
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
JeanClaude Bajard, Laurent Imbert, Christophe N?gre, "Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation," IEEE Transactions on Computers, vol. 55, no. 9, pp. 11671177, September, 2006.  
BibTex  x  
@article{ 10.1109/TC.2006.136, author = {JeanClaude Bajard and Laurent Imbert and Christophe N?gre}, title = {Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation}, journal ={IEEE Transactions on Computers}, volume = {55}, number = {9}, issn = {00189340}, year = {2006}, pages = {11671177}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2006.136}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation IS  9 SN  00189340 SP1167 EP1177 EPD  11671177 A1  JeanClaude Bajard, A1  Laurent Imbert, A1  Christophe N?gre, PY  2006 KW  Finite field arithmetic KW  optimal extension fields KW  Newton interpolation KW  Euclidean algorithm KW  elliptic curve cryptography. VL  55 JA  IEEE Transactions on Computers ER   
[1] N. Koblitz, “Elliptic Curve Cryptosystems,” Math. Computation, vol. 48, no. 177, pp. 203209, Jan. 1987.
[2] V.S. Miller, “Uses of Elliptic Curves in Cryptography,” Advances in Cryptology, Proc. CRYPTO '85, H.C. Williams, ed., pp. 417428, 1986.
[3] A. Menezes, P.C. Van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1997.
[4] IEEE, IEEE 13632000 Standard Specifications for PublicKey Cryptography, 2000.
[5] Nat'l Inst. of Standards and Technology, FIPS PUB 1862: Digital Signature Standard (DSS), Jan. 2000.
[6] D. Bailey and C. Paar, “Optimal Extension Fields for Fast Arithmetic in PublicKey Algorithms,” Advances in Cryptography, Proc. CRYPTO '98, H. Krawczyk, ed., pp. 472485, 1998.
[7] D. Bailey and C. Paar, “Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography,” J. Cryptology, vol. 14, no. 3, pp. 153176, 2001.
[8] D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography. SpringerVerlag, 2004.
[9] N.P. Smart and E.J. Westwood, “Point Muliplication on Ordinary Elliptic Curves over Fields of Characteristic Three,” Applicable Algebra in Eng., Comm., and Computing, vol. 13, no. 6, pp. 485497, Apr. 2003.
[10] J.A. Solinas, “Improved Algorithms for Arithmetic on Anomalous Binary Curves,” Research Report CORR9946, Center for Applied Cryptographic Research, Univ. of Waterloo, Canada, updated version of the paper appearing in the Proc. CRYPTO '97, 1999.
[11] N. Koblitz, “CM Curves with Good Cryptographic Properties,” Advances in Cryptography, Proc. CRYPTO '91, pp. 279287, 1992.
[12] D.H. Lehmer, “Euclid's Algorithm for Large Numbers,” Am. Math. Monthly, vol. 45, no. 4, pp. 227233, 1938.
[13] J. Von Zur Gathen and J. Gerhard, Modern Computer Algebra. Cambridge Univ. Press, 1999.
[14] P.L. Montgomery, “Modular Multiplication without Trial Division,” Math. Computation, vol. 44, no. 170, pp. 519521, Apr. 1985.
[15] Ç.K. Koç and T. Acar, “Montgomery Multiplication in ${\rm GF}(2^k)$ ,” Designs, Codes, and Cryptography, vol. 14, no. 1, pp. 5769, Apr. 1998.
[16] V. Lefèvre, “Multiplication by an Integer Constant,” Research Report 4192, INRIA, May 2001.
[17] N. Boullis and A. Tisserand, “Some Optimizations of Hardware Multiplication by Constant Matrices,” IEEE Trans. Computers, vol. 54, no. 10, pp. 12711282, Oct. 2005.
[18] J.C. Bajard, L. Imbert, C. Nègre, and T. Plantard, “Multiplication in ${\rm GF}(p^k)$ for Elliptic Curve Cryptography,” Proc. 16th IEEE Symp. Computer Arithmetic, pp. 181187, 2003.
[19] D.E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, third ed. Reading, Mass.: AddisonWesley, 1997.
[20] R. Crandall and C. Pomerance, Prime Numbers. A Computational Perspective. SpringerVerlag, 2001.
[21] J. Sorenson, “Two Fast GCD Algorithms,” J. Algorithms, vol. 16, no. 1, pp. 110144, 1994.
[22] J. Sorenson, “An Analysis of Lehmer's Euclidean Algorithm,” Proc. 1995 Int'l Symp. Symbolic and Algebraic Computation (ISSAC '95), pp. 254258, 1995.
[23] J.M. Pollard, “Monte Carlo Methods for Index Computation mod $p$ ,” Math. Computation, vol. 32, no. 143, pp. 918924, July 1978.
[24] P. Gaudry, “Index Calculus for Abelian Varieties and the Elliptic Curve Discrete Logarithm Problem,” preprint, Oct. 2004.
[25] R.M. Avanzi, H. Cohen, C. Doche, G. Frey, T. Lange, K. Nguyen, and F. Vercauteren, Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, 2005.