Abstract
Canetti, Lin and Paneth in TCC 2013 showed a O>(log1+εn) rounds public-coin concurrent zero-knowledge argument system (CZK) based on the existence of collision resistant hash functions, which is currently known as round optimal public-coin CZK from standard assumptions. In this paper, we further address this problem and present an alternative construction of public-coin CZK argument system with succinct slot. The key technique involves a new variant of Barak’s non-black-box simulate approach. In particular, the original protocol uses n commitments in each slot, while our construction uses one commitment in each slot. Through our simulation techniques, the simulator recovers any previous state needed for the probabilistically checkable proof (PCP) from the current committed state, which, in our view, may be of independent interest. Furthermore, the public-coin CZK argument system can be transformed into a resettable security protocol based on the one way functions assumption. Therefore, we present a new construction of the simultaneous resettable zero-knowledge argument system.
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Goldwasser S, Micali S, Rackoff C. The knowledge complexity of interactive proof systems. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, Providence, 1989. 186–208
Dwork C, Naor M, Sahai A. Concurrent zero-knowledge. In: Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, Dallas, 1998. 409–418
Chung K M, Ostrovsky R, Pass R, et al. 4-round resettably-sound zero knowledge. In: Proceedings of the 11th International Conference on Theory of Cryptography (TCC), San Diego, 2014. 192–216
Chongchitmate W, Ostrovsky R, Visconti I. Resettably-sound resettable zero knowledge in constant rounds. In: Proceedings of the 15th International Conference on Theory of Cryptography (TCC), Baltimore, 2017. 111–138
Chung K M, Pass R, Seth K. Non-black-box simulation from one-way functions and applications to resettable security. SIAM J Comput, 2016, 45: 415–458
Ostrovsky R, Scafuro A, Venkitasubramaniam M. Resettably sound zero-knowledge arguments from OWFs — The (semi) black-box way. In: Proceedings of the 12th International Conference on Theory of Cryptography (TCC), Warsaw, 2015. 345–374
Benhamouda F, Lin H. k-round MPC from k-round OT via garbled interactive circuits. In: Proceedings of the 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, 2018. 500–532
Garg S, Srinivasan A. Two-round multiparty secure computation from minimal assumptions. In: Proceedings of the 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, 2018. 468–499
Ishai Y, Mittal M, Ostrovsky R. On the message complexity of secure multiparty computation. In: Proceedings of the 21st IACR International Conference on Practice and Theory of Public-Key Cryptography (PKC), Rio de Janeiro, 2018. 698–711
Badrinarayanan S, Goyal V, Jain A, et al. Round optimal concurrent MPC via strong simulation. In: Proceedings of the 15th International Conference (TCC), 2017. 743–775
Garg S, Kiyoshima S, Pandey O. A new approach to black-box concurrent secure computation. In: Proceedings of the 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, 2018. 566–599
Broadnax B, Döttling N, Hartung G, et al. Concurrently composable security with shielded super-polynomial simulators. In: Proceedings of the 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Paris, 2017. 351–381
Badrinarayanan S, Khurana D, Ostrovsky R, et al. Unconditional UC-secure computation with (stronger-malicious) PUFs. In: Proceedings of the 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Paris, 2017. 382–411
Kiyoshima S, Lin H, Venkitasubramaniam M. A unified approach to constructing black-box UC protocols in trusted setup models. In: Proceedings of the 15th International Conference (TCC), Baltimore, 2017. 776–809
Richardson R, Kilian J. On the concurrent composition of zero-knowledge proofs. In: Proceedings of International Conference on the Theory and Application of Cryptographic Techniques, Prague, 1999. 415–431
Canetti R, Kilian J, Petrank E, et al. Black-box concurrent zero-knowledge requires (logn) rounds. In: Proceedings of Annual ACM Symposium on Theory of Computing (STOC), Heraklion, 2001. 570–579
