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Volumn 48, Issue 178, 1987, Pages 757-780

A probabilistic factorization algorithm with quadratic forms of negative discriminant

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EID: 84966252702     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1987-0878705-X     Document Type: Article
Times cited : (33)

References (43)
  • 2
    • 84966240840 scopus 로고
    • Teorija Cisel
    • Moscow, 1964 English transi., Academic Press, New York and London
    • Z.I. Borevic, I.R. Safarevic, Teorija. Cisel, Izdat Nauka, Moscow, 1964 English transi., Academic Press, New York and London, 1966.
    • (1966) Izdat Nauka
    • Borevic, Z.I.1    Safarevic, I.R.2
  • 3
    • 0043216363 scopus 로고
    • On the number of positive integers free of prime factors
    • N.G. de Bruijn, On the number of positive integers free of prime factors., Nederl.Akad. Wetensch. Proc. Ser. A, 69, 1966, 239-247.
    • (1966) Nederl.Akad. Wetensch. Proc. Ser. A , vol.69 , pp. 239-247
    • De Bruijn, N.G.1
  • 4
    • 0002768224 scopus 로고
    • On a problem of Oppenheimer concerning factorisatio numerorum
    • E.R. Canfield, P. Erdos, C. Pomerance, On a problem of Oppenheimer concerning factorisatio numerorum, J. Number Theory, 17, 1983, 1-28.
    • (1983) J. Number Theory , vol.17 , pp. 1-28
    • Canfield, E.R.1    Erdos, P.2    Pomerance, C.3
  • 6
    • 0010999635 scopus 로고
    • On the asymptotic complexity of matrix multiplication
    • D. Coppersmith, S. Winograd, On the asymptotic complexity of matrix multiplication, SIAMJ. Comput., 11, 1982, 472-492.
    • (1982) SIAMJ. Comput. , vol.11 , pp. 472-492
    • Coppersmith, D.1    Winograd, S.2
  • 8
    • 84966249438 scopus 로고
    • Asymptotically fast factorization of integers
    • J.D. Dixon, Asymptotically fast factorization of integers, Math. Comp., 36, 1981, 255-260.
    • (1981) Math. Comp , vol.36 , pp. 255-260
    • Dixon, J.D.1
  • 12
    • 0003340059 scopus 로고
    • The Art of Computer Programming
    • Addison Wesley, Reading, Mass
    • D.E. Knuth, The Art of Computer Programming, 2, Seminumerical Algorithms, Addison Wesley, Reading, Mass., 1981.
    • (1981) Seminumerical Algorithms , vol.2
    • Knuth, D.E.1
  • 13
    • 0001722589 scopus 로고
    • Worst case complexity bounds for algorithms in the theory of integral quadraticforms
    • J.C. Lagarias, Worst case complexity bounds for algorithms in the theory of integral quadraticforms, J. Algorithms, 1, 1980, 142-186.
    • (1980) J. Algorithms , vol.1 , pp. 142-186
    • Lagarias, J.C.1
  • 14
    • 84919107874 scopus 로고
    • A bound for the last prime ideal in the Chebotarev density theorem
    • J.C. Lagarias, H.L. Montgomery, A.M. Odlyzko, A bound for the last prime ideal in the Chebotarev density theorem, Invent. Math., 54, 1975, 137-144.
    • (1975) Invent. Math. , vol.54 , pp. 137-144
    • Lagarias, J.C.1    Montgomery, H.L.2    Odlyzko, A.M.3
  • 15
    • 0002111950 scopus 로고
    • Effective versions of the Chebotarev density theorem in Algebraic Number Fields
    • Academic Press, Londonand New York
    • J.C. Lagarias, A.M. Odlyzko, Effective versions of the Chebotarev density theorem, in Algebraic Number Fields, L Functions and Galois Properties, Academic Press, Londonand New York, 1977, 409-464.
    • (1977) L Functions and Galois Properties , pp. 409-464
    • Lagarias, J.C.1    Odlyzko, A.M.2
  • 16
    • 84966242147 scopus 로고    scopus 로고
    • Vorlesungen uber Zahlentheorie
    • Hirzel, Leipzig, 1927 reprinted, Chelsea, New York
    • E. Landau, Vorlesungen uber Zahlentheorie, Band 1 Elementare and additive Zahlentheorie, Hirzel, Leipzig, 1927 reprinted, Chelsea, New York, 1982.
    • Band Elementare and Additive Zahlentheorie , pp. 1982
    • Landau, E.1
  • 17
    • 84966220097 scopus 로고
    • Algebraic Number Theory, Addison Wesley, Reading
    • S. Lang, Algebraic Number Theory, Addison Wesley, Reading, Mass., 1968.
    • (1968) Mass
    • Lang, S.1
  • 22
    • 84966241531 scopus 로고
    • A Monte Carlo factoring algorithm with linear storage
    • H.W. Lenstra, C.P. Schnorr, A Monte Carlo factoring algorithm with linear storage, Math. Comp., 43, 1984, 289-311.
    • (1984) Math. Comp , vol.43 , pp. 289-311
    • Lenstra, H.W.1    Schnorr, C.P.2
  • 25
    • 84880585800 scopus 로고
    • Algorithmes de Factorisation dEntiers
    • Universite Paris Sud
    • L. Monier, Algorithmes de Factorisation dEntiers, These dInformatique, Universite Paris Sud, 1980.
    • (1980) These Dinformatique
    • Monier, L.1
  • 26
    • 84966244737 scopus 로고
    • A method of factorization and the factorization of F7
    • M.A. Morrison, J. Brillhart, A method of factorization and the factorization of F7, Math.Comp., 29, 1975, 331-334.
