Cryptoprotocols: Subscription to a Public Key, The Secret Blocking and The Multi-Player Mental Poker Game (extended abstract)

  • Mordechai Yung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 196)

Abstract

Investigating the capabilities of public key and related cryptographic techniques has recently become an important area of cryptographic research. In this paper we present some new algorithms and cryptographic protocols (Cryptoprotocols) which enlarge the range of applications of public key systems and enable us to perform certain transactions in communication networks. The basic cryptographic tools used are Rabin’s Oblivious Transfer Protocol and an algorithm we developed for Number Embedding which is provably hard to invert.

We introduce the protocol Subscription to a Public Key, which gives a way to transfer keys over insecure communication channels and has useful applications to cryptosystems. We develop the Secret Blocking Protocol, specified as follows : ‘A transfers a secret to B, B can block the message. If B does not block it, there is a probability P that he might get it. (1/2 ≤ P < 1, where we can control the size of P). A does not know if the message was blocked (but he can find out later)’.

The classic cryptotransaction is the Mental Poker Game. A cryptographically secure solution to the Multi Player Mental Poker Game is given. The approach used in constructing the solution provides a general methodology of provable and modular Protocol Composition

References

  1. 1.
    Angluin D. Lecture notes on the complexity of some problems in number theory. Tech. Rept. 243, Dep. of Computer Science, Yale University, August, 1982.Google Scholar
  2. 2.
    Berlekamp E.R. “Factoring Polynomials over Large Finite Fields.” Mathematics of Computation 24 (July 1970), 713–735.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Blum M. and S. Goldwasser. An Efficient Probabilistic Public-Key Scheme Which Hides All Partial Information. to appear in Proceedings of Crypto84, 1984.Google Scholar
  4. 4.
    Blum M. Three Application of the Oblivious Transfer. University of California at Berkely, September, 1981.Google Scholar
  5. 5.
    Blum M. Mental Poker. University of California at Berkely, 1982. to appearGoogle Scholar
  6. 6.
    Blum M. “How to Exchange (Secret) Keys.” ACM Transactions on Computer Systems 1,2 (May 1983), 175–193.CrossRefGoogle Scholar
  7. 7.
    Diffie W., and M.E. Hellman. “New Directions in Cryptography.” IEEE Transactions of Information Theory IT-22 (November 1976), 644–654.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldwasser, S. and Micali S. Probabilistic Encryption and How to Play Mental Poker Keeping Secret All Partial Information. Proceedings of the 14 Annual ACM Symp. on Theory of Computing, ACM-SIGACT, May, 1982, pp. 365–377.Google Scholar
  9. 9.
    Knuth D. E.. The Art of Computer Programming. Volume 2: Seminumerical Algorithms. Addison-Wesly, Reading, Massachusetts, 1981.MATHGoogle Scholar
  10. 10.
    Lipton R. How to Cheat at Mental Poker. Proceeding of the AMS short course on Cryptography, AMS, January, 1981.Google Scholar
  11. 11.
    Niven I. and Zuckerman H.S.. An Introduction to the Theory of Numbers. Wiley, New York, 1981.Google Scholar
  12. 12.
    Rabin M. Digitalized Signatures and Public-key Functions as Intractable as Factorization. Tech. Rept. LCS/TR-212, MIT, January”, 1979.Google Scholar
  13. 13.
    Rabin M. Probabilistic Algorithms in Finite Fields. Tech. Rept. LCS/TR-213, MIT, January, 1979.Google Scholar
  14. 14.
    Rackoff C., S. Micali and M. Fischer. A Secure Protocol for the Oblivious Transfer. Eurocrypt 84, La Sorbonne, Paris, April, 1984.Google Scholar
  15. 15.
    Rivest R., Shamir A., Adleman L. “A Method for Obtaining Digital Signatures and Public Key Cryptosystems.” Communications of the ACM 21,2 (February 1978), 120–126.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Shamir A. “How to Share a Secret.” Communication of the ACM 22,11 (November 1979), 612–613.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Shamir A., Rivest R. Adleman L. Mental Poker. In Mathematical Gardner, Klarner D. E., Ed., Wadsworth Intrntl, 1981, pp. 37–43.Google Scholar
  18. 18.
    Solovay R., and Strassen V. “A Fast Monte-Carlo Test of Primality.” SIAM Journal on Computing 6 (March 1977), 84–85.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Yung M. K-Player Mental Poker. Master Th., Tel-Aviv University, March 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Mordechai Yung
    • 1
  1. 1.Department of Computer ScienceColumbia UniversityNew YorkUSA

Personalised recommendations