Prabhakaran M, Rosen A, Sahai A. Concurrent zero knowledge with logarithmic round-complexity. In: Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS), Vancouver, 2002. 366–375
Goldreich O, Kahan A. How to construct constant-round zero-knowledge proof systems for NP. J Cryptol, 1996, 9: 167–190
Pass R, Dustin Tseng W L, Venkitasubramaniam M. Concurrent zero knowledge, revisited. J Cryptol, 2014, 27: 45–66
Feige U, Shamir A. Witness indistinguishable and witness hiding protocols. In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing (STOC), Baltimore, 1990. 416–426
Barak B. How to go beyond the black-box simulation barrier. In: Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS), 2001. 106–115
Pass R, Rosen A, Tseng W L D. Public-coin parallel zero-knowledge for NP. J Cryptol, 2013, 26: 1–10
Canetti R, Lin H, Paneth O. Public-coin concurrent zero-knowledge in the global hash model. In: Proceedings of the 10th Theory of Cryptography Conference, Tokyo, 2013. 80–99
Chung K, Lin H, Pass R. Constant-round concurrent zero knowledge from p-certificates. In: Proceedings of Annual IEEE Symposium on Foundations of Computer Science (FOCS), Berkeley, 2013. 50–59
Goyal V. Non-black-box simulation in the fully concurrent setting. In: Proceedings of Symposium on Theory of Computing Conference (STOC), Palo Alto, 2013. 221–230
Kiyoshima S. An alternative approach to non-black-box simulation in fully concurrent setting. In: Proceedings of the 12th Theory of Cryptography Conference (TCC), Warsaw, 2015. 290–318
Pandey O, Prabhakaran M, Sahai A. Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for NP. In: Proceedings of the 12th Theory of Cryptography Conference (TCC), Warsaw, 2015. 638–667
Chung K, Lin H, Pass R. Constant-round concurrent zero-knowledge from indistinguishability obfuscation. In: Proceedings of the 35th Annual Cryptology Conference (CRYPTO), Santa Barbara, 2015. 287–307
Kilian J, Petrank E. Concurrent and resettable zero-knowledge in poly-loalgorithm rounds. In: Proceedings of Annual ACM Symposium on Theory of Computing, Heraklion, 2001. 560–569
Barak B, Goldreich O, Sha G, et al. Resettably-sound zero-knowledge and its applications. In: Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS), 2001. 116–125
Bitansky N, Paneth O. On non-black-box simulation and the impossibility of approximate obfuscation. SIAM J Comput, 2015, 44: 1325–1383
Chung K M, Ostrovsky R, Pass R, et al. Simultaneous resettability from one-way functions. In: Proceedings of the 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Berkeley, 2013. 60–69
Deng Y, Goyal V, Sahai A. Resolving the simultaneous resettability conjecture and a new non-black-box simulation strategy. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Atlanta, 2009. 251–260
Cho C, Ostrovsky R, Scafuro A, et al. Simultaneously resettable arguments of knowledge. In: Proceedings of the 12th International Conference on Theory of Cryptography (TCC), Warsaw, 2015. 530–547
HÅstad J, Impagliazzo R, Levin L A, et al. A pseudorandom generator from any one-way function. SIAM J Comput, 1999, 28: 1364–1396
Naor M. Bit commitment using pseudorandomness. J Cryptol, 1991, 4: 151–158
Blum M. How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, 1986. 1444–1451
Barak B, Goldreich O. Universal arguments and their applications. SIAM J Comput, 2008, 38: 1661–1694
Bellare M, Yee B. Forward-security in private-key cryptography. In: Proceedings of The Cryptographers’ Track at the RSA Conference, San Francisco, 2003. 1–18
Acknowledgements
This work was supported in part by National Natural Science Foundation of China (Grant No. 61772521), Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-SYS035), and Open Project Program of the State Key Laboratory of Cryptology.
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Yan, Z., Deng, Y. A novel approach to public-coin concurrent zero-knowledge and applications on resettable security. Sci. China Inf. Sci. 62, 32110 (2019). https://doi.org/10.1007/s11432-018-9627-x
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DOI: https://doi.org/10.1007/s11432-018-9627-x