Skip to main content
SpringerLink
Log in

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments

  • Published:
computational complexity Aims and scope Submit manuscript

Abstract

We present barriers to provable security of two important cryptographic primitives, perfect non-interactive zero knowledge (NIZK) and non-interactive non-alleable commitments:

  1. ○

    Black-box reductions cannot be used to demonstrate adaptive soundness (i.e., that soundness holds even if the statement to be proven is chosen as a function of the common reference string) of any statistical NIZK for NP based on any “standard” intractability assumptions.

  2. ○

    Black-box reductions cannot be used to demonstrate non-malleability of non-interactive, or even 2-message, commitment schemes based on any “standard” intractability assumptions.

We emphasize that the above separations apply even if the construction of the considered primitives makes a non-black-box use of the underlying assumption.

As an independent contribution, we suggest a taxonomy of game-based intractability assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Masayuki Abe & Serge Fehr (2007). Perfect NIZK with Adaptive Soundness. In Theory of Cryptography Conference, 118–136.

  • Adi Akavia, Oded Goldreich, Shafi Goldwasser & Dana Moshkovitz (2006). On basing one-way functions on NP-hardness. In ACM Symposium on Theory of Computing Conference (STOC), 701–1657 710.

  • Boaz Barak (2001). How to Go Beyond the Black-Box Simulation Barrier. In IEEE Symposium on Foundations of Computer Science (FOCS), 106–115.

  • Boaz Barak (2002). Constant-Round Coin-Tossing with a Man in the Middle or Realizing the Shared Random String Model. In IEEE Symposium on Foundations of Computer Science (FOCS).

  • Mihir Bellare, Chanathip Namprempre, David Pointcheval, Michael Semanko (2003) The One-More-RSA-Inversion Problems and the Security of Chaum’s Blind Signature Scheme. J. Cryptology 16(3): 185–215

    Article  MathSciNet  MATH  Google Scholar 

  • Mihir Bellare & Adriana Palacio (2002). GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks. In Advances in Cryptology (CRYPTO), 162–177.

  • Mihir Bellare & Phillip Rogaway (1993). Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. In ACM Conference on Computer and Communications Security, 62–73.

  • Mihir Bellare, Moti Yung (1996) Certifying Permutations: Non interactive Zero-Knowledge Based on Any Trapdoor Permutation. J. Cryptology 9(3): 149–166

    Article  MathSciNet  MATH  Google Scholar 

  • Manuel Blum, Paul Feldman & Silvio Micali (1988). Non-Interactive Zero-Knowledge and Its Applications (Extended Abstract). In ACM Symposium on Theory of Computing (STOC), 103–112.

  • Manuel Blum, Silvio Micali (1984) How to Generate Crypto graphically Strong Sequences of Pseudo-Random Bits. SIAM Journal on Computing 13(4): 850–864

    Article  MathSciNet  MATH  Google Scholar 

  • Andrej Bogdanov & Luca Trevisan (2003). On Worst-Case to Average-Case Reductions for NP Problems. In IEEE Symposium on Foundations of Computer Science (FOCS), 308–317.

  • Dan Boneh & Ramarathnam Venkatesan (1998). Breaking RSA May Not Be Equivalent to Factoring. In Advances in Cryptology (EuroCrypt), 59–71.

  • Gilles Brassard (1983) Relativized cryptography. IEEE Transactions on Information Theory 29(6): 877–893

    Article  MathSciNet  MATH  Google Scholar 

  • Emmanuel Bresson, Jean Monnerat & Damien Vergnaud (2008). Separation Results on the ”One-More” Computational Problems. In RSA Conference Cryptographers’ Track, 71–87.

  • Ran Canetti, Oded Goldreich, Shafi Goldwasser & Silvio Micali (2000). Resettable zero-knowledge. In ACM Symposium on Theory of Computing (STOC), 235–244. ISBN 1-58113-184-4.

  • Ran Canetti, Oded Goldreich, Shai Halevi (2004) The random oracle methodology, revisited. J. ACM 51(4): 557–594

    Article  MathSciNet  MATH  Google Scholar 

  • Kai-min Chung, Huijia Lin, Mohammad Mahmoody & Rafael Pass (2013). On the Power of Non-uniform Proof of Security. In Innovations in Theoretical Computer Science.

  • Kai-min Chung, Mohammad Mahmoody & Rafael Pass (2009). A Note on Black-Box Reductions. Manuscript.

  • Giovanni Di Crescenzo, Yuval Ishai & Rafail Ostrovsky (1998). Non-Interactive and Non-Malleable Commitment. In ACM Symposium on Theory of Computing (STOC), 141–150.

