) 39th ACM STOC, pp. 21–30. ACM Press, June 2007
Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Cryptography with constant computational overhead. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 433–442. ACM Press, May 2008
Jawurek, M., Kerschbaum, F., Orlandi, C.: Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently. In: Sadeghi, A.R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 955–966. ACM Press, November 2013
Kales, D., Zaverucha, G.: An attack on some signature schemes constructed from five-pass identification schemes. In: Krenn, S., Shulman, H., Vaudenay, S. (eds.) CANS 2020. LNCS, vol. 12579, pp. 3–22. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-65411-5_1
Katz, J., Kolesnikov, V., Wang, X.: Improved non-interactive zero knowledge with applications to post-quantum signatures. In: Lie, D., Mannan, M., Backes, M., Wang, X. (eds.) ACM CCS 2018, pp. 525–537. ACM Press, October 2018
Keller, M., Pastro, V., Rotaru, D.: Overdrive: making SPDZ great again. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part III. LNCS, vol. 10822, pp. 158–189. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_6
Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: 24th ACM STOC, pp. 723–732. ACM Press, May 1992
Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_4
Lund, C., Fortnow, L., Karloff, H.J., Nisan, N.: Algebraic methods for interactive proof systems. In: 31st FOCS, pp. 2–10. IEEE Computer Society Press, October 1990
Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 2111–2128. ACM Press, November 2019
Microsoft Corporation: Picnic. https://microsoft.github.io/Picnic/
Miers, I., Garman, C., Green, M., Rubin, A.D.: Zerocoin: anonymous distributed E-cash from Bitcoin. In: 2013 IEEE Symposium on Security and Privacy, pp. 397–411. IEEE Computer Society Press, May 2013
Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: 31st ACM STOC, pp. 245–254. ACM Press, May 1999
Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_40
Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: 2013 IEEE Symposium on Security and Privacy, pp. 238–252. IEEE Computer Society Press, May 2013
Reingold, O., Rothblum, G.N., Rothblum, R.D.: Constant-round interactive proofs for delegating computation. In: Wichs, D., Mansour, Y. (eds.) 48th ACM STOC, pp. 49–62. ACM Press, June 2016
Setty, S.: Spartan: efficient and general-purpose zkSNARKs without trusted setup. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part III. LNCS, vol. 12172, pp. 704–737. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56877-1_25
Setty, S., Lee, J.: Quarks: quadruple-efficient transparent zkSNARKs. Cryptology ePrint Archive, Report 2020/1275 (2020). https://eprint.iacr.org/2020/1275
Trail of Bits: Reverie (2021). https://github.com/trailofbits/reverie
Wahby, R.S., Tzialla, I., shelat, A., Thaler, J., Walfish, M.: Doubly-efficient zkSNARKs without trusted setup. In: 2018 IEEE Symposium on Security and Privacy, pp. 926–943. IEEE Computer Society Press, May 2018
Weng, C., Yang, K., Katz, J., Wang, X.: Wolverine: fast, scalable, and communication-efficient zero-knowledge proofs for boolean and arithmetic circuits. Cryptology ePrint Archive (2020)
Xie, T., Zhang, J., Zhang, Y., Papamanthou, C., Song, D.: Libra: succinct zero-knowledge proofs with optimal prover computation. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 733–764. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_24
Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole - reducing data transfer in garbled circuits using half gates. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8
Zhang, J., Xie, T., Zhang, Y., Song, D.: Transparent polynomial delegation and its applications to zero knowledge proof. In: 2020 IEEE Symposium on Security and Privacy, pp. 859–876. IEEE Computer Society Press, May 2020
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This material is supported by a Google PhD Fellowship, the DARPA SIEVE program under Agreement No. HR00112020021, and the National Science Foundation under Grants No. 1414119, 1718135, 1739000, 1801564, 1915763, and 1931714.
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Gvili, Y., Ha, J., Scheffler, S., Varia, M., Yang, Z., Zhang, X. (2021). TurboIKOS: Improved Non-interactive Zero Knowledge and Post-quantum Signatures. In: Sako, K., Tippenhauer, N.O. (eds) Applied Cryptography and Network Security. ACNS 2021. Lecture Notes in Computer Science(), vol 12727. Springer, Cham. https://doi.org/10.1007/978-3-030-78375-4_15
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