Abstract
We are now ready to explain the Brillhart-Morrison Continued Fraction Algorithm (commonly known as CFRAC) for factoring large numbers. The original idea is actually due to D. H. Lehmer and R. E. Powers in 1931 and it draws much of its inspiration from Legendre who used the continued fraction expansion in a procedure that restricted the congruence classes of possible divisors, but it was put in its present form by John Brillhart and Michael Morrison who published a thorough account of it in 1975.
“Mazes intricate, Eccentric, interwov’d, yet regular Then most, when most irregular they seem.”
- John Milton
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References
D. H. Lehmer, “An extended theory of Lucas’ functions,” Ann. of Math., 31(1930), 419–448.
D. H. Lehmer and R. E. Powers, “On factoring large numbers,” Bull. Amer. Math. Soc., 37(1931), 770–776.
Michael A. Morrison and John Brillhart, “A Method of Factoring and the Factorization of F7,” Math. of Comput., 29(1975), 183–205.
Carl Pomerance, “Analysis and comparison of some integer factoring algorithms,” pp. 89–139 in Computational Methods in Number Theory, Part I, H. W. Lenstra, Jr. and R. Tijdeman, eds., Mathematical Centre Tracts # 154, Matematisch Centrum, Amsterdam, 1982.
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© 1989 Springer-Verlag New York, Inc.
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Bressoud, D.M. (1989). Continued Fractions Continued, Applications. In: Factorization and Primality Testing. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4544-5_11
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DOI: https://doi.org/10.1007/978-1-4612-4544-5_11
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