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Original Articles

Factoring Integers with Large-Prime Variations of the Quadratic Sieve

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Pages 257-273 | Published online: 03 Apr 2012

REFERENCES

  • Alford , W. R. and Pomerance . 1995 . “Implementing the self-initializing quadratic sieve on a distributed network”. ” . In Number-theoretic and algebraic methods in computer science Edited by: van der Poorten , A. J. 163 – 174 . River Edge , NJ : World Scientific. . [Alford and Pomerance 1995], NTAMCS ′93: Moscow, 1993
  • Atkins , D. , Graff , M. , Lenstra , A. K. and Leyland , P. C. 1995 . “The magic words are squeamish ossifrage”. ” . In Advances in cryptology Edited by: Pieprzyk , J. and Safavi-Naini , R. 263 – 277 . Berlin : Springer. . [Atkins et al. 1995], (ASIACRYPT ′94: Wollongong, 1994), Lecture Notes in Comp. Sci. 917
  • Bollobás , B. 1985 . Random graphs London and Orlando , FL : Academic Press. . [Bollobás 1985]
  • Brent , R. P. and te Riele , H. J. J. June 1992 . “Factorizations of an± 1, 13 ≤ a < 100” June , Amsterdam , , The Netherlands : Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ. . [Brent and te Riele 1992], Technical Report NM–R9212, Updates to this report have appeared as CWI Report NM–R9419, September 1994 and CWI Report NM–R9609, March 1996, with P. L. Montgomery as a coeditor. The complete tables, incorporating these updates, are available at ftp://nimbus.anu.edu.au/pub/Brent/factors or ftp://ftp.cwi.nl/pub/hermcin/factors
  • Bressoud , D. M. 1989 . Factorization and primality testing New York : Springer. . [Bressoud 1989], Undergraduate Texts in Math.
  • Davis , J. A. and Holdridge , D. B. 1983 . “Factorization using the quadratic sieve algorithm” Albuquerque , NM : Sandia National Laboratories. . [Davis and Holdridge 1983], Technical Report Sand 83–1346
  • Denny , T. F. 1993 . “Faktorisieren mit dem quadratischen Sieb” , Master's thesis Saarbrücken : Universität des Saarlandes. . [Denny 1993]
  • Denny , T. F. , Dodson , B. , Lenstra , A. K. and Manasse , M. S. 1994 . “On the factorization of RSA-120”. ” . In Advances in Cryptology Edited by: Stinson , D. R. 166 – 174 . Berlin : Springer. . [Denny et al. 1994], (CRYPTO ′93: Santa Barbara, CA, 1993), Lecture Notes in Comp. Sci. 773
  • Erdös , P. and Rényi , A. 1959 . “On random graphs I” . Publ. Math. Debrecen , 6 : 290 – 297 . [Erdös and Rényi 1959]
  • Erdös , P. and Rényi , A. 1960 . “On the evolution of random graphs” . Publ. Math. Inst. Hungar. Acad. Sci. , 5 : 17 – 61 . [Erdös and Rényi 1960]
  • Erdös , P. and Rényi , A. 1961 . “On the evolution of random graphs” . Bull. Inst. Int. Statist. Tokyo , 38 : 343 – 347 . [Erdös and Rényi 1961]
  • Kraitchik , M. 1929 . Recherches sur la théorie des nombres Vol. II , Paris : Gauthier–Villars. . [Kraitchik 1929]
  • Lehmer , D. H. and Powers , R. E. 1931 . “On factoring large numbers” . Bull. Amer. Math. Soc. , 37 : 770 – 776 . [Lehmer and Powers 1931]
  • Lenstra , A. K. and Lenstra , H. W. Jr. 1993 . The development of the number field sieve Berlin : Springer. . [Lenstra and Lenstra 1993], Lecture Notes in Math. 1554
  • Lenstra , A. K. and Manasse , M. S. 1994 . “Factoring with two large primes” . Math. Comp. , 63 : 785 – 798 . [Lenstra and Manasse 1994]
  • Morrison , M. A. and Brillhart , J. 1975 . “A method of factoring and the factorization of F7“ . Math. Comp. , 29 : 183 – 205 . [Morrison and Brillhart 1975]
  • Parkinson , D. and Wunderlich , W. 1984 . “A compact algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers” . Parallel Comput. , 1 : 65 – 73 . [Parkinson and Wunderlich 1984]
  • Paton , K. 1969 . “An algorithm for finding a fundamental set of cycles of a graph” . Comm. ACM , 12 : 514 – 518 . [Paton 1969]
  • Peralta , R. “Implementation of the hypercube variation of the multiple polynomial quadratic sieve” [Peralta ≥ 1997], To appear
  • Pomerance , C. 1982 . “Analysis and comparison of some integer factoring algorithms”. ” . In Computational methods in number theory Edited by: Lenstra , H. W. Jr. and Tijdeman , R. 89 – 139 . Amsterdam : Mathematisch Centrum. . [Pomerance 1982]
  • Pomerance , C. 1985 . “The quadratic sieve factoring algorithm”. ” . In Advances in cryptology Edited by: Beth , T. 169 – 182 . New York : Springer–Verlag. . [Pomerance 1985], (EUROCRYPT ′84: Paris, 1984), Lecture Notes in Comp. Sci. 209
  • Pomerance , C. , Smith , J. W. and Tuler , R. 1988 . “A pipeline architecture for factoring large integers with the quadratic sieve algorithm” . SIAM J. Comput. , 17 : 387 – 403 . [Pomerance et al. 1988]
  • te Riele , H. J. J. , Lioen , W. M. and Winter , D. T. “Factoring with the quadratic sieve on large vector computers” . J. Comp. Appl. Math. , 27 267 – 278 . [te Riele et al. 1989]
  • te Riele , H. , Lioen , W. and Winter , D. 1991 . “Factorization beyond the googol with MPQS on a single computer” . CWI Quarterly , 4 March : 69 – 72 . [te Riele et al. 1991]
  • Riesel , H. 1985 . Prime numbers and computer methods for factorization Boston : Birkhäuser. . [Riesel 1985], Progress in Math. 126
  • Silverman , R. D. 1987 . “The multiple polynomial quadratic sieve” . Math. Comp. , 48 : 329 – 339 . [Silverman 1987]
  • Wagstaff , S. S. Jr. December 13 1993 . December 13 , [Wagstaff 1993], Regular letter to subscribers describing the state of the Cunningham factorization project

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