Continued Fraction Factorization Algorithm
المؤلف:
Morrison, M. A. and Brillhart, J.
المصدر:
"A Method of Factoring and the Factorization of F_7." Math. Comput. 29
الجزء والصفحة:
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10-9-2020
988
Continued Fraction Factorization Algorithm
A prime factorization algorithm which uses residues produced in the continued fraction of 
for some suitably chosen 
to obtain a square number. The algorithm solves
by finding an 
for which 
(mod 
) has the smallest upper bound. The method requires (by conjecture) about 
steps, and was the fastest prime factorization algorithm in use before the quadratic sieve, which eliminates the 2 under the square root (Pomerance 1996), was developed.
REFERENCES:
Morrison, M. A. and Brillhart, J. "A Method of Factoring and the Factorization of 
." Math. Comput. 29, 183-205, 1975.
Pomerance, C. "A Tale of Two Sieves." Not. Amer. Math. Soc. 43, 1473-1485, 1996.
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