Abderrahmane Nitaj

Ph.D., HDR

Africacrypt Conferences

Web page

NORMANDIE 2024

Cryptography and Algorithmic Number Theory, CAEN, July 2-4, 2024

AFRICACRYPT 2024

Presentation

Douala, Cameroon, July 10-12, 2024

CRYPTOLOGY 2024

Cyberjaya, Selangor, Malaysia
24-26 September 2024

International Conference on Transformative Technologies: Secure Networks & Decision Empowerments (ICTT’24)

ICTT'24

Moroccan Journal of Algebra and Geometry with Applications

MJAGA

The abc conjecture

Research Interests

Publications

Informal Notes

Talk slides

Math Links

Cultures

Conferences

Contact

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, Cryptanalysis, The discrete logarithm problem, Elliptic curves.
Implementation of Computer Algebra Algorithms :

PARI, MAGMA, MAPLE, PYTHON
Fractals :(Amateur)

Fractal pictures, Animations.

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:

Small Public Exponent Brings More: Improved Partial Key Exposure Attacks against RSA (with Yansong Feng and Yanbin Pan,), IACR Communications in Cryptology, vol. 1, no. 3, Oct 07, 2024, doi: 10.62056/ahjbhey6b.
Partial Exposure Attacks on a New RSA Variant (with Rahmani, Mohammed and Mhammed Ziane). Cryptography 2024, 8, 44. https://doi.org/10.3390/cryptography8040044Securing Data Exchange with Elliptic Curve Cryptography:
A Novel Hash-Based Method for Message Mapping and Integrity Assurance (withLahraoui Younes, Saiida Lazaar, Amal Youssef ). Cryptography 8(2): 23 (2024)
Cryptanalysis of a cubic Pell variant of RSA with primes sharing least significant bits (with Nurul Nur Hanisah Adenan, Muhammad Rezal Kamel Ariffin, Nur Azman Abu), Journal of Information & Optimization Sciences, Vol. 45 (2024), No. 5, pp. 1263–1280 (2024)
Partial Prime Factor Exposure Attacks on Some RSA Variants (with Yansong Feng and Yanbin Pan), Theoretical Computer Sciences, 999: 114549 (2024)
Solving Modular Cubic Equations with Coppersmith's Method (with Virgile Dossou-Yovo and Alain Togbé), Information and Computation Elsevier, 298: 105169 (2024)
A New Quantum-Resistant Electronic Voting Based on Fully Homomorphic Encryption (with Semmouni, M.C., Belkasmi, Azougaghe, A.). 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 )

Cryptanalysis of RSA with smooth prime sum (with Semmouni, M. C., Belkasmi, M.). 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]
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]

Math Links

Cultures

The Poet Omar Khayyam

The Arabian Nights

African Art

Samarkand

Contact

e-mail address: abderrahmane.nitaj(at)unicaen.fr

Address:

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

Conferences

ICANTA-OUJDA 2023

Oujda, Morocco, November 2-4, 2023

AFRICACRYPT 2023

[Call for papers]

Sousse, Tunisia, July 19-21, 2023

CRYPTOLOGY2022

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

CAI 2022

Selected Areas in Cryptography (SAC 2022)

University of Windsor, Ontario, Canada

August 24 to 26, 2022

SAC 2022

IEEE International Mediterranean Conference on Communications and Networking

Athens, Greece

5–8 September 2022

MeditCom 2022

The 5th International Conference on Advanced Communication Technologies and Networking

Marrakesh, Morocco

December 12-14, 2022

CommNet 2022

I4CS22

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

EMA Senegal

Selected Areas in Cryptography SAC 2021, September 29 - October 01, 2021

SAC 2021

AFRICACRYPT 2020

International Conference on Recent Advances in Applied Mathematics 2020 (ICRAAM2020), January 4-6, 2020, Kuala Lumpur, Malaysia

ICRAAM2020

3rd International Conference on Mathematics and Its Applications (ICMACASA2020), February 28-29, 2020, Casablanca, Morocco

ICMACASA2020

INTERNATIONAL CONFERENCE IN CYBERSECURITY AND RECENT TRENDS IN MATHEMATICAL MODELING (SMM'2020), April 20-21, 2020, Tangier, Morocco

SMM'2020

Scientific Event on Information Technology (SEIT'19), April 24-25, 2019 - INPT, Rabat - Morocco

SEIT'19

3rd International Congress Algebra, Number Theory and Applications, April 24-27, 2019, Oujda, Morocco

ICANTA 2019

The 13th International Conference on Provable and Practical Security (PROVSEC 2019), Cairns, Australia, 1 - 4 October 2019

PROVSEC 2019

The 2nd International Conference on Advanced Communication Systems and Information Security (ACOSIS 2019), Marrakesh, Morocco, 20 - 22 November 2019

ACOSIS 2019

Algebra, Codes and Cryptology (A2C 2019), Dakar, Senegal, December 5- 7, 2019

A2C 2019

International Conference on Intelligent Systems and Advanced Computing Sciences, Taza, Morocco, December 26-27, 2019

ISACS'19

AFRICACRYPT 2019

[Presentation]

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

C2SI 2019

ACROCRYPT 2018 (Arithmétique, Codes et Cryptographie), November 19-20, 2018, Caen, France

ACROCRYPT 2018

2nd International Conference on Applied Mathematics, Fez, October 26-27, 2018

Cryptography and Algorithmic Number Theory, CAEN, June 20th-22nd, 2018

AFRICACRYPT 2017

May 24-26, 2017, Dakar, Senegal