Africacrypt Conferences
Cryptography and Algorithmic Number Theory, CAEN, July 2-4, 2024
Douala, Cameroon, July 10-12, 2024
Cyberjaya, Selangor,
Malaysia
24-26 September 2024
International Conference on Transformative Technologies: Secure Networks & Decision Empowerments (ICTT’24)
Moroccan Journal of Algebra and Geometry with Applications
The abc conjecture |
To the abc conjecture home page
Research Interests |
Number Theory :
Arithmetic Geometry :
Cryptography :
Implementation of Computer Algebra Algorithms :
Fractals :(Amateur)
Publications |
Books:
Progress in Cryptology – AFRICACRYPT 2020 Nitaj, Abderrahmane, Youssef, Amr (Eds.), Lecture Notes in Computer Science, Vol. 12174 , Online version
Progress in Cryptology – AFRICACRYPT 2019, Buchmann, Johannes, Nitaj, Abderrahmane, Rachidi, Tajjeeddine (Eds.), Lecture Notes in Computer Science, Vol. 11627, Online version
Codes, Cryptology, and Information Security C2SI 2019, Claude Carlet, Sylvain Guilley, Abderrahmane Nitaj, El Mamoun Souidi (Eds.), Lecture Notes in Computer Science, Vol. 11445, Online version
Progress in Cryptology -- AFRICACRYPT 2018 , Joux, Antoine, Nitaj, Abderrahmane, Rachidi, Tajjeddine (Eds.), Lecture Notes in Computer Science, Vol. 10831, Online version
Progress in Cryptology -- AFRICACRYPT 2017 , Joye, Marc, Nitaj, Abderrahmane (Eds.), Lecture Notes in Computer Science, Vol. 10239, Online version
Codes, Cryptology, and Information Security C2SI 2017, Said El Hajji, Abderrahmane Nitaj, El Mamoun Souidi (Eds.), Lecture Notes in Computer Science, Vol. 10194, Online version
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 C2SI 2015, 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:
Semmouni, M.C., Belkasmi, M., Nitaj, A., Azougaghe, A. (2024). A New Quantum-Resistant Electronic Voting Based on Fully Homomorphic Encryption. In: Mathew, J., Gopal, L., Juwono, F.H. (eds) Artificial Intelligence for Sustainable Energy. GENCITY 2023. Lecture Notes in Electrical Engineering, vol 1142. Springer, Singapore. https://doi.org/10.1007/978-981-99-9833-3_13 (GENCITY 2023)
Semmouni, M. C., Nitaj, A., Belkasmi, M. (2024). Cryptanalysis of RSA with smooth prime sum. Journal of Discrete Mathematical Sciences & Cryptography, Vol. 26 (2023), No. 8, pp. 2183–2203. JDMSC
Applications of Neural Network-Based AI in Cryptography (with Tajjeeddine Rachidi), Crypotography 2023, 7, 39. Cryptography 2023
Generalized Implicit Factorization Problem (with Yansong Feng and Yanbin Pan), In: Carlet, C., Mandal, K., Rijmen, V. (eds) Selected Areas in Cryptography – SAC 2023. SAC 2023. Lecture Notes in Computer Science, vol 14201. Springer, Cham. arXiv:2304.08718 arXiv 2023
Enhanced S-boxes for the Advanced Encryption Standard with maximal periodicity and better avalanche property (with Willy Susilo, Joseph Tonien), Computer Standards & Interfaces, Volume 87, January 2024, 103769 Computer Standards & Interfaces, 2023
Improved Cryptanalysis of the Multi-Power RSA Cryptosystem Variant (with Maher Boudabra), In: El Mrabet, N., De Feo, L., Duquesne, S. (eds) Progress in Cryptology - AFRICACRYPT 2023. AFRICACRYPT 2023. Lecture Notes in Computer Science, vol 14064. Springer, Cham. https://doi.org/10.1007/978-3-031-37679-5_11 Africacrypt 2023
A New RSA Variant Based on Elliptic Curves (with Maher Boudabra), Cryptography 2023, 7, 37. https://doi.org/10.3390/cryptography7030037 : Cryptography 2023
A new attack on some RSA variants (with Willy Susilo, Joseph Tonien), Theoretical Computer Science, Volume 960, 2023, 113898, ISSN 0304-3975. Theoretical Computer Science 2023
Cryptanalysis of the Multi-Power RSA Cryptosystem Variant (with D. Alquié, G. Chassé), In: Beresford, A.R., Patra, A., Bellini, E. (eds) Cryptology and Network Security. CANS 2022. Lecture Notes in Computer Science, vol 13641. Springer, Cham. https://doi.org/10.1007/978-3-031-20974-1_12 CANS 2022
A Generalized Attack on the Multi-prime Power RSA (with Willy Susilo, Joseph Tonien), In L. Batina and J. Daemen (Eds.): AFRICACRYPT 2022, LNCS 13503, pp. 537–549, 2022.
