Pseudoprimes, Poker and Remote Coin Tossing
In this chapter we take a closer look at numbers that are not primes, but are tantalizingly close to primes in some respects. Of course, a given number n > 1 is either prime or composite — in other words, n is either “pregnant” with factors or not; there is no third alternative. But nevertheless, it makes sense to define and, as we do in this chapter, discuss such odd entities as pseudoprimes, absolute (or universal) pseudoprimes and strong pseudoprimes. When talking about extremely large numbers, pseudoprimality is sometimes the only evidence we can go by.
KeywordsElliptic Curf Fermat Number Sporadic Simple Group Poker Player Composite Number
Unable to display preview. Download preview PDF.
- 19.5S. 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
- 19.6S. Micali (personal communication)Google Scholar
- 19.14L. 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)MathSciNetMATHCrossRefGoogle Scholar