Jean-Claude Bajard, Jérémy Marrez, Thomas Plantard, Pascal Véron. On Polynomial Modular Number Systems over $ \mathbb{Z}/{p}\mathbb{Z} $. Advances in Mathematics of Communications, AIMS, In press, ⟨10.3934/amc.2022018⟩. ⟨hal-03611829⟩

Jean-Claude Bajard, Sylvain Duquesne. Montgomery-friendly primes and applications to cryptography. Journal of Cryptographic Engineering, Springer, 2021, 11 (4), p. 399-415. ⟨10.1007/s13389-021-00260-z⟩. ⟨hal-02883333⟩

Jérôme Courtois, Lokman A. Abbas-Turki, Jean-Claude Bajard. Resilience of randomized RNS arithmetic with respect to side-channel leaks of cryptographic computation. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2019, 68 (12), pp.1720-1730. ⟨10.1109/TC.2019.2924630⟩. ⟨hal-02174744⟩

Jean-Claude Bajard, Paulo Martins, Leonel Sousa, Vincent Zucca. Improving the Efficiency of SVM Classification with FHE. IEEE Transactions on Information Forensics and Security, Institute of Electrical and Electronics Engineers, 2019, 15, pp.1709-1722. ⟨10.1109/TIFS.2019.2946097⟩. ⟨hal-02309744⟩

Jean-Claude Bajard, Julien Eynard, Nabil Merkiche. Montgomery reduction within the context of residue number system arithmetic. Journal of Cryptographic Engineering, Springer, 2018, 8 (3), pp.189-200. ⟨10.1007/s13389-017-0154-9⟩. ⟨hal-01494547⟩

Paulo Martins, Julien Eynard, Jean-Claude Bajard, Leonel Sousa. Arithmetical Improvement of the Round-Off for Cryptosystems in High-Dimensional Lattices. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2017, PP (Issue: 99), ⟨10.1109/TC.2017.2690420⟩. ⟨hal-01527945⟩

Jean-Claude Bajard, Sylvain Duquesne, Milos Ercegovac. Combining leak–resistant arithmetic for elliptic curves defined over Fp and RNS representation. Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, Publications mathématiques de Besançon, 2013, pp.67-87. ⟨hal-01098795⟩

Filippo Gandino, Fabrizio Lamberti, Gianluca Paravati, Jean-Claude Bajard, Paolo Montuschi. An Algorithmic and Architectural Study on Montgomery Exponentiation in RNS. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2012, 61 (8), pp.1071-1083. ⟨10.1109/tc.2012.84⟩. ⟨hal-01098799⟩

Samuel Antão, Jean-Claude Bajard, Leonel Sousa. RNS-Based Elliptic Curve Point Multiplication for Massive Parallel Architectures. The Computer Journal, Oxford University Press (UK), 2012, 55 (5), pp.629-647. ⟨10.1093/comjnl/bxr119⟩. ⟨hal-01098800⟩

Jean-Claude Bajard, Laurent Imbert, Christophe Negre. Arithmetic Operations in Finite Fields of Medium Prime Characteristic using the Lagrange Representation. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2006, 55 (9), pp.1167-1177. ⟨lirmm-00102865⟩

Jean-Claude Bajard, Laurent Imbert. A Full RNS Implementation of RSA. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2004, 53 (6), pp.769-774. ⟨lirmm-00108553⟩

A. Skaf, Jean-Claude Bajard, A. Guyot, Jean-Michel Muller. A VLSI circuit for on-line polynomial computing: application to exponential, trigonometric and hyperbolic functions. IFIP-Transactions-A-Computer-Science-and-Technology, 1994, A-42, pp.93-100. ⟨hal-00014954⟩

Jean-Michel Muller, Jean-Claude Bajard, Sylvanus Kla. BKM: a new hardware algorithm for complex elementary functions. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 1994, 43 (8), pp.955-963. ⟨10.1109/12.295857⟩. ⟨ensl-00086894⟩

