Cryptographic Computation: Secure Fault-Tolerant Protocols and the Public-Key Model (Extended Abstract)

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 293)


We give a general procedure for designing correct, secure, and fault-tolerant cryptographic protocols for many parties, thus enlarging the domain of tasks that can be performed efficiently by cryptographic means. We model the most general sort of feasible adversarial behavior, and describe fault-recovery procedures that can tolerate it. Our constructions minimize the use of cryptographic resources. By applying the complexity-theoretic approach to knowledge, we are able to measure and control the computational knowledge released to the various users, as well as its temporal availability.


  1. 1.
    Abadi M., and J. Feigenbaum. A Simple Protocol for Secure Circuit Evaluation. Preprint, 1987.Google Scholar
  2. 2.
    Alexi, W., Chor, B., Goldreich O. and Schnorr C.P. RSN/Rabin Bits are 1/2 + (1/poly(k)) Secure. Proc. 25th FOCS, IEEE, 1984, pp. 449–457.Google Scholar
  3. 3.
    Barrington, D.A. Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages in NC1. 18th STOC, ACM, May, 1986, pp. 1–5.Google Scholar
  4. 4.
    Ben Or, M., O. Goldreich, S. Micali, and R. Rivest A Fair Protocol for Signing Contracts. Proceedings of ICALP-85, July, 1985, pp. 43–52.Google Scholar
  5. 5.
    Benaloh, J.C. and Yung M. Distributing the Power of a Government to Enhance the Privacy of Voters. Proc. 5th PODC, ACM, 1986, pp. 52–62.Google Scholar
  6. 6.
    Blum, M. and Micali, S. How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. Proc. 23rd FOCS, IEEE, 1982, pp. 112–117. Also in: SIAM Journal on Computing, November 1984, 850–864.Google Scholar
  7. 7.
    Blum, M. and S. Goldwasser. An Efficient Probabilistic Public-Key Scheme Which Hides All Partial Information. Proceedings of Crypto84, 1985, pp. 289–301.Google Scholar
  8. 8.
    Blum, L., Blum M. and Shub M. Comparison of Two Pseudo-Random Number Generators. Proceedings of Crypto82, August, 1982, pp. 61–78.Google Scholar
  9. 9.
    Blum, M. “How to Exchange (Secret) Keys”. ACM Transactions on Computer System 1,2 (May 1983), 175–193.CrossRefGoogle Scholar
  10. 10.
    Boppana, R.B. and R. Hirschfeld. Pseudorandom Generators and Complexity Classes. Preprint, 1986.Google Scholar
  11. 11.
    Chaum D., I. Damgard, and J. van de Graaf. Multiparty Computations Ensuring Secrecy of Each Party’s Input and Correctness of the Output. These proceedings.Google Scholar
  12. 12.
    Chor, B. and Rabin M.O. Achieving Independence in Logarithmic Number of Rounds. 6th PODC, ACM, August, 1987.Google Scholar
  13. 13.
    Chor, B., Goldwasser S., Micali S. and Awerbuch B. Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults. Proc. 26th FOCS, IEEE, 1985, pp. 383–395.Google Scholar
  14. 14.
    Cohen, J.C. (Benaloh) and Fischer M.J. A Robust and Verifiable Cryptographically Secure Election Scheme. Proc. 26th FOCS, IEEE, 1985, pp. 372–383.Google Scholar
  15. 15.
    DeMillo, R.A., N. Lynch and M. Merritt. Cryptographic Protocols. 14th STOC, ACM-SIGACT, May, 1982, pp. 383–400.Google Scholar
  16. 16.
    Diffie, W., and Hellman M.E. “New Directions in Cryptography”. IEEE Transactions of Information Theory IT-22 (November 1976), 644–654.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Even, S., Goldreich O. and Lempel A. “A Randomized Protocol for Signing Contracts”. Communications of the ACM 28,6 (June 1985), 637–647.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Feige, U., A. Fiat and A. Shamir. Zero-Knowledge Proofs of Identity. 19th STOC, 1986, pp. 210–217.Google Scholar
  19. 19.
    Fischer, M., S. Micali, C. Rackoff, and D. Wittenberg. An Oblivious Transfer Protocol Equivalent to Factoring. Manuscript, 1986.Google Scholar
  20. 20.
