Test de primalité et méthodes de factorisation

Jean-Louis Nicolas

Publications mathématiques et informatique de Rennes (1985)

  • Volume: 4, Issue: 4, page 148-162

How to cite

top

Nicolas, Jean-Louis. "Test de primalité et méthodes de factorisation." Publications mathématiques et informatique de Rennes 4.4 (1985): 148-162. <http://eudml.org/doc/274777>.

@article{Nicolas1985,
author = {Nicolas, Jean-Louis},
journal = {Publications mathématiques et informatique de Rennes},
keywords = {primality testing; factorization methods; computational number theory; Pollard method; Schnorr-Lenstra method; Lenstra's elliptic curve method; Pomerance's quadratic sieve method},
language = {fre},
number = {4},
pages = {148-162},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Test de primalité et méthodes de factorisation},
url = {http://eudml.org/doc/274777},
volume = {4},
year = {1985},
}

TY - JOUR
AU - Nicolas, Jean-Louis
TI - Test de primalité et méthodes de factorisation
JO - Publications mathématiques et informatique de Rennes
PY - 1985
PB - Département de Mathématiques et Informatique, Université de Rennes
VL - 4
IS - 4
SP - 148
EP - 162
LA - fre
KW - primality testing; factorization methods; computational number theory; Pollard method; Schnorr-Lenstra method; Lenstra's elliptic curve method; Pomerance's quadratic sieve method
UR - http://eudml.org/doc/274777
ER -

References

top
  1. [Adl] L.M. Adelman, C. Pomerance, R.S. Rumely : On distinguishing prime numbers from composite numbers. Ann. Math.117 (1983), p. 173-206. Zbl0526.10004MR683806
  2. [Can] E.R. Canfield, P. Erdös and C. Pomerance : On a problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory17, 1983, p. 1-28. Zbl0513.10043MR712964
  3. [Coh 1] H. Cohen : Méthodes de factorisation et nombre de classes des corps quadratiques, Séminaire D.P.P., Paris, 14e année 1972-73, G7. Zbl0317.10012MR409333
  4. [Coh 2] H. Cohen and H.W. Lenstra Jr : Primality testing and Jacobi Sums, Math. of Comp.42, 1984, p. 297-330. Zbl0578.10004MR726006
  5. [Coh 3] H. Cohen and A.K. Lenstra : Implementation of a new primality test, preprint, Center for mathematics and Computer Science, Amsterdam. Zbl0608.10001MR797070
  6. [De B] N.G. De Bruijn : On the number of positive integers x and free of prime factors XMLgt y, II, Nederl. Akad. Wetensch. Proc. Ser.A, 69, 1966, p. 239-247 Zbl0139.27203
  7. N.G. De Bruijn : On the number of positive integers x and free of prime factors XMLgt y, = Indag. Math., 28, 1966, p. 239-247. Zbl0139.27203MR205945
  8. [Dix] J.D. Dixon : Factorization and primality tests, Amer. Math. Monthly91, 1984, p.333-352. Zbl0548.10003MR750520
  9. [Guy] R.K. Guy : How to factor a number, Congressus Numerantium XVI, Proc. of the fifth Manitoba Conference on numerical mathematics, 1975, p. 49-89. Zbl0338.10001MR404120
  10. [Hil] A. Hildebrand and G. Tenenbaum : On integers free of large prime factors, to appear. Zbl0601.10028MR837811
  11. [Kob] N. Koblitz : Introduction to elliptic curves and modular forms, Springer Verlag, 1984, Graduate texts in mathematics n° 97. Zbl0553.10019MR766911
  12. [Len] H.W. Lenstra Jr : Prime factorization using elliptic curves, to appear. 
  13. [Mai] H. Maier : On integers free of large prime divisors, Preprint. 
  14. [Mon] L. Monier : Algorithmes de factorisation d'entiers, Thèse de 3e cycle, Orsay, 1980. 
  15. [Nic] J.-L. Nicolas : Tests de primalité, Expositiones Mathematicae2, 1984, p. 223-234. Zbl0533.10004MR783136
  16. [Pol] J.-M. Pollard : Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc.76, 1974, p. 521-528. Zbl0294.10005MR354514
  17. [Pom 1] C. Pomerance : Analysis and comparison of some integer factoring algorithms, Computational methods in number theory, R. Tijdeman, H. Lenstra (Eds), Mathematisch Centrum, Amsterdam, Tract 154, 1982, p. 89-139 Zbl0508.10004MR700260
  18. [Pom 2] C. Pomerance : The quadratic sieve factoring algorithm, à paraitre aux compte-rendus d'EUROCRYPT84. Zbl0596.10006
  19. [Rie] H.I. Riesel : Prime numbers and computer methods for factorization, Birkhäuser, 1985, progress in Math. Vol. 57. Zbl0582.10001MR897531
  20. [Sch] C.P. Schnorr and H.W. Lenstra Jr : A Monte-Carlo Factoring Algorithm with linear storage, Math, of Comp.43, 1984, p. 289-311. Zbl0559.10004MR744939
  21. [Sha] D. Shanks : Class number, a theory of factorization and genera, Proc. Symp. Pure Math.20, A.M.S., 1971, p. 415-440. Zbl0223.12006MR316385
  22. [Sil] J. Silverman : Arithmetic of elliptic curves, à paraitre, Springer Verlag, Graduate texts in mathematics. Zbl0585.14026
  23. [Wie] D. Wiedemann : Solving sparse linear equations over finite fields, preprint. Zbl0607.65015MR831560

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.