Constant-Round Concurrent Zero Knowledge From Falsifiable Assumptions

Abstract : We present a constant-round concurrent zero-knowledge protocol for NP. Our protocol is sound against uniform polynomial-time attackers, and relies on the existence of families of collision-resistant hash functions, and a new (but in our eyes, natural) falsifiable intractability assumption: Roughly speaking, that Micali's non-interactive CS-proofs are sound for languages in P.

[1]  Vipul Goyal.  Positive Results for Concurrently Secure Computation in the Plain Model , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[2]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[3]  Paul Valiant,et al.  Incrementally Verifiable Computation or Proofs of Knowledge Imply Time/Space Efficiency , 2008, TCC.

[4]  Toshiaki Tanaka,et al.  On the Existence of 3-Round Zero-Knowledge Protocols , 1998, CRYPTO.

[5]  Moni Naor,et al.  On Cryptographic Assumptions and Challenges , 2003, CRYPTO.

[6]  Amit Sahai,et al.  Concurrent Zero-Knowledge: Reducing the Need for Timing Constraints , 1998, CRYPTO.

[7]  Joe Kilian,et al.  Improved Efficient Arguments (Preliminary Version) , 1995, CRYPTO.

[8]  Mihir Bellare,et al.  Forward-Security in Private-Key Cryptography , 2003, CT-RSA.

[9]  C. Moler,et al.  Advances in Cryptology , 2000, Lecture Notes in Computer Science.

[10]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[11]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[12]  Adi Shamir,et al.  Witness indistinguishable and witness hiding protocols , 1990, STOC '90.

[13]  Oded Goldreich,et al.  Concurrent zero-knowledge with timing, revisited , 2002, STOC '02.

[14]  Nir Bitansky,et al.  Recursive composition and bootstrapping for SNARKS and proof-carrying data , 2013, STOC '13.

[15]  Rafail Ostrovsky,et al.  Concurrent Zero Knowledge in the Bounded Player Model , 2013, TCC.

[16]  Shafi Goldwasser,et al.  Delegation of Computation without Rejection Problem from Designated Verifier CS-Proofs , 2011, IACR Cryptol. ePrint Arch..

[17]  Alon Rosen,et al.  A Note on the Round-Complexity of Concurrent Zero-Knowledge , 2000, CRYPTO.

[18]  Rafael Pass,et al.  On Constant-Round Concurrent Zero-Knowledge , 2008, TCC.

[19]  Nir Bitansky,et al.  From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again , 2012, ITCS '12.

[20]  Ran Canetti,et al.  Towards a Theory of Extractable Functions , 2009, TCC.

[21]  Moni Naor,et al.  Bit commitment using pseudorandomness , 1989, Journal of Cryptology.

[22]  Rafael Pass,et al.  On Deniability in the Common Reference String and Random Oracle Model , 2003, CRYPTO.

[23]  Richard E. Overill,et al.  Foundations of Cryptography: Basic Tools , 2002, J. Log. Comput..

[24]  Amit Sahai,et al.  Resolving the Simultaneous Resettability Conjecture and a New Non-Black-Box Simulation Strategy , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[25]  David Chaum,et al.  Minimum Disclosure Proofs of Knowledge , 1988, J. Comput. Syst. Sci..

[26]  Yehuda Lindell,et al.  Resettably-sound zero-knowledge and its applications , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[27]  Moni Naor,et al.  Concurrent zero-knowledge , 2004, JACM.

[28]  Rafael Pass,et al.  Concurrent Zero Knowledge, Revisited , 2012, Journal of Cryptology.

[29]  Joe Kilian,et al.  Concurrent and resettable zero-knowledge in poly-loalgorithm rounds , 2001, STOC '01.

[30]  Ivan Damgård,et al.  Secure Two-Party Computation with Low Communication , 2012, IACR Cryptol. ePrint Arch..

[31]  Rafael Pass,et al.  Bounded-concurrent secure multi-party computation with a dishonest majority , 2004, STOC '04.

[32]  Silvio Micali,et al.  Computationally Sound Proofs , 2000, SIAM J. Comput..