    • (1975) Math.Comp , vol.29 , pp. 331-334
    • Morrison, M.A.1    Brillhart, J.2
  • 27
    • 0000442252 scopus 로고
    • Versions effectives du theoreme de Chebotarev sous lhypothese de Riemanngeneralise
    • Asterisque
    • J. Oesterle, Versions effectives du theoreme de Chebotarev sous lhypothese de Riemanngeneralise, in Asterisque 61, Journes Arithmetiques de Luminy, Soc. Math, de France, 1979, 165-167.
    • (1979) Journes Arithmetiques de Luminy, Soc. Math, de France , vol.61 , pp. 165-167
    • Oesterle, J.1
  • 28
    • 84976113380 scopus 로고
    • Theorems on factorisation and primality testing
    • J.M. Pollard, Theorems on factorisation and primality testing, Proc. Cambridge Philos. Soc, 76, 1974, 521-528.
    • (1974) Proc. Cambridge Philos. Soc , vol.76 , pp. 521-528
    • Pollard, J.M.1
  • 29
    • 0005599967 scopus 로고
    • Analysis and comparison of some integer factoring algorithms
    • Mathematisch Centrum, Amsterdam
    • C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational Methods in Number Theory, Mathematisch Centrum, Amsterdam, 154, 1982, 89-139.
    • (1982) Computational Methods in Number Theory , vol.154 , pp. 89-139
    • Pomerance, C.1
  • 31
    • 0000426805 scopus 로고
    • The difference between two consecutive prime numbers
    • London
    • R.A. Rankin, The difference between two consecutive prime numbers, London, Math. Soc, 13, 1938, 242-297.
    • (1938) Math. Soc , vol.13 , pp. 242-297
    • Rankin, R.A.1
  • 32
    • 0017930809 scopus 로고
    • A method for obtaining digital signatures and public keycryptosystems
    • R.L. Rivest, A. Shamir, L. Adleman, A method for obtaining digital signatures and public keycryptosystems, Comm. ACM, 21, 1978, 120-126.
    • (1978) Comm. ACM , vol.21 , pp. 120-126
    • Rivest, R.L.1    Shamir, A.2    Adleman, L.3
  • 33
    • 34250146057 scopus 로고
    • Ein Effizienz vergleich der Faktorisierungsverfahren von Morrison Brillhart and Schroeppel
    • J. Sattler, C.P. Schnorr, Ein Effizienz vergleich der Faktorisierungsverfahren von Morrison Brillhart and Schroeppel, Computing, 30, 1983, 91-110.
    • (1983) Computing , vol.30 , pp. 91-110
    • Sattler, J.1    Schnorr, C.P.2
  • 34
    • 49049131184 scopus 로고
    • Refined analysis and improvements on some factoring algorithms
    • C.P. Schnorr, Refined analysis and improvements on some factoring algorithms, J. Algorithms, 2, 1982, 101-127.
    • (1982) J. Algorithms , vol.2 , pp. 101-127
    • Schnorr, C.P.1
  • 36
    • 0038933271 scopus 로고
    • Quadratic fields and factorisation
    • Mathematisch Centrum, Amsterdam
    • R.J. SCHOOF, Quadratic fields and factorisation, Computational Methods in Number Theory, Mathematisch Centrum, Amsterdam, 154, 1982, 235-286.
    • (1982) Computational Methods in Number Theory , vol.154 , pp. 235-286
    • Schoof, R.J.1
  • 37
    • 84966238489 scopus 로고
    • Einige Bemerkungen zu der vorstehenden Arbeit des Herrn G. Polya Uber dieVerteilung der quadratischen Reste und Nichtreste
    • Springer, Berlin
    • I. SCHUR, Einige Bemerkungen zu der vorstehenden Arbeit des Herrn G. Polya Uber dieVerteilung der quadratischen Reste und Nichtreste, Nachr. Kon. Ges. Wiss. Gottingen, Math. Phys., In: Gesammelte Abhandlungen, Springer, Berlin, 1973, 239-245.
    • (1973) Nachr. Kon. Ges. Wiss. Gottingen, Math. Phys., In: Gesammelte Abhandlungen , pp. 239-245
    • Schur, I.1
  • 38
    • 84966250601 scopus 로고
    • Class Number, A Theory of Factorization and Genera
    • Providence, R. I
    • D. Shanks, Class Number, A Theory of Factorization and Genera, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R. I., 1971, 415-440.
    • (1971) Proc. Sympos. Pure Math., Amer. Math. Soc , pp. 415-440
    • Shanks, D.1
  • 39
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • V. Strassen, Gaussian elimination is not optimal, Numer. Math., 13, 1969, 354-356.
    • (1969) Numer. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 40
    • 0039014701 scopus 로고
    • Einige Resultate uber Berechnungskomplexitat
    • V. Strassen, Einige Resultate uber Berechnungskomplexitat, Jber. Deutsch. Math. Verein., 78, 1976, 1-8.
    • (1976) Jber. Deutsch. Math. Verein , vol.78 , pp. 1-8
    • Strassen, V.1
  • 41
    • 0003943048 scopus 로고
    • Matrix Iterative Analysis
    • Prentice Hall, Englewood Cliffs
    • R.S. Varga, Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, N. J., 1962.
    • (1962) N. J.
    • Varga, R.S.1
  • 43
    • 0022583143 scopus 로고
    • Solving sparse linear equations over finite fields
    • D. Wiedemann, Solving sparse linear equations over finite fields, IEEE Trans. Inform. Theory, 32, 1986, 54-62.
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 54-62
    • Wiedemann, D.1


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