  • Ivan Damgård (1991). Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks. In Advances in Cryptology (CRYPTO), 445–456.

  • Yevgeniy Dodis, Roberto Oliveira & Krzysztof Pietrzak (2005). On the Generic Insecurity of the Full Domain Hash. In Advances in Cryptology (CRYPTO), 449–466.

  • Danny Dolev, Cynthia Dwork, Moni Naor (2000) Nonmal leable Cryptography. SIAM Journal on Computing 30(2): 391–437

    Article  MathSciNet  MATH  Google Scholar 

  • Uriel Feige, Dror Lapidot & Adi Shamir (1990). Multiple non interactive zero knowledge proofs based on a single random string. In IEEE Symposium on Foundations of Computer Science (FOCS), 308–317.

  • Joan Feigenbaum, Lance Fortnow (1993) Random-self reducibility of complete sets. SIAM Journal on Computing 22(5): 994–1005

    Article  MathSciNet  MATH  Google Scholar 

  • Amos Fiat & Adi Shamir (1987). How to prove yourself: practical solutions to identification and signature problems. In Advances in cryptology (CRYPTO).

  • Marc Fischlin & Dominique Schröder (2010). On the Impossibility of Three-Move Blind Signature Schemes. In Advances in Cryptology (EuroCrypt), 197–215.

  • Craig Gentry & Daniel Wichs (2011). Separating succinct non-interactive arguments from all falsifiable assumptions. In ACM Symposium on Theory of Computing (STOC), 99–108.

  • Oded Goldreich (2001). Foundations of Cryptography– Basic Tools. Cambridge University Press.

  • Oded Goldreich, Shafi Goldwasser, Silvio Micali (1986) How to construct random functions. J. ACM 33(4): 792–807

    Article  MathSciNet  Google Scholar 

  • Oded Goldreich & Hugo Krawczyk (1996) On the composition of zero-knowledge proof systems. SIAM Journal on Computing 25(1), 169–192. ISSN 0097-5397.

  • Oded Goldreich & Leonid A. Levin (1989). A Hard-Core Predicate for all One-Way Functions. In ACM Symposium on Theory of Computing (STOC), 25–32.

  • Oded Goldreich, Yair Oren (1994) Definitions and properties of zero-knowledge proof systems. Journal of Cryptology 7: 1–32

    MathSciNet  MATH  Google Scholar 

  • Oded Goldreich, Ron D Rothblum (2013) Enhancements of trapdoor permutations. Journal of cryptology 26(3): 484–512

    Article  MathSciNet  MATH  Google Scholar 

  • Shafi Goldwasser & Yael Tauman Kalai (2003). On the (In)security of the Fiat-Shamir Paradigm. In IEEE Symposium on Foundations of Computer Science (FOCS), 102–111.

  • Shafi Goldwasser, Silvio Micali (1984) Probabilistic Encryption. J. Comput. Syst. Sci. 28(2): 270–299

    Article  MathSciNet  MATH  Google Scholar 

  • Shafi Goldwasser, Silvio Micali, Charles Rackoff (1989) The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18(1): 186–208

    Article  MathSciNet  MATH  Google Scholar 

  • Shafi Goldwasser, Silvio Micali, Ronald L. Rivest (1988) A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. SIAM J. Comput. 17(2): 281–308

    Article  MathSciNet  MATH  Google Scholar 

  • Vipul Goyal (2011). Constant round non-malleable protocols using one way functions. In ACM Symposium on Theory of Computing (STOC), 695–704.

  • Jens Groth, Rafail Ostrovsky & Amit Sahai (2006). Perfect Non-interactive Zero Knowledge for NP. In Advances in Cryptology (EuroCrypt), 339–358.

  • Iftach Haitner & Thomas Holenstein (2009). On the (Im)Possibility of Key Dependent Encryption. In Theory of Cryptography Conference, 202–219.

  • Iftach Haitner, Alon Rosen & Ronen Shaltiel (2009). On the (Im)Possibility of Arthur-Merlin Witness Hiding Protocols. In TCC ’09, 220–237.

  • Johan Håstad, Russell Impagliazzo, Leonid Levin, Michael Luby (1999) A pseudorandom generator from any one-way function. SIAM Journal on Computing 28: 12–24

    MathSciNet  MATH  Google Scholar 

  • Johan Håstad, Rafael Pass, Douglas Wikström & Krzysztof Pietrzak (2010). An Efficient Parallel Repetition Theorem. In TCC’10, 1–18.