[33]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[34]  Joe Kilian,et al.  Lower bounds for zero knowledge on the Internet , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[35]  Omer Paneth,et al.  Public-Coin Concurrent Zero-Knowledge in the Global Hash Model , 2013, TCC.

[36]  Claus-Peter Schnorr,et al.  Efficient signature generation by smart cards , 2004, Journal of Cryptology.

[37]  Craig Gentry,et al.  Separating succinct non-interactive arguments from all falsifiable assumptions , 2011, IACR Cryptol. ePrint Arch..

[38]  Ivan Damgård,et al.  Efficient Concurrent Zero-Knowledge in the Auxiliary String Model , 2000, EUROCRYPT.

[39]  Rafael Pass,et al.  Simulation in Quasi-Polynomial Time, and Its Application to Protocol Composition , 2003, EUROCRYPT.

[40]  Leonard J. Schulman.  Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, Cambridge, Massachusetts, USA, 5-8 June 2010 , 2010, STOC.

[41]  Boaz Barak,et al.  How to go beyond the black-box simulation barrier , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[42]  Amit Sahai,et al.  Concurrent zero knowledge with logarithmic round-complexity , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[43]  Hugo Krawczyk,et al.  On the Composition of Zero-Knowledge Proof Systems , 1990, ICALP.

[44]  K. Popper,et al.  Conjectures and refutations;: The growth of scientific knowledge , 1972 .

[45]  Joe Kilian,et al.  On the Concurrent Composition of Zero-Knowledge Proofs , 1999, EUROCRYPT.

[46]  K. Popper,et al.  Conjectures and refutations;: The growth of scientific knowledge , 1972 .

[47]  Oded Goldreich,et al.  Universal arguments and their applications , 2002, Proceedings 17th IEEE Annual Conference on Computational Complexity.

[48]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[49]  Yehuda Lindell,et al.  Lower bounds for non-black-box zero knowledge , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[50]  Oded Goldreich,et al.  A uniform-complexity treatment of encryption and zero-knowledge , 1993, Journal of Cryptology.

[51]  Rafael Pass,et al.  Bounded-concurrent secure two-party computation in a constant number of rounds , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[52]  Ivan Damgård,et al.  Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks , 1991, CRYPTO.

[53]  Rafael Pass,et al.  On the Composition of Public-Coin Zero-Knowledge Protocols , 2009, CRYPTO.

[54]  Rafael Pass,et al.  Concurrent non-malleable commitments , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[55]  Vipul Goyal,et al.  On the round complexity of covert computation , 2010, STOC '10.

[56]  Leonid A. Levin,et al.  Checking computations in polylogarithmic time , 1991, STOC '91.

[57]  Salil P. Vadhan,et al.  Derandomization in Cryptography , 2003, SIAM J. Comput..

[58]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[59]  Nir Bitansky,et al.  From the Impossibility of Obfuscation to a New Non-Black-Box Simulation Technique , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[60]  Boaz Barak,et al.  Constant-round coin-tossing with a man in the middle or realizing the shared random string model , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[61]  Yehuda Lindell,et al.  Bounded-concurrent secure two-party computation without setup assumptions , 2003, STOC '03.

[62]  Rafael Pass,et al.  On the Possibility of One-Message Weak Zero-Knowledge , 2004, TCC.

[63]  Mihir Bellare,et al.  Towards Plaintext-Aware Public-Key Encryption Without Random Oracles , 2004, ASIACRYPT.

[64]  Rafael Pass,et al.  New and improved constructions of non-malleable cryptographic protocols , 2005, STOC '05.

[65]  Aggelos Kiayias,et al.  BiTR: Built-in Tamper Resilience , 2011, IACR Cryptol. ePrint Arch..

[66]  Amit Sahai,et al.  How to play almost any mental game over the net - concurrent composition via super-polynomial simulation , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[67]  Ralph C. Merkle,et al.  A Certified Digital Signature , 1989, CRYPTO.

[68]  Donald Beaver,et al.  Cryptographic Protocols Provably Secure Against Dynamic Adversaries , 1992, EUROCRYPT.

[69]  Rafael Pass,et al.  Public-Coin Parallel Zero-Knowledge for NP , 2011, Journal of Cryptology.