Jean-Claude Bajard, Kazuhide Fukushima, Shinsaku Kiyomoto, Thomas Plantard, Arnaud Sipasseuth, et al.. Generating Residue Number System Bases. ARITH 2021- IEEE 28th Symposium on Computer Arithmetic, Jun 2021, Virtual, France. pp.86-93, ⟨10.1109/ARITH51176.2021.00027⟩. ⟨hal-03457951⟩

Jean-Claude Bajard, Julien Eynard, Paulo Martins, Leonel Sousa, Vincent Zucca. An asymptotically faster version of FV supported on HPR. ARITH-2020 - 27th IEEE International Symposium on Computer Arithmetic, Jun 2020, Portland, United States. ⟨hal-02883325⟩

Paulo Martins, Jérémy Marrez, Jean-Claude Bajard, Leonel Sousa. HyPoRes: An Hybrid Representation System for ECC. 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH), Jun 2019, Kyoto, Japan. pp.207-214, ⟨10.1109/ARITH.2019.00049⟩. ⟨hal-02337787⟩

Jean-Claude Bajard, Julien Eynard, Nabil Merkiche. Multi-fault Attack Detection for RNS Cryptographic Architecture. IEEE 23rd Symposium on Computer Arithmetic (ARITH 23), Jul 2016, Santa Clara, CA, United States. ⟨10.1109/ARITH.2016.16⟩. ⟨hal-01346597⟩

Jean-Claude Bajard, Julien Eynard, Anwar Hasan, Vincent Zucca. A Full RNS Variant of FV like Somewhat Homomorphic Encryption Schemes. Selected Areas in Cryptography - SAC, Aug 2016, St. John's, Newfoundland and Labrador, Canada. ⟨10.1007/978-3-319-69453-5_23⟩. ⟨hal-01371941⟩

Jean-Claude Bajard, Julien Eynard, Nabil Merkiche, Thomas Plantard. RNS Arithmetic Approach in Lattice-based Cryptography Accelerating the " Rounding-off " Core Procedure. 2015 IEEE 22nd Symposium on Computer Arithmetic, Jun 2015, Lyon, France. pp.113-120, ⟨10.1109/ARITH.2015.30⟩. ⟨hal-01170577⟩

Paulo Martins, Leonel Sousa, Julien Eynard, Jean-Claude Bajard. Programmable RNS lattice-based parallel cryptographic decryption. IEEE ASAP 2015 Conference, Jul 2015, Totonto, Canada. ⟨10.1109/ASAP.2015.7245723⟩. ⟨hal-01202056⟩

Jean-Claude Bajard, Julien Eynard, Nabil Merkiche, Thomas Plantard. Babaï Round-Off CVP method in RNS Application to Lattice based cryptographic protocols. International Symposium on Integrated Circuits, ISIC 2014, Dec 2014, Singapore, Singapore. pp.440-443, ⟨10.1109/ISICIR.2014.7029534⟩. ⟨hal-01098802⟩

Jean-Claude Bajard, Nabil Merkiche. Double Level Montgomery Cox-Rower Architecture, New Bounds. CARDIS 2014, 13th Smart Card Research and Advanced Application Conference, Nov 2014, Paris, France. pp.139-153, ⟨10.1007/978-3-319-16763-3_9⟩. ⟨hal-01098803⟩

Jean-Claude Bajard, Julien Eynard, Filippo Gandino. Fault Detection in RNS Montgomery Modular Multiplication. 21st IEEE Symposium on Computer Arithmetic, Apr 2013, Austin, United States. pp.119 - 126, ⟨10.1109/ARITH.2013.31⟩. ⟨hal-01065507⟩

Filippo Gandino, Fabrizio Lamberti, Paolo Montuschi, Jean-Claude Bajard. A general approach for improving RNS Montgomery exponentiation using pre-processing. ARITH 2011 - 20th IEEE Symposium on Computer Arithmetic, Jul 2011, Tübingen, Germany. pp.195-204, ⟨10.1109/ARITH.2011.35⟩. ⟨hal-01098806⟩

