Cheating at Mental Poker

  • Don Coppersmith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 218)


We review the “mental poker” scheme described by Shamir, Rivest and Adleman [SRA]. We present two possible means of cheating, depending on careless implementation of the SRA scheme. One will work if the prime p is such that p-1 has a small prime divisor. In the other scheme, the names of the cards “TWO OF CLUBS” have been extended by random-looking bits. chosen by the cheater.


Discrete Logarithm Discrete Logarithm Problem Quadratic Residue Yorktown Height Linear Diophantine Equation 


  1. [Adl]
    L.M. Adleman, “A subexponential algorithm for the discrete logarithm problem with applications to cryptography,” Proc. 20th IEEE Found. Comp. Sci. Symp. (1979), 55–60.Google Scholar
  2. [COS]
    D. Coppersmith, A.M. Odlyzko and R. Schroeppel, “Discrete Logarithms in GF(p),” Research Report RC 10985, IBM T.J. Watson Research Center, Yorktown Heights, N.Y., 10598, February 14, 1985.Google Scholar
  3. [DDDHL]
    R.A. DeMillo, G.I. Davida, D.P. Dobkin, M.A. Harrison and R.J. Lipton, Applied Cryptology, Cryptographic Protocols, and Computer Security Models, vol. 29, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, 1983. Chapter 4.11, “Compromising Protocols.”Google Scholar
  4. [GM]
    S. Goldwasser and S. Micali, “Probabilistic Encryption & How To Play Mental Poker Keeping Secret All Partial Information,” Proc. 14th ACM Symposium on Theory of Computing (1982), 365–377.Google Scholar
  5. [Lag]
    J.C. Lagarias, “Knapsack Public Key Cryptosystems and Diophantine Approximation (Extended Abstract),” Advances in Cryptology, Proceedings of Crypto 83, (Ed.: D. Chaum), Plenum Press, New York, 1983, 289–301.Google Scholar
  6. [LLL]
    A.K. Lenstra, H.W. Lenstra, Jr. and L. Lovasz, “Factoring Polynomials with Rational Coefficients,” Math. Annalen. 261 (1982), 515–534.MATHCrossRefMathSciNetGoogle Scholar
  7. [PH]
    S.C. Pohlig and M. Hellman, “An improved algorithm for computing logarithms over GF(p) and its cryptographic significance,” IEEE Trans. Inform. Theory IT-24 (1978), 106–110.CrossRefMathSciNetGoogle Scholar
  8. [SRA]
    A. Shamir, R.L. Rivest and L.M. Adleman, “Mental Poker,” MIT/LCS/TM-125, Laboratory for Computer Science, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, February 1979.Google Scholar
  9. [WM]
    A.E. Western and J.C.P. Miller, Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, vol. 9, Cambridge Univ. Press, 1968.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Don Coppersmith
    • 1
  1. 1.IBM ResearchYorktown Heights

Personalised recommendations