    Galil, Z., Haber S. and Yung M. A private Interactive Test of a Boolean Predicate and Minimum-Knowledge Public-Key Cqposystems. Proc. 26th FOCS, IEEE, 1985, pp. 360–371.Google Scholar
  21. 21.
    Goldreich, O., S. Goldwasser, and S. Micali. How to Construct Random Functions. Proc. 25th FOCS, IEEE, 1984, pp. 464–479.Google Scholar
  22. 22.
    Goldreich O., and R. Vainish. How to Solve Any Protocol Problem: an Efficiency Improvement. These proceedings.Google Scholar
  23. 23.
    Goldreich, O., S. Micali and A. Wigderson. Proofs that Yield Nothing But their Validity and a Methodology of Cryptogrphic Protocol Design. 27th FOCS, IEEE, October, 1986, pp. 174–187.Google Scholar
  24. 24.
    Goldreich, O., S. Micali and A. Wigderson. How to Play Any Mental Game. 19th STOC, 1987, pp. 218–229.Google Scholar
  25. 25.
    Goldwasser, S. and Micali S. Probabilistic Encryption and How to Play Mental Poker Keeping Secret All Partial Information. Proceedings of the 14th Annual ACM Symp. on Theory of Computing, ACM-SIGACT, May, 1982, pp. 365–377.Google Scholar
  26. 26.
    Goldwasser, S., S. Micali and C. Rackoff. The Knowledge Complexity of Interactive Proof-Systems. 17 STOC, ACM-SIGACT, May, 1985, pp. 291–304.Google Scholar
  27. 27.
    Halpern, J. and Rabin M.O. A Logic to Reason about Likehood. Proc. 15th STOC, ACM, 1983, pp. 310–319.Google Scholar
  28. 28.
    Hastad, J. and A. Shamir. The Cryptographic Security of Truncated Linearly Related Variables. 17th STOC, ACM-SIGACT, May, 1985, pp. 356–362.Google Scholar
  29. 29.
    Impagliazzo R., and M. Yung. Direct Minimum-Knowledge Computations. These proceedings.Google Scholar
  30. 30.
    Kranakis, E.. Primality and Cryptography. John Wiley and sons, Chichester. 1986.zbMATHGoogle Scholar
  31. 31.
    Levin, L. One-way Functions and Pseudorandom Generators. Proc. 17th STOC, ACM, 1985.Google Scholar
  32. 32.
    Luby, M., Micali S. and Rackoff C. How to Simultaneously Exchange a Secret Bit by Flipping a Symmetrically-Biased Coin. 24 FOCS, IEEE, November, 1983, pp. 11–22.Google Scholar
  33. 33.
    Pippenger, N., and M.J. Fischer. “Relations among Complexity Measures”. Journal of the ACM 26 (1979), 361–381.MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Rabin. M. O. Digitalized Signatures and Public-key Functions as Intractable as Factorization. LCS/TR-212, MIT, January“, 1979.Google Scholar
  35. 35.
    Rivest, R., Shamir A., Adleman L. “A Method for Obtaining Digital Signatures and Public Key Cryptosystems”. Commications of the ACM 21,2 (February 1978), 120–126.MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Shamir, A. “How to Share a Secret”. Communicarions of the ACM 22,11 (November 1979), 612–613.MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Shamir, A., Rivest R. Adleman L. Mental Poker. In Mathematical Gardner. Klarner D. E., Ed., Wadsworth Intrntl, 1981, pp. 37–43.Google Scholar
  38. 38.
    Vazirani, U. and Vazirani V. Efficient and Secure Pseudo-Random Number Generation. Proc. 25th FOCS, IEEE, 1984, pp. 458–463.Google Scholar
  39. 39.
    Vazirani, U. and Vazirani V. Trapdoor Pseudo-random Number Generators, with Applications to Protocol Design. 24th FOCS, IEEE, November, 1983, pp. 23–30.Google Scholar
  40. 40.
    Yao, A. Protocols for Secure Computations. 23rd FOCS, IEEE, November, 1982, pp. 160–164.Google Scholar
  41. 41.
    Yao, A. Theory and Applications of Trapdoor Functions. 23rd FOCS, IEEE, November, 1982, pp. 80–91.Google Scholar
  42. 42.
    Yao, A. How to Generate and Exchange Secrets. 27th FOCS, IEEE, October, 1986, pp. 162–167.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  1. 1.Department of Computer ScienceColumbia UniversityColumbia
  2. 2.Department of Computer ScienceTel Aviv UniversityTel Aviv

Personalised recommendations