A note on efficient zero-knowledge proofs and arguments (extended abstract)

ABSTRACT

In this note, we present new zero-knowledge interactive proofs and arguments for languages in NP. To show that x ε L, with an error probability of at most 2^-k, our zero-knowledge proof system requires O(|x|^c₁)+O(lg^c₂|x|)k ideal bit commitments, where c₁ and c₂ depend only on L. This construction is the first in the ideal bit commitment model that achieves large values of k more efficiently than by running k independent iterations of the base interactive proof system. Under suitable complexity assumptions, we exhibit zero knowledge arguments that require O(lg^c|x|kl bits of communication, where c depends only on L, and l is the security parameter for the prover. This is the first construction in which the total amount of communication can be less than that needed to transmit the NP witness. Our protocols are based on efficiently checkable proofs for NP[4].

References

1. 1.J. Boyar, G. Brassard and R. Peralta. Subquadratic Zero-knowledge Proc. of Focsgl
2. 2.G. Brassard and C. Cr#peau. Non-Transitive Transfer of Confidence: A Perfect Zero-Knowledge Interactive Protocol for SAT and Beyond, Proc. of FOCS86.
3. 3.G. Brassard, D. Chaum, and C. Cr#peau. Minimum Disclosure Proofs of Knowledge, J. Comp#t. System Sci. 37 (1988), 156-189.
4. 4.L. Bahai, L. Fortnow, L. Levin and M. Szegedy. Checking computation in polylogarithmic time. Proc. of STOC91
5. 5.J. Boyar, M. Krentel and S. Kurtz. A discrete logarithm implementation of perfect zero-knowledge blobs. Journal of Cryptology, Vol. 2, No. 2, pp. 63- 76, 1990.
6. 6.S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems, SIAM J. Comput. 18 (1989), 186-208.
7. 7.S. Goldwasser, S. Micali, and R. Rivest. A Paradoxical Solution to the Signature Problem. Proc. of. FOCS84
8. 8.O. Goldreich, S. Micali, and A. Wigderson. Proofs that Yield Nothing but Their Validity and a Methodology of Cryptographic Protocol Design, Proc. of FOCS86.
9. 9.O. Goldreich, S. Micali, and A. Wigderson. How to Play ANY Mental Game, Proc. of STOC87.
10. 10.R. Impagliazzo and M. Yung. Direct Minimum- Knowledge Computation, Proc. of CRYPTO87.
11. 11.J. Kilian, S. Micali and R. Ostrovsky. Minimum Resource Zero-Knowledge Proofs, Proc. of FOCS89.

Index Terms

• Computing methodologies

  • Symbolic and algebraic manipulation

    • Symbolic and algebraic algorithms

      • Theorem proving algorithms

• Theory of computation

  • Computational complexity and cryptography

    • Complexity classes

  • Logic

    • Proof theory

  • Models of computation