Jean-Claude Bajard, Laurent-Stéphane Didier, Thibault Hilaire. Rho-Direct Form transposed and Residue Number Systems for Filter implementations. IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS), Aug 2011, Seoul, South Korea. pp.1-4, ⟨10.1109/MWSCAS.2011.6026263⟩. ⟨hal-01098805⟩

Augustin Sarr, Philippe Elbaz-Vincent, Jean-Claude Bajard. A New Security Model for Authenticated Key Agreement. Seventh Conference on Security and Cryptography for Networks (SNC), Sep 2010, Amalfi, Italy. pp.219 - 234, ⟨10.1007/978-3-642-15317-4_15⟩. ⟨hal-01099279⟩

Augustin Sarr, Philippe Elbaz-Vincent, Jean-Claude Bajard. A Secure and Efficient Authenticated Diffie–Hellman Protocol. EUROPKI'09 - 6th European Workshop on Public Key Services, Applications and Infrastructures, Sep 2009, Pisa, Italy. pp.83-98, ⟨10.1007/978-3-642-16441-5_6⟩. ⟨hal-01099442⟩

Jean-Claude Bajard, Heinrich Hördegen. Pseudo-Random Generator Based on Chinese Remainder Theorem. SPIE 2009, Advanced Signal Processing Algorithms, Architectures, and Implementations XIX, Aug 2009, San-Diego, United States. pp.8. ⟨lirmm-00416194⟩

Jean-Claude Bajard, Marcelo Kaihara, Thomas Plantard. Selected RNS Bases for Modular Multiplication. ARITH'2009: 19th Symposium on Computer Arithmetic, Jun 2009, Portland, Oregon, United States. pp.25-35, ⟨10.1109/ARITH.2009.20⟩. ⟨lirmm-00394985⟩

Jean-Claude Bajard, Philippe Langlois, Dominique Michelucci, Géraldine Morin, Nathalie Revol. Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics. Advanced Signal Processing Algorithms, Architectures, and Implementations XVIII, Aug 2008, San Diego, United States. 70740M (12 p.), ⟨10.1117/12.796597⟩. ⟨hal-00321291⟩

Jean-Claude Bajard, Nadia El Mrabet. Pairing in Cryptography: an Arithmetic Point of View. Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, Aug 2007, San Diego, California, United States. ⟨10.1117/12.733789⟩. ⟨lirmm-00181362⟩

Julien Francq, Jean-Baptiste Rigaud, Pascal Manet, Jean-Claude Bajard, Arnaud Tisserand. Amélioration de la sécurité des circuits intégrés par codage de l'information. JNRDM'07: 10ème Journées Nationales du Réseau Doctoral en Microélectronique, Lille, France. ⟨lirmm-00182636⟩

Jean-Claude Bajard. A Residue Approach of the Finite Fields Arithmetics. The Asilomar Conference on Signals, Systems, and Computers, Nov 2007, Asilomar Conference Center California US, pp.5. ⟨lirmm-00182693⟩

Jean-Claude Bajard, Sylvain Duquesne, Milos Ercegovac, Nicolas Méloni. Residue systems efficiency for modular products summation: Application to Elliptic Curves Cryptography. Proceedings of SPIE : Advanced Signal Processing Algorithms, Architectures, and Implementations XVI, Aug 2006, pp.0. ⟨lirmm-00146450⟩

Benoit Badrignans, Daniel Mesquita, Jean-Claude Bajard, Lionel Torres, Gilles Sassatelli, et al.. Implémentation Matérielle d'une Arithmétique Résistante aux Fuites. RenPar'17 Rencontres Francophones en Parallélisme, CFSE'5 : Conférence Française sur les Systèmes d'Exploitation,SympAAA'06 : Symposium en Architecture et Adéquation Algorithme Architecture, Oct 2006, Canet en Roussillon (France), pp.57-74. ⟨lirmm-00107317⟩

