The expectation of success using a Monte Carlo factoring methodsome statistics on quadratic class numbers
Author:
Duncan A. Buell
Journal:
Math. Comp. 43 (1984), 313327
MSC:
Primary 11Y05; Secondary 11A51, 11R29, 11Y40
MathSciNet review:
744940
Fulltext PDF Free Access
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Abstract: A method has been proposed for factoring an integer N by using the structure of the class groups of quadratic fields of radicand for various small multipliers k. We discuss the method and an implementation of the method, and various theoretical questions which have an impact on the practical use of the method in factoring. Some of the theoretical questions relate to the nature of class numbers and class groups; we present extensive statistical results on the class numbers and class groups of imaginary quadratic fields.
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 Alexander M. Mood & Franklin A. Graybill, Introduction to the Theory of Statistics, 2nd ed., McGrawHill, New York, 1963, pp. 126129.
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 Carl Pomerance, private communication.
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 Carl Pomerance, "Analysis and comparison of some integer factoring methods," Computational Methods in Number Theory (H. W. Lenstra, Jr., R. Tijdeman, eds.), Math. Centrum, Amsterdam, 1982. MR 700260 (84i:10005)
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 Carl Pomerance & Samuel S. Wagstaff, Jr., "Implementation of the continued fraction integer factoring algorithm." (To appear.) MR 703581 (85c:11124)
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 C. P. Schnorr & H. W. Lenstra, Jr., "A Monte Carlo factoring algorithm with finite storage." (To appear.) (Extended abstract appears in Lecture Notes in Comput. Sci., Vol. 145, SpringerVerlag, New York, pp. 1934.) MR 695351 (84d:10003)
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 Daniel Shanks, Class Number, A Theory of Factorization, and Genera, Proc. Sympos. Pure Math., Vol. 20, Amer. Math. Soc., Providence, R. I., 1971, pp. 415440. MR 0316385 (47:4932)
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 H. G. Zimmer, Computational Problems, Methods, and Results in Algebraic Number Theory, Lecture Notes in Math., Vol. 262, SpringerVerlag, New York, 1972. MR 0323751 (48:2107)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407449401
PII:
S 00255718(1984)07449401
Article copyright:
© Copyright 1984
American Mathematical Society
