Publications and Preprints

Empirical Optimization of Divisor Arithmetic on Hyperelliptic Curves over F_2^m, with M. J. Jacobson, Jr. 2012 (submitted)
On the maximal weight of (p,q)-ary chain partitions with bounded parts, with F. Disanto and F. Philippe. 2012 (submitted)
Parallel modular multiplication on multi-core processors, with P. Giorgi and T. Izard. 2012 (to appear at Arith 21)
On the robustness of an RNS-based implementation of RSA against electromagnetic collision attacks, with P. Maurine, G. Perin and L. Torres. 2012 (submitted)

Hybrid binary-ternary number system for elliptic curve cryptosystems, with J. Adikari and V. Dimitrov. IEEE Transactions on Computers, vol. 60, no. 2, pp. 254-265, 2011. [doi: 10.1109/TC.2010.138]

Fast ideal cubing in quadratic number and function fields, with M. J. Jacobson Jr. and A. Schmidt. Advances in Mathematics of Communications, vol. 4, no. 2, pp. 237-260, 2010. [doi: 10.3934/amc.2010.4.237]
Strictly chained (p,q)-ary partitions, with F. Philippe. Contributions to Discrete Mathematics, vol. 5, no. 2, pp. 119--136, 2010. [http://cdm.ucalgary.ca/index.php/cdm/article/view/179]

Accelerating query-by-humming on GPU, with P. Ferraro, P. Hanna and T. Izard, Proceedings of the 10th International Society for Music Information Retrieval Conference, ISMIR 2009, pp. 279-284, Kobe, Japan, October 26-30, 2009.
Optimizing elliptic curve scalar multiplication for small scalars, with P. Giorgi and T. Izard, Mathematics for Signal and Information Processing, volume 7444 of Proceedings of SPIE, pp. 74440N. SPIE Ed., San-Diego, USA, August 2009. [doi: 10.1117/12.827689]
Hybrid binary-ternary joint sparse form and its application in elliptic curve cryptography, with J. Adikari and V. Dimitrov In Proceedings of the 19th IEEE Symposium on Computer Arithmetic, ARITH19, pp 76-82, IEEE Computer Society, Portland, USA, June 8-10 2009. [doi: 10.1109/ARITH.2009.10]
Strictly chained (p,q)-ary partitions, Invited talk, Alberta Number Theory Day, Calgary, Canada, April 30, 2009.
Diophantine approximation, Ostrowski numeration and the double-base number system, with V. Berthé, Discrete Mathematics & Theoretical Computer Science. vol 11, no. 1, pp. 153-172, 2009. [http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/1011]

The Double-Base Number System in Elliptic Curve Cryptography, with C. Doche, In Conference Records of the 42nd Asilomar Conference on Signals, Systems and Computers, pp. 777-780, Pacific Grove, CA, October 26-29, 2008. [doi: 10.1109/ACSSC.2008.5074514]
Arithmexotiques, Habilitation à diriger les recherche, Université Montpellier 2, France, April 11, 2008.
The Double-base Number System and its Application to Elliptic Curve Cryptography, with V. Dimitrov and P. K. Mishra, Mathematics of Computation, vol. 77, no 262, pp. 1075-1104, April 2008. [doi: 10.1090/S0025-5718-07-02048-0]

A Library for Prototyping the Computer Arithmetic Level in Elliptic Curve Cryptography, with A. Pereira and A. Tisserand, In Advanced Signal Processing Algorithms, Architectures and Implementations XVII, Proceedings of SPIE, vol. 6697, pp. 66970N. SPIE Ed., San-Diego, USA, Aug. 2007. [doi: 10.1117/12.733652]
Multiplication by a Constant is Sublinear with V. Dimitrov and A. Zakaluzny. In Proceedings 18th IEEE Symposium on Computer Arithmetic, pp. 261-268, Montpellier, France, June 24-27, 2007. [doi: 10.1109/ARITH.2007.24]
Multi-mode Operator for SHA-2 Hash Functions, with R. Glabb, G. A. Jullien, A. Tisserand and N. Veyrat-Charvillon, Journal of Systems Architecture, special issue on Embedded Hardware for Cryptosystems, vol. 53, issues 2-3, pp. 127-138, Feb-Mar, 2007. [doi: 10.1016/j.sysarc.2006.09.006]