Finding Points on Elliptic Curves with Coppersmith’s Method (with Virgile Dossou-Yovo, Alain Togbé), In D. Poulakis and G. Rahonis (Eds.): CAI 2022, LNCS 13706, pp. 69–80, 2022.
Security Issues of Novel RSA Variant (with Muhammad Rezal Kamel Ariffin, Nurul Nur Hanisah Adenan, Terry Shue Chien Lau, Jiahui Chen), IEEE Access ( Volume: 10) pp. 53788 - 53796 (2022)
The Cubic Pell Digital Algorithm CP256-1299 (with Nur Azman Abu), Proceedings of the 8th International Cryptology and Information Security Conference 2022 (CRYPTOLOGY 2022)
Cryptanalysis of RSA with smooth prime sum (with Meryem Cherkaoui Semmouni, Mostafa Belkasmi), Journal of Discrete Mathematical Sciences and Cryptography, 18 Aug 2022
A New Quantum Resistant Electronic Voting Scheme Based On Fully Homomorphic Encryption (with Meryem Cherkaoui Semmouni, Mostafa Belkasmi, Ali Azougaghe), Advances in Dynamical Systems and Applications, Volume 16, Number 2, (2021) pp. 1637-1652.
Classical Attacks on a Variant of the RSA Cryptosystem (with Muhammad Rezal Bin Kamel Ariffin, Nurul Nur Hanisah Adenan, Nur Azman Abu), LatinCrypt 2021
Exponential Increment of RSA Attack Range via Lattice Based Cryptanalysis (with Muhammad Rezal Kamel Ariffin, Nurul Nur Hanisah Adenan, Domenica Stefania Merenda, and Ali Ahmadian), Multimedia Tools and Applications
Increment of insecure RSA private exponent bound through perfect square RSA diophantine parameters cryptanalysis (with Wan Nur Aqlili Ruzai, Muhammad Rezal Kamel Ariffna, Zahari Mahada, Muhammad Asyraf Asbullaha), to appear in Computer Standards & Interfaces
Cryptanalysis of RSA Variants with Primes Sharing Most Significant Bits (with Meryem Cherkaoui-Semmouni, Willy Susilo, Joseph Tonien), In: Liu, J.K., Katsikas, S., Meng, W., Susilo, W., Intan, R. (eds) Information Security. ISC 2021. Lecture Notes in Computer Science(), vol 13118. Springer, Cham.
