July 4-8, 2011
Dakar, Senegal
Presentation
To the abc conjecture
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- Number Theory :
- Diophantine Equations, the abc conjecture, Polynomials.
- Arithmetic Geometry :
-
Elliptic curves, Szpiro's conjecture.
- Cryptography :
-
Cryptosystems, The discrete logarithm problem, Elliptic curves.
- Implementation of Computer Algebra Algorithms
:
- SIMATH,
APECS,
PARI,
MAGMA,
MAPLE,
UBASIC,
LIDIA
- Fractals :
(Amateur)
- Fractal pictures, Animations.
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Conséquences et aspects expérimentaux des conjectures
abc et de Szpiro.
[DVI] [Postscript]
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- New vulnerabilities in RSA
, Submitted to J Appl Math Comput.
[PDF]
- A New Vulnerable Class of Exponents in RSA
, Submitted to JP Journal of Algebra, Number Theory and Applications.
[PDF]
- New weak RSA keys
, Submitted to JP Journal of Algebra, Number Theory and Applications.
[PDF]
- NTRU et ses variantes, sécurité et applications
, Submitted to Gazette des Mathématiciens.
[PDF]
- 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
- Application of ECM to a class of RSA keys,
Journal
of Discrete Mathematical Sciences & Cryptography , 12, No. 2, 121-137 (2009).
[PS] [PDF]
- Cryptanalysis of RSA with constrained keys.
International Journal of Number Theory (IJNT), V. 5, p. 311-325 (2009)
[PS] [PDF]
- 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
- Isogènes des courbes elliptiques définies sur les
rationnels,
J. Computational Math. 4 (2002), 337-448.
[DVI] [Postscript]
- Invariants des courbes de Frey-Hellegouarch et grands groupes de
Tate-Shavarevich,
Acta Arithmetica 93 (2000), no. 4, pp. 303-327.
[DVI] [Postscript]
- (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]
- Détermination de courbes elliptiques pour la conjecture de
Szpiro,
Acta Arithmetica 85 (1998), pp. 351-376.
[DVI] [Postscript]
- Aspects expérimentaux de la conjecture $abc$,
Séminaire de Théorie des Nombres de Paris, London Math. Soc.
235 (1996), pp. 145-156.
[DVI] [Postscript]
- La conjecture $abc$,
L'Enseignement Mathématique 42 (1996), pp. 3-24.
[DVI] [Postscript]
- L'algorithme de Cornacchia,
Expositiones Math. 13 (1995), pp. 358-365.
[DVI] [Postscript]
- On a conjecture of Erdos on 3-powerful numbers,
Bulletin of the London Mathematical Society 27 (1995), pp. 317-318.
[DVI] [Postscript]
- Algorithms for finding good examples for the $abc$ and the
Szpiro conjectures,
Experimental Mathematics 3 (1993), pp. 223-230.
[Postscript]
- 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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- Cryptanalyse de RSA
[Course, PDF]
- Cryptanalyse de RSA
[Maple 12 Worksheet]
- Cryptanalyse de RSA
Talk at Ecole CIMPA de Cryptography Oujda (Morocco).
[PDF]
- Introduction aux courbes elliptiques
Talk at Journées Cryptographie Rabat(Morocco).
[PDF]
- RSA and a higher degree diophantine equation,
[PS] [PDF]
- Clés faibles pour le cryptosystème RSA
Talk at Symposium Cryptographie Et Sécurité de l’Information Oujda (Morocco).
[PDF]
- Le cryptosystème NTRU, réalités et perspectives
Talk at Symposium Cryptographie Et Sécurité de l’Information Oujda (Morocco).
[PDF]
- RSA et les équations diophantiennes
Seminar talk at Cryptography
Groupe, Caen.
[PDF] , [PS]
- Cryptanalysis of RSA with constrained keys
Seminar talk at MyCrypt
2005,.
[PDF] , [PS]
- Cryptanalyse de certains RSA par les fractions continues et l'algorithme
LLL.
Seminar talk at Cryptography
Groupe, Caen.
[PDF] , [PS]
- Petites hauteurs des polynômes par l'algorithme LLL
Seminar talk at Cryptography
Groupe, Caen.
[PDF] , [PS]
- A Maple Worksheet for elliptic curves
This Maple Worksheet gives an explicit model for all elliptic curves defined
over Q with a non trivial torsion rational point and for all their
isogenous curves associated to isogenies with cyclic kernels consisting of
rational points.
- Le problème du logarithme discret elliptique :
Index et Xedni
[DVI] , [PS]
- Le cryptosystème NTRU.
[DVI] , [PS]
- Table of all good abc examples
[PDF] , [DVI] , [PS]
- Table of all good abc-Szpiro examples
[PDF] , [DVI] , [PS]
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North African Cultures
and Adventures
The Poet Omar
Khayyam
The Arabian
Nights
African Art
Samarkand
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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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AFRICACRYPT 2011
July 2011
Dakar, Senegal
AFRICACRYPT 2010
May 03-06, 2010
Stellenbosch, 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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