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Pseudoprimes, Poker and Remote Coin Tossing

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

Keywords

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)zbMATHGoogle Scholar
  2. 19.2
    C. Pomerance: Recent developments in primality testing. Math. Intelligencer 3, 97–105 (1981)MathSciNetzbMATHCrossRefGoogle 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)zbMATHCrossRefGoogle 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)MathSciNetzbMATHGoogle 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)MathSciNetzbMATHGoogle Scholar
  9. 19.9
    M. O. Rabin: Probabilistic algorithm for testing primality. J. Number Theory 12, 128–138 (1980)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 19.10
    C. F. Gauss: Disquisitiones Arithmeticae [English transl. by A. A. Clarke, Yale University Press, New Haven 1966]zbMATHGoogle Scholar
  11. 19.11
    J. D. Dixon: Asymptotically fast factorization of integers. Math. Comp. 36, 255–260 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 19.12
    E. Lucas: Théorie des Nombres (Blanchard, Paris 1961)zbMATHGoogle 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)MathSciNetzbMATHGoogle 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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© Springer-Verlag Berlin Heidelberg 2006

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