Pseudoprimes, Poker and Remote Coin Tossing

Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


Elliptic Curf Great Common Divisor Fermat Number Sporadic Simple Group Poker Player 
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Chapter 19

  1. 19.1
    P. Ribenboim: The New Book of Prime Number Records (Springer, New York 1996)MATHGoogle Scholar
  2. 19.2
    C. Pomerance: Recent developments in primality testing. Math. Intelligencer 3, 97–105 (1981)MathSciNetMATHCrossRefGoogle Scholar
  3. 19.3
    A. J. van der Poorten, A. Rotkiewicz: On strong pseudoprimes in arithmetic progressions. J. Austral. Math. Soc. 29, 316–321 (1980)MATHCrossRefGoogle Scholar
  4. 19.4
    A. Rotkiewicz: On Euler-Lehmer pseudoprimes and strong pseudoprimes with parameters L, Q in arithmetic progressions. Math. Comp. 39, 239–247 (1982)MathSciNetMATHGoogle Scholar
  5. 19.5
    S. Goldwasser, S. Micali: “Probabilistic Encryption and How To Play Mental Poker,” in Proceedings of the 4th ACM Symposium on the Theory of Computing (Assoc. Comp. Machinery, New York 1982) pp. 365–377Google Scholar
  6. 19.6
    S. Micali (personal communication)Google Scholar
  7. 19.7
    A. Shamir, R. L. Rivest, L. M. Adleman: “Mental Poker,” in The Mathematical Gardener, ed. by D. Klarner (Prindle Weber Schmidt, Boston 1981) pp. 37–43Google Scholar
  8. 19.8
    S. S. Wagstaff: Large Carmichael numbers. Math. J. Okayama Univ. 22, 33–41 (1980)MathSciNetMATHGoogle Scholar
  9. 19.9
    M. O. Rabin: Probabilistic algorithm for testing primality. J. Number Theory 12, 128–138 (1980)CrossRefMathSciNetMATHGoogle Scholar
  10. 19.10
    C. F. Gauss: Disquisitiones Arithmeticae [English transl. by A. A. Clarke, Yale University Press, New Haven 1966]MATHGoogle Scholar
  11. 19.11
    J. D. Dixon: Asymptotically fast factorization of integers. Math. Comp. 36, 255–260 (1981)MathSciNetMATHCrossRefGoogle Scholar
  12. 19.12
    E. Lucas: Théorie des Nombres (Blanchard, Paris 1961)MATHGoogle Scholar
  13. 19.13
    J. Brillhart, D. H. Lehmer, J. L. Selfridge: New primality criteria and factorizations of 2m ± 1. Math Comp. 29, 620–647 (1975)MathSciNetMATHGoogle Scholar
  14. 19.14
    L. M. Adleman, C. Pomerance, R. S. Rumely: On distinguishing prime numbers from composite numbers. Ann. Math. (2) 117, 173–206 (1983). See also: M. J. Coster, B. A. LaMacchia, C.P. Schnorr, J. Stern: Improved low-density subset sum algorithms. J. Computational Complexity 2, 111–128 (1992)MathSciNetCrossRefGoogle Scholar
  15. 19.15
    I. L. Chuang, R. Laflamme, P. W. Shor, W. H. Zurek: Science 270, 1633 (1995)MathSciNetADSCrossRefGoogle Scholar

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