  • Russell Impagliazzo, Ragesh Jaiswal & Valentine Kabanets (2007). Chernoff-type direct product theorems. In CRYPTO ’07, 500–516.

  • Russell Impagliazzo & Steven Rudich (1988). Limits on the Provable Consequences of One-way Permutations. In Advances in Cryptology (CRYPTO), 8–26.

  • Huijia Lin & Rafael Pass (2009). Non-malleability amplification. In ACM Symposium on Theory of Computing (STOC), 189–198.

  • Huijia Lin & Rafael Pass (2011). Constant-round non-malleable commitments from any one-way function. In ACM Symposium on Theory of Computing (STOC), 705–714.

  • Huijia Lin, Rafael Pass & Muthuramakrishnan Venkitasubramaniam (2008). Concurrent Non-malleable Commitments from Any One-Way Function. In Theory of Cryptography Conference, 571–588.

  • Moses Liskov, Anna Lysyanskaya, Silvio Micali, Leonid Reyzin & Adam Smith (2001). Mutually Independent Commitments. In Advances in Cryptology (Asiacrypt), 385–401.

  • Moni Naor (2003). On Cryptographic Assumptions and Challenges. In Advances in Cryptology (CRYPTO), 96–109.

  • Moni Naor & Moti Yung (1989). Universal One-Way Hash Functions and their Cryptographic Applications. In STOC, 33–43.

  • Rafail Ostrovsky (1991). One-Way Functions, Hard on Average Problems, and Statistical Zero-Knowledge Proofs. In Structure in Complexity Theory Conference, 133–138.

  • Rafail Ostrovsky & Avi Wigderson (1993). One-way functions are essential for non-trivial zero-knowledge. In Theory and Computing Systems, 1993, 3–17.

  • Omkant Pandey, Rafael Pass & Vinod Vaikuntanathan (2008). Adaptive One-Way Functions and Applications. In Advances in Cryptology (CRYPTO), 57–74.

  • Rafael Pass (2003). On Deniability in the Common Reference String and Random Oracle Model. In Advances in Cryptology (CRYPTO), 1807 316–337.

  • Rafael Pass (2006). Parallel Repetition of Zero-Knowledge Proofs and the Possibility of Basing Cryptography on NP-Hardness. In IEEE Conference on Computational Complexity, 96–110.

  • Rafael Pass (2011). Limits of provable security from standard as sumptions. In ACM Symposium on Theory of Computing (STOC), 109–118.

  • Rafael Pass & Alon Rosen (2003). Bounded-Concurrent Secure Two-Party Computation in a Constant Number of Rounds. In IEEE Symposium on Foundations of Computer Science (FOCS), 404–413.

  • Rafael Pass & Alon Rosen (2005a). Concurrent Non-Malleable Commitments. In IEEE Symposium on Foundations of Computer Science (FOCS), 563–572.

  • Rafael Pass & Alon Rosen (2005b). New and improved constructions of non-malleable cryptographic protocols. In ACM Symposium on Theory of Computing (STOC), 533–542.

  • Rafael Pass & Abhi Shelat (2005). Unconditional Characterizations of Non-interactive Zero-Knowledge. In Advances in Cryptology (CRYPTO), 118–134.

  • Rafael Pass, Wei-Lung Dustin Tseng & Muthuramakrishnan Venkitasubramaniam (2011). Towards Non-Black-Box Lower Bounds in Cryptography. In Theory of Cryptography Conference, 579– 1829 596.

  • Rafael Pass & Hoeteck Wee (2010). Constant-round Non-Malleable Commitment from Strong One-Way Functions. In Advances in Cryptology (Eurocrypt), 638–655.

  • Omer Reingold, Luca Trevisan & Salil P. Vadhan (2004). Notions of Reducibility between Cryptographic Primitives. In Theory of Cryptography Conference, 1–20.

  • John Rompel (1990). One-Way Functions are Necessary and Sufficient for Secure Signatures. In ACM Symposium on Theory of Computing (STOC), 387–394.

  • Guy N. Rothblum & Salil P. Vadhan (2010). Are PCPs Inherent in Efficient Arguments? Computational Complexity 19(2), 265-304.

  • Hoeteck Wee (2010). Black-Box, Round-Efficient Secure Computation via Non-Malleability Amplification. In IEEE Symposium on Foundations of Computer Science (FOCS), 531–540.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, New York, NY, 10011, USA

    Rafael Pass

Authors
  1. Rafael Pass
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rafael Pass.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pass, R. Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments. comput. complex. 25, 607–666 (2016). https://doi.org/10.1007/s00037-016-0122-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00037-016-0122-2

Keywords

Subject classification

Search

Navigation