Extended Double-Base Number System with Applications to Elliptic Curve Cryptography, with C. Doche, In Progress in Cryptology - INDOCRYPT 2006, LNCS 4329, pp 335-348, Kolkata, India, Dec. 11-13, 2006. [doi: 10.1007/11941378_24]
Arithmetic Operations in Finite Fields of Medium Prime Characteristic using the Lagrange Representation, with J.-C. Bajard and C. Negre, IEEE Transactions on Computers, vol. 55, no. 9, pp. 1167-1177, Sep. 2006. [doi: 10.1109/TC.2006.136]
Sublinear Constant Multiplication Algorithms, with V. Dimitrov and A. Zakaluzny, In Proceedings of SPIE, Advanced Signal Processing Algorithms, Architectures and Implementations XVI, vol. 6316, pp. 631305 (2006). [doi: 10.1117/12.680289]
Multi-mode Operator for SHA-2 Hash Functions, with R. Glabb, G. A. Jullien, A. Tisserand and N. Veyrat-Charvillon, In Proceedings 2006 International Conference on Engineering of Reconfigurable Systems and Algorithms - ERSA'06, pp. 207-210, June 2006. [http://ww1.ucmss.com/books/LFS/CSREA2006/ERS8208.pdf]

Efficient and Secure Elliptic Curve Point Multiplication using Double-Base Chains, with V. S. Dimitrov and P. K. Mishra, In Advances in Cryptology - ASIACRYPT 2005, LNCS 3788, pp. 59-78, Chennai, India, Dec. 4-8, 2005. [doi: 10.1007/11593447_4]
A Fault-Tolerant Modulus Replication Complex FIR Filter, with I. Steiner, P. Chan, G. A. Jullien, V. S. Dimitrov and G. H. McGibney, In Proceedings 16th IEEE International Conference on Application-Specific Systems, Architecture Processors - ASAP'05, pp. 387-392, Samos, Greece, July 23-25, 2005. [doi: 10.1109/ASAP.2005.6]
A CRT-Based Montgomery Multiplication for Finite Fields of Small Characteristic, with J.-C. Bajard, G. A. Jullien and H. C. Williams, In Proceedings 17th IMACS World Congress, Scientific Computation, Applied Mathematics and Simulation, pp. 101-107, July 11-15, 2005.
Parallel Montgomery Multiplication in GF(2^k) using Trinomial Residue Arithmetic, with J.-C. Bajard and G. A. Jullien, In Proceedings 17th IEEE Symposium on computer Arithmetic, pp. 164-171, 2005. [doi: 10.1109/ARITH.2005.34]
Arithmetic Operations in the Polynomial Modular Number System, with J.-C. Bajard and T. Plantard. In Proceedings 17th IEEE Symposium on computer Arithmetic, pp. 206-213, Cape Cod, USA, June 27-29, 2005. [doi: 10.1109/ARITH.2005.11]

A Full RNS Implementation of RSA, with J.-C. Bajard, IEEE Transactions on Computers, vol. 53, no. 6, pp. 769-774, 2004. 10.1109/TC.2004.2
Modular Number Systems: Beyond the Mersenne Family, with J.-C. Bajard and T. Plantard, In Proceedings 11th International Workshop on Selected Areas in Crytography, SAC 2004, LNCS 3357, pp. 159-169, 2005.
Fault-Tolerant Computations Within Complex FIR Filters, with P. Chan, G. A. Jullien, V. Dimitrov and G. H. McGibney. In Proceedings of the 2004 IEEE Workshop on Signal Processing Systems, SIPS 2004, pp. 316-320, 2004.
On Converting Numbers to the Double-Base Number System, with V. Berthé, In Proceedings of SPIE, vol. 5559, Advanced Signal Processing Algorithms, Architectures and Implementations XIV, pp. 70-78, 2004.
Leak resistant arithmetic, with J.-C. Bajard, P.-Y. Liardet and Y. Teglia, In Cryptographic Hardware and Embedded Systems - CHES 2004, LNCS 3156, pp. 62-75, 2004.
Calcul et arithmétique des ordinateurs, chapter 5, Arithmétique multiprécision, pp. 155-179, Traité IC2, Série Informatique et Systèmes d'Information, J.-C. Bajard and J.-M. Muller, Ed. Hermès science publications, 2004.