José Marconi Rodrigues, William Puech, Peter Meuel, Jean-Claude Bajard, Marc Chaumont. Face Protection by Fast Selective Encryption in a Video. IET THE CRIME AND SECURITY Conference, Jun 2006, pp.420-425. ⟨lirmm-00109723⟩

Jean-Claude Bajard, Laurent Imbert, Graham A. Jullien, Hugh C. Williams. A CRT-Based Montgomery Multiplication for Finite Fields of Small Characteristic. IMACS: Scientific Computation, Applied Mathematics and Simulation, Jul 2005, Paris, France. ⟨lirmm-00106455⟩

Jean-Claude Bajard, Nicolas Méloni, Thomas Plantard. Efficient RNS Bases for Cryptography. 17th IMACS World Congress Scientific Computation, Applied Mathematics and Simulation, Jul 2005, Paris, France. ⟨lirmm-00106470⟩

Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Arithmetic Operations in the Polynomial Modular Number System. ARITH'05: 17th IEEE Symposium on Computer Arithmetic, 2005, USA, pp.206-213. ⟨lirmm-00387051⟩

Jean-Claude Bajard, Nicolas Méloni, Thomas Plantard. Study of Modular Inversion in RNS. SPIE'05: Advanced Signal Processing AlgorithmsArchitectures and Implementations XV, Jul 2005, San Diego, CA (USA). ⟨lirmm-00106063⟩

Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Modular Number Systems: Beyond the Mersenne Family. SAC'04: 11th International Workshop on Selected Areas in Cryptography, Aug 2005, University of Waterloo, Ontario (Canada), pp.159-169. ⟨lirmm-00105957⟩

Jean-Claude Bajard, Laurent Imbert, G.A. Jullien. Parallel Montgomery Multiplication in GF(2^k) Using Trinomial Residue Arithmetic. ARITH'17: IEEE Symposium on Computer Arithmetic, Jun 2005, Cape Cod, Massachusetts (USA), pp.164-171. ⟨lirmm-00106024⟩

Jean-Claude Bajard, Laurent Imbert, Pierre-yvan Liardet, y. Teglia. Leak Resistant Arithmetic. CHES'04: Cryptographic Hardware and Embedded Systems, Aug 2004, Boston, MA, (USA), pp.62-75. ⟨lirmm-00108863⟩

Jean-Claude Bajard, Thomas Plantard. RNS Bases and Conversions. SPIE'04: Advanced Signal Processing AlgorithmsArchitectures and Implementations XIV, Aug 2004, Denver, Colorado (USA), pp.60-69. ⟨lirmm-00108875⟩

Jean-Claude Bajard, Laurent Imbert, Christophe Negre, Thomas Plantard. Efficient Multiplication in GF (p^k) for Elliptic Curve Cryptography. ARITH-16'03: IEEE Symposium on Computer Arithmetic, Jun 2003, Santiago de Compostela, Spain. pp.181-187. ⟨lirmm-00269538⟩

Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Improving Euclidean Division and Modular Reduction for Some Classes of Divisors. Asilomar Conference on Signals, Systems and Computers, Nov 2003, Asilomar, CA, United States. pp.2218-2221, ⟨10.1109/ACSSC.2003.1292374⟩. ⟨lirmm-00269572⟩

Jean-Claude Bajard, Laurent Imbert, Christophe Negre. Modular Multiplication in GF (p^k) Using Lagrange Representation. IndoCryp: International Cryptology Conference in India, 2002, Hyderabad, India. pp.275-284. ⟨lirmm-00268466⟩

Jean-Claude Bajard, A. Guyot, Jean-Michel Muller, A. Skaf. Design of a VLSI circuit for on-line evaluation of several elementary functions using their Taylor expansions. Proceedings.-International-Conference-on-Application-Specific-Array-Processors-Cat.-No.93TH0572-8. 1993:, 1993, Venice, Italy. pp.526-35, ⟨10.1109/ASAP.1993.397172⟩. ⟨hal-00014928⟩