A Unified Method for Private Exponent Attacks on RSA Using Lattices (with Hatem M. Bahig, Dieaa I. Nassr, Ashraf Bhery), International Journal of Foundations of Computer Science, Vol. 31, No. 02, pp. 207-231 (2020)
A New Improved AES S-box With Enhanced Properties (with Willy Susilo, Joseph Tonien), In: Liu, J., Cui, H. (eds) Information Security and Privacy. ACISP 2020. Lecture Notes in Computer Science(), vol 12248. Springer, Cham. https://link.springer.com/chapter/10.1007/978-3-030-55304-3_7
Bitcoin Security With Post Quantum Cryptography (with Meryem Cherkaoui Semmouni, Mostafa Belkasmi), Networked Systems, In: Atig M., Schwarzmann A. (eds) Networked Systems. Lecture Notes in Computer Science, vol 11704. Springer, Cham (2019)
A new public key cryptosystem based on Edwards curves (with Maher Boudabra), Journal of Applied Mathematics and Computing, October 2019, Volume 61, Issue 1–2, pp 431–450, 2019
A new attack on RSA and Demytko’s elliptic curve cryptosystem (with Emmanuel Fouotsa), Journal of Discrete Mathematical Sciences and Cryptography, 2019 [PDF]
Cryptanalysis of the Randomized Version of a Lattice-Based Signature Scheme from PKC'08 (with Haoyu Li, Renzhang Liu and Yanbin Pan), In: Susilo W., Yang G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science, vol 10946. Springer, Cham. [PDF]
A Generalized Attack on Some Variants of the RSA Cryptosystem (with Yanbin Pan and Joseph Tonien), In: Cid C., Jacobson Jr. M. (eds) Selected Areas in Cryptography – SAC 2018. SAC 2018. Lecture Notes in Computer Science, vol 11349. Springer, Cham.
Cryptanalysis of RSA-type cryptosystems based on Lucas sequences, Gaussian integers and elliptic curves (with Martin Bunder, Willy Susilo and Joseph Tonien), Journal of Information Security and Applications, Volume 40, June 2018, Pages 193-198. [PDF]
A generalized attack on RSA type cryptosystems (with Martin Bunder, Willy Susilo and Joseph Tonien), Theoretical Computer Science, Volume 704, 15 December 2017, Pages 74-81. [PDF]
A new generalization of the KMOV cryptosystem (with Maher Boudabra), Journal of Applied Mathematics and Computing, June 2018, Volume 57, Issue 1–2, pp 229–245. [PDF]
Dirichlet product for boolean functions (with Willy Susilo and Joseph Tonien), Journal of Applied Mathematics and Computing, no. 1-2, 293–312, 2016 [PDF]
A new attack on three variants of the RSA cryptosystem (with Martin Bunder, Willy Susilo and Joseph Tonien), ACISP, the 21st Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 9723, 2016, 258-268 [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, Bulletin of the Korean Mathematical Society 51 (5), 1347–1356 (2014) [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]
Some polynomial identities related to the $abc$- conjecture (With G. Greaves), 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]
[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]
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]
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]
Math Links |
Cultures |
Contact |
e-mail address: abderrahmane.nitaj(at)unicaen.fr
Address:
Département de MathématiquesConferences |
Oujda, Morocco, November 2-4, 2023
Sousse, Tunisia, July 19-21, 2023
8th International Cryptology and Information Security Conference 2022 (CRYPTOLOGY2022)
Port Dickson, N. Sembilan, Malaysia, July 26-28, 2022
CIMPA Research School
Cryptography, theoretical and computational aspects of number theory
African Institute of Mathematical Sciences AIMS (M'bour) Senegal
August 15-26, 2022
CIMPA Research School, AIMS Senegal
9th International Conference on Algebraic Informatics
Aristotle University of Thessaloniki, Greece
October 27 – October 29, 2022
Selected Areas in Cryptography (SAC 2022)
University of Windsor, Ontario, Canada
August 24 to 26, 2022
IEEE International Mediterranean Conference on Communications and Networking
