Abderrahmane Nitaj

The abc conjecture

To the abc conjecture home page

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Research Interests

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Thesis

Conséquences et aspects expérimentaux des conjectures abc et de Szpiro (1994).
[DVI] [Postscript]

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Publications

  1. Cryptanalysis of RSA using the ratio of the primes, AFRICACRYPT2009, In Bart Preneel (Ed.): Progress in Cryptology - AFRICACRYPT 2009, Lecture Notes in Computer Science 5580 Springer 2009. Slides
  2. Another generalization of Wiener's attack on RSA, AFRICACRYPT2008, In Serge Vaudenay (Ed.): Progress in Cryptology - AFRICACRYPT 2008, Lecture Notes in Computer Science 5023 Springer 2008. Slides
  3. Application of ECM to a class of RSA keys, Journal of Discrete Mathematical Sciences & Cryptography , To appear
    [PS] [PDF]
  4. RSA and a higher degree diophantine equation, Submitted to Journal of Computational Mathematics.
    [PS] [PDF]
  5. Cryptanalysis of RSA with constrained keys. International Journal of Number Theory (IJNT), V. 5, p. 311-325 (2009)
    [PS] [PDF]
  6. Isogènes des courbes elliptiques définies sur les rationnels, J. Computational Math. 4 (2002), 337-448.
    [DVI] [Postscript]
  7. Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shavarevich, Acta Arithmetica 93 (2000), no. 4, pp. 303-327.
    [DVI] [Postscript]
  8. (With G. Greaves) Some polynomial identities related to the $abc$- conjecture, Gyoery, Kalman (ed.) et al., Number theory in progress. Proceedings of the international conference organized by the Stefan Banach International Mathematical Center in honor of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, June 30--July 9, 1997. Volume 1: Diophantine problems and polynomials. Berlin: de Gruyter (1999), 229-236.
    [DVI] [Postscript]
  9. Détermination de courbes elliptiques pour la conjecture de Szpiro, Acta Arithmetica 85 (1998), pp. 351-376.
    [DVI] [Postscript]
  10. Aspects expérimentaux de la conjecture $abc$, Séminaire de Théorie des Nombres de Paris, London Math. Soc. 235 (1996), pp. 145-156.
    [DVI] [Postscript]
  11. La conjecture $abc$, L'Enseignement Mathématique 42 (1996), pp. 3-24.
    [DVI] [Postscript]
  12. L'algorithme de Cornacchia, Expositiones Math. 13 (1995), pp. 358-365.
    [DVI] [Postscript]
  13. On a conjecture of Erdös on 3-powerful numbers, Bulletin of the London Mathematical Society 27 (1995), pp. 317-318.
    [DVI] [Postscript]
  14. Algorithms for finding good examples for the $abc$ and the Szpiro conjectures, Experimental Mathematics 3 (1993), pp. 223-230.
    [Postscript]
  15. An algorithm for finding good $abc$-examples, Comptes Rendus de l'Académie des Sciences de Paris, 317 (1993), pp. 811-815.
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Informal Notes

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Math Links

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Cultures
  North African Cultures and Adventures

  The Poet Omar Khayyam

  The Arabian Nights

  African Art

  Samarkand

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Contact

e-mail address:
nitaj@math.unicaen.fr

Address:

Département de Mathématiques
Université de Caen
Campus II
Boulevard Maréchal Juin
BP 5186 - 14032 Caen Cedex
France

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Conferences

AFRICACRYPT 2010

May 03-06, 2010

Cape Town, South Africa

AFRICACRYPT 2009

June 21-25, 2009

Gammarth, TUNISIA

AFRICACRYPT 2008

June 11-14, 2008

Casablanca, MOROCCO

SLIDES

Africacrypt 2008 web page

Presentation

Ecole CIMPA de Cryptographie - Oujda

Ecole CIMPA de Cryptographie - Oujda

18 - 30 mai 2009

OUJDA, MAROC

Cours: Cryptanalyse de RSA (pdf)

TP: Cryptanalyse de RSA avec maple 12

Slides du cours

ENSIAS-AMC 2008 Cryptography days

October 28-November 2, 2008

RABAT, MOROCCO

Programme

Programme (pdf)

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