Abderrahmane Nitaj

Africacrypt Conferences

The abc conjecture

To the abc conjecture home page

Research Interests

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.

Thesis

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

Publications

Books:

Progress in Cryptology -- AFRICACRYPT 2016 , Pointcheval, David, Nitaj, Abderrahmane, Rachidi, Tajjeeddine (Eds.), Lecture Notes in Computer Science, Vol. 9646, Online version
Codes, Cryptology, and Information Security, Said El Hajji, Abderrahmane Nitaj, Claude Carlet, El Mamoun Souidi (Eds.), Lecture Notes in Computer Science, Vol. 9084, Online version
Progress in Cryptology -- AFRICACRYPT 2013 , Youssef, Amr; Nitaj, Abderrahmane; Hassanien, Aboul Ella (Eds.), Lecture Notes in Computer Science, Vol. 7918, Online version
Progress in Cryptology -- AFRICACRYPT 2011 , Abderrahmane Nitaj, David Pointcheval (Eds.), Lecture Notes in Computer Science, Vol. 6737, Online version

Book Chapters:

The Mathematics of the NTRU Cryptosystem . In Addepalli VN Krishna (Eds.), Emerging Security Solutions Using Public and Private Key Cryptography: Mathematical Concepts, IGI Global, June, 2015. [PDF]
The Mathematical Cryptography of the RSA Cryptosystem . In Cryptography: Protocols, Design and Applications, Kamol Lek and Naruemol Rajapakse (Eds.) [PDF]
Diophantine and Lattice Cryptanalysis of the RSA Cryptosystem . Artificial Intelligence, Evolutionary Computation and Metaheuristics (AIECM) --In the footsteps of Alan Turing, p. 139-168 (2012). [PDF]

Papers:

Dirichlet product for boolean functions (with Willy Susilo and Joseph Tonien), Journal of Applied Mathematics and Computing, 2016 [PDF]
New attacks on RSA with moduli $n=p^rq$ (with Tajjeeddine Rachidi), in S. El Hajji, A. Nitaj, C. Carlet, E.M. Souidi (Eds.), Codes, Cryptology, and Information Security, LNCS 9084, Springer, pp. 352-360, 2015. [PDF]
Factoring RSA modulus with weak primes (with Tajjeeddine Rachidi), in S. El Hajji, A. Nitaj, C. Carlet, E.M. Souidi (Eds.), Codes, Cryptology, and Information Security, LNCS 9084, Springer, pp. 361-374, 2015. [PDF]
Implicit factorization of unbalanced RSA moduli (with M.R.K. Ariffin), Journal of Applied Mathematics and Computing, , June 2015, Volume 48, Issue 1-2, pp. 349-363, Springer Berlin Heidelberg, [PDF]
New attacks on the RSA cryptosystem (with M.R.K. Ariffin, D.I. Nassr, H.M. Bahig), in D. Pointcheval and D. Vergnaud (Eds.): AFRICACRYPT 2014, LNCS 8469, pp. 178–198, 2014. Springer 2014 [PDF]
A new attack on the KMOV cryptosystem, To appear in Bulletin of the Korean Mathematical Society [PDF]
A new attack on RSA with a composed decryption exponent (with M.O. Douh), International Journal on Cryptography and Information Security (IJCIS), Vol.3, No. 4, December 2013. [PDF]
An Attack on RSA Using LSBs of Multiples of the Prime Factors, in A. Youssef, A. Nitaj, A.E. Hassanien (Eds.): AFRICACRYPT 2013, LNCS 7918, pp. 297–310, 2013. Springer-Verlag Berlin Heidelberg 2013 [PDF]
A New Attack on RSA with Two or Three Decryption Exponents, Journal of Applied Mathematics and Computing (JAMC), November 2012, [PDF]
Cryptanalysis of NTRU with two public keys, International Journal of Network Security, 16(2): 112-117 (2014), [PDF]
A new attack on RSA and CRT-RSA, in A. Mitrokotsa and S. Vaudenay (Eds.): AFRICACRYPT 2012 LNCS 7374, pp. 221–233, 2012. Springer-Verlag Berlin Heidelberg 2012. [PDF]
New vulnerabilities in RSA , Discrete Mathematics, Algorithms and Applications (DMAA) [PDF]
A New Vulnerable Class of Exponents in RSA , JP Journal of Algebra, Number Theory and Applications. Volume 21, Number 2, 2011, Pages 203-220. [PDF]
New weak RSA keys , JP Journal of Algebra, Number Theory and Applications. Volume 23, Number 2, 2011, Pages 131-148. [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 or [PDF]
Application of ECM to a class of RSA keys, Journal of Discrete Mathematical Sciences & Cryptography , 12, No. 2, 121-137 (2009). [PS] or [PDF]
Cryptanalysis of RSA with constrained keys. International Journal of Number Theory (IJNT), V. 5, p. 311-325 (2009) [PS] or [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 and [PDF]
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.

Informal Notes

La cryptographie et la confiance numérique [PDF]
Quantum and post quantum cryptography [PDF]
La cryptographie du futur [PDF]
Applications de l'algorithme LLL en cryptographie [PDF]
Cryptanalyse de RSA [PDF]
Cryptanalyse de RSA [Maple 12 Worksheet]
NTRU et ses variantes, sécurité et applications , Survey, [PDF]
RSA and a higher degree diophantine equation, [PS] [PDF]
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]

Talk slides

Cryptanalysis of NTRU with two public keys
Talk at Wotic'11, Casablanca (Morocco) and University of Caen (France). [PDF]
La cryptographie du futur
Talk at ENSIAS, Rabat (Morocco). [PDF]
RSA versus NTRU
Talk at Universite Hassan II, Casablanca (Morocco). [PDF]
Cryptanalyse de RSA
Talk at Ecole CIMPA de Cryptography Oujda (Morocco). [PDF]
Introduction aux courbes elliptiques
Talk at Journées Cryptographie Rabat(Morocco). [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]