Athens, Greece
5–8 September 2022
The 5th International Conference on Advanced Communication Technologies and Networking
Marrakesh, Morocco
December 12-14, 2022
International Conference on Cryptology, Codes and Cyber Security 2022
Casablanca, Morocco, October 29-28, 2022
Écoles Mathématiques Africaines | CIMPA school
Introduction to Number Theory, Cryptography and related courses
African Institute of Mathematical Sciences AIMS (M'bour) Senegal
September 6-19, 2021
Selected Areas in Cryptography SAC 2021, September 29 - October 01, 2021
International Conference on Recent Advances in Applied Mathematics 2020 (ICRAAM2020), January 4-6, 2020, Kuala Lumpur, Malaysia
3rd International Conference on Mathematics and Its Applications (ICMACASA2020), February 28-29, 2020, Casablanca, Morocco
INTERNATIONAL CONFERENCE IN CYBERSECURITY AND RECENT TRENDS IN MATHEMATICAL MODELING (SMM'2020), April 20-21, 2020, Tangier, Morocco
Scientific Event on Information Technology (SEIT'19), April 24-25, 2019 - INPT, Rabat - Morocco
3rd International Congress Algebra, Number Theory and Applications, April 24-27, 2019, Oujda, Morocco
The 13th International Conference on Provable and Practical Security (PROVSEC 2019), Cairns, Australia, 1 - 4 October 2019
The 2nd International Conference on Advanced Communication Systems and Information Security (ACOSIS 2019), Marrakesh, Morocco, 20 - 22 November 2019
Algebra, Codes and Cryptology (A2C 2019), Dakar, Senegal, December 5- 7, 2019
International Conference on Intelligent Systems and Advanced Computing Sciences, Taza, Morocco, December 26-27, 2019
Rabat, Morocco, July 9-11, 2019
3rd International Conference C2SI-2019 on Codes, Cryptology and Information Security In honor of Pr. Said El Hajji April 22 - 24, 2019, Rabat - Morocco
ACROCRYPT 2018 (Arithmétique, Codes et Cryptographie), November 19-20, 2018, Caen, France
2nd International Conference on Applied Mathematics, Fez, October 26-27, 2018
Cryptography and Algorithmic Number Theory, CAEN, June 20th-22nd, 2018
May 24-26, 2017, Dakar, Senegal
Codes, Cryptology and Information Security, C2SI-Carlet 2017
April 10-12, 2017, Rabat, Morocco
October 17-19, 2016, Marrakesh, Morocco
November 11-12, 2016, Taza, Morocco
The International Conference on Algebra and its Applications (ICAA 2017)
April 26-28, 2017, Errachidia, Morocco
CRYPTOLOGY 2016, The 5th International Cryptology and Information Security Conference 2016
31st MAY - 2nd JUNE 2016, Sabah, Malaysia
April 13-15, 2016, Fes, Morocco
Théorie Algorithmique des Nombres et Cryptographie
Ecole de Recherche Cimpa, Nouakchott, Mauritanie, 15-26 Février 2016
Codes, Cryptology and Information Security, C2SI-Berger2015 2015
May 26-28, 2015, Rabat, Morocco
AFRICACRYPT 2014
May 28-30, 2014
Marrakech, Morocco
Web page at ENSIAS, Web page at ENS
Cryptology 2014
June 24-26, 2014
Putrajaya, Malaysia
Recent
Attacks on the RSA Cryptosystem
[PDF]
Conference
talk at Cryptology
2014
Lattice
Based Cryptography [PDF]
Workshop talk at Workshop
on advances of Cryptology 2014
Applications
of Lattice Reduction in Cryptography
[PDF]
Workshop talk at Workshop
on advances of Cryptology 2014
4th Workshop on Codes, Cryptography and Communication Systems - WCCCS 2013
November 07-08, 2013
Meknes, Morocco
June 22-24, 2013
Cairo, Egypt
National Security Days - JNS3 2013
April 26-27, 2013
Rabat, Morocco
July 10-12, 2012
Ifrane, Morocco
Workshop on Advancements in Cryptanalytic Techniques 2012
30 May-1 June 2012
Universiti Putra Malaysia
JNS2 2012
April 21-22, 2012
Marrakech, Morocco
NTCCCS 2012
April 26-28, 2012
Oujda, Morocco
June 19-17, 2011
Rabat, Morocco
July 4-8, 2011
Dakar, Senegal
May 03-06, 2010
Stellenbosch, South Africa
June 21-25, 2009
Gammarth, Tunisia
June 11-14, 2008
Casablanca, Morocco
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
ENSIAS-AMC 2008 Cryptography days
October 28-November 2, 2008
RABAT, MOROCCO