Fault-Tolerant Computations over Replicated Finite Rings, with V. Dimitrov and G. A. Jullien, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 7, pp. 858-864, 2003. 10.1109/TCSI.2003.814085
Improving Euclidean division and modular reduction for some classes of divisors, with J.-C. Bajard and T. Plantard. In Conference Records of the 37th IEEE Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 2218-2221, 2003.
Comparison of modular multipliers on FPGAs, with J.-L. Beuchat and A. Tisserand. In Proceedings of SPIE, vol. 5205, Advanced Signal Processing Algorithms, Architectures and Implementations XIII, pp. 490-498, 2003.
Efficient Multiplication in GF(p^k) for Elliptic Curve Cryptography, with J.-C. Bajard, C. Negre and T. Plantard. In Proceedings 16th IEEE Symposium on computer Arithmetic, pp. 181-187, 2003.

Modular multiplication in GF(p^k) using Lagrange representation, with J.-C. Bajard and C. Negre, In Progress in Cryptology - INDOCRYPT 2002, LNCS 2551, pp. 275-284, 2002.

Fault-tolerant computation of large inner-products, with G. A. Jullien, IEE Electronics Letters, vol. 37, no. 9, pp. 551-552, 2001. 10.1049/el:20010378
Évaluation des fonctions élémentaires en multiprécision, with J.-C. Bajard and F. Rico, Technique et Science Informatiques, vol. 20, no. 1, pp. 91-110, 2001.
Fault tolerant complex FIR filter architectures using a redundant MRRNS, with G. A. Jullien, V. Dimitrov and A. Garg, In Conference Records of the 35th IEEE Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 1222-1226, 2001.
Efficient fault tolerant arithmetic using a symmetrical modulus replication RNS, with G. A. Jullien, In Proceedings of the 2001 IEEE Workshop on Signal Processing Systems, Design and Implementation, SIPS 2001, pp. 93-100, 2001.
The use of the multi-dimensional logarithmic number system in DSP applications, with V. S. Dimitrov, J. Eskritt, G. A. Jullien and W. C. Miller, In Proceedings 15th IEEE symposium on Computer Arithmetic, pp. 247-254, 2001.

Improving Goldschmidt division, square root and square root reciprocal, with M. D. Ercegovac, D. W. Matula, J.-M. Muller and G. Wei, IEEE Transactions on Computers, vol. 49, no. 7, pp. 759-763, 2000. 10.1109/12.863046
A radix-10 BKM algorithm for computing transcendentals on pocket computers, with J.-M. Muller and F. Rico, Journal of VLSI Signal Processing, vol. 25, no. 2, pp. 179-186, 2000. 10.1023/A:1008127208220
Comparison of different techniques to compute the complex exponential for hundred bit precision, with C. Moreau and F. Rico, In Proceedings of SCAN 2000, the 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, pp. 124-125, 2000.
Fast evaluation of elementary functions with combined shift-and-add and polynomial methods, with J.-C. Bajard, M. D. Ercegovac and F. Rico. In Proceedings of the 4th Conference on Real Numbers and Computers, pp. 75-87, 2000.

Evaluation of complex elementary functions: a new version of BKM, with J.-C. Bajard, In Proceedings of SPIE, vol. 2807, Advanced Signal Processing Algorithms, Architectures and Implementations IX, pp. 2-9, 1999.
Évaluation de l'exponentielle du sinus et du cosinus à base d'additions de décalages et de polynômes, with J.-C. Bajard and F. Rico, In Actes de la conférence SympA'5, 5ième symposium en architectures nouvelles de machines, pp. 19-26, 1999.