Jean-Claude Bajard, J.M. Muller. Calcul et Arithmétique des Ordinateurs. Hermes Science, 226 p., 2004, 2-7462-0861-X. ⟨lirmm-00109152⟩

Jean-Claude Bajard, Julien Eynard. RNS Approach in Lattice-Based Cryptography. Springer International Publishing. Embedded Systems Design with Special Arithmetic and Number Systems, pp 345-368, 2017, 978-3-319-49741-9. ⟨10.1007/978-3-319-49742-6_13⟩. ⟨hal-01496793⟩

Jean-Claude Bajard. Calcul sur les Corps Finis. Traité IC2 (Série Informatique et Systèmes d'Information) Calcul et Arithmétique des Ordinateurs, Hermes Science, pp.207-226, 2004. ⟨lirmm-00109154⟩

Julien Francq, Jean-Baptiste Rigaud, Pascal Manet, Jean-Claude Bajard, Arnaud Tisserand. Amélioration de la sécurité des circuits intégrés par codage de l'information. 2007. ⟨emse-00494265⟩

Jean-Claude Bajard, Jérémy Marrez, Thomas Plantard, Pascal Véron. On Polynomial Modular Number Systems over Z/pZ. 2020. ⟨hal-02883341⟩

Nadia El Mrabet, Giorgio Di Natale, Marie-Lise Flottes, Bruno Rouzeyre, Jean-Claude Bajard. Differential Power Analysis against the Miller Algorithm. RR-08021, 2008. ⟨lirmm-00323684⟩

Jean-Claude Bajard, Sylvain Duquesne, Nicolas Méloni. Combining Montgomery Ladder for Elliptic Curves Defined over $\F_p$ and RNS Representation. [Research Report] 06041, LIR. 2006. ⟨lirmm-00102859⟩

Jean-Claude Bajard, Laurent Imbert, Christophe Negre. Arithmetic Operations in Finite Fields of Medium Prime Characteristic for Elliptic Curve Cryptography. 05028, 2005. ⟨lirmm-00106633⟩

Jean-Claude Bajard, Laurent Imbert, Graham A. Jullien, Thomas Plantard. Fast Modular Reduction for a Large Class of Moduli. [Research Report] 04007, LIRMM (UM, CNRS). 2004. ⟨lirmm-00109210⟩

Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Modular Number Systems: Beyond the Mersenne Family. [Research Report] 04006, LIRMM. 2004. ⟨lirmm-00109208⟩

Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Arithmetic Operations in the Polynomial Modular Number System. 04030, 2004, 26 p. ⟨lirmm-00109201⟩

Jean-Claude Bajard, Laurent Imbert, Pierre-yvan Liardet. Leak Resistant Arithmetic. 03021, 2003, pp.P nd. ⟨lirmm-00269571⟩

Jean-Claude Bajard, Laurent Imbert, Pierre-yvan Liardet. Leak Resistant Arithmetic. 03021, 2003. ⟨lirmm-00269442⟩

Jean-Claude Bajard, Laurent Imbert, Pierre-yvan Liardet. Leak Resistant Arithmetic. 03021, 2003, pp.P nd. ⟨lirmm-00191922⟩

Laurent Imbert, Jean-Claude Bajard. An Optimised Implementation of RSA in the Residue Number System. 02130, 2002, pp.P nd. ⟨lirmm-00268425⟩

Laurent Imbert, Jean-Claude Bajard. A Full RNS Implementation of RSA. 02068, 2002. ⟨lirmm-00090366⟩

Jean-Claude Bajard, Laurent Imbert, Christophe Negre. Modular Multiplication in GF (p^k) Using Lagrange Representation. 02131, 2002. ⟨lirmm-00090350⟩