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Darrel Hankerson, Koray Karabina, Alfred Menezes, "Analyzing the GalbraithLinScott Point Multiplication Method for Elliptic Curves over Binary Fields," IEEE Transactions on Computers, vol. 58, no. 10, pp. 14111420, October, 2009.  
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@article{ 10.1109/TC.2009.61, author = {Darrel Hankerson and Koray Karabina and Alfred Menezes}, title = {Analyzing the GalbraithLinScott Point Multiplication Method for Elliptic Curves over Binary Fields}, journal ={IEEE Transactions on Computers}, volume = {58}, number = {10}, issn = {00189340}, year = {2009}, pages = {14111420}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2009.61}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Analyzing the GalbraithLinScott Point Multiplication Method for Elliptic Curves over Binary Fields IS  10 SN  00189340 SP1411 EP1420 EPD  14111420 A1  Darrel Hankerson, A1  Koray Karabina, A1  Alfred Menezes, PY  2009 KW  Elliptic curve cryptography KW  computer arithmetic KW  efficiency. VL  58 JA  IEEE Transactions on Computers ER   
[1] E. AlDaoud, R. Mahmod, M. Rushdan, and A. Kilicman, “A New Addition Formula for Elliptic Curves over ${GF}(2^n)$ ,” IEEE Trans. Computers, vol. 51, no. 8, pp. 972975, Aug. 2002.
[2] R. Avanzi, “Another Look at Square Roots (And Other Less Common Operations) in Fields of Even Characteristic,” Proc. Int'l Workshop Selected Areas in Cryptography (SAC '07), pp. 138154, 2007.
[3] R. Avanzi and N. Thériault, “Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic,” Proc. Int'l Workshop Arithmetic of Finite Fields (WAIFI '07), pp. 6984, 2007.
[4] D. Bernstein, T. Lange, and R. Farashahi, “Binary Edwards Curves,” Proc. Workshop Cryptographic Hardware and Embedded Systems (CHES '08), pp. 244265, 2008.
[5] R.P. Brent, P. Gaudry, E. Thomé, and P. Zimmermann, “Faster Multiplication in ${GF}(2)[x]$ ,” Proc. Symp. Algorithmic Number Theory (ANTSVIII), pp. 153166, 2008.
[6] C. Diem and E. Thomé, “Index Calculus in Class Groups of NonHyperelliptic Curves of Genus Three,” J. Cryptology, vol. 21, pp.593611, 2008.
[7] A. Enge and P. Gaudry, “A General Framework for Subexponential Discrete Logarithm Algorithms,” Acta Arithmetica, vol. 102, pp.83103, 2002.
[8] K. Fong, D. Hankerson, J. López, and A. Menezes, “Field Inversion and Point Halving Revisited,” IEEE Trans. Computers, vol. 53, no. 8 pp. 10471059, Aug. 2004.
[9] S. Galbraith, “Constructing Isogenies between Elliptic Curves over Finite Fields,” LMS J. Computation and Math., vol. 2, pp. 118138, 1999.
[10] S. Galbraith, F. Hess, and N. Smart, “Extending the GHS Weil Descent Attack,” Proc. Advances in Cryptology (EUROCRYPT '02), pp. 2944, 2002.
[11] S. Galbraith, X. Lin, and M. Scott, “Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves,” Proc. Advances in Cryptology (EUROCRYPT '09), pp. 518535, 2009.
[12] R. Gallant, R. Lambert, and S. Vanstone, “Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms,” Proc. Advances in Cryptology (CRYPTO '01), pp. 190200, 2001.
[13] P. Gaudry, F. Hess, and N. Smart, “Constructive and Destructive Facets of Weil Descent on Elliptic Curves,” J. Cryptology, vol. 15, pp. 1946, 2002.
[14] S. Gueron and M. Kounavis, “CarryLess Multiplication and Its Usage for Computing the GCM Mode,” white paper, Intel Corporation, http://softwarecommunity.intel.com/articles/ eng3787.htm, 2008.
[15] S. Gueron and M. Kounavis, “A Technique for Accelerating Characteristic 2 Elliptic Curve Cryptography,” Proc. Fifth Int'l Conf. Information Technology: New Generations (ITNG '08), pp. 265272, 2008.
[16] D. Hankerson, A. Menezes, and M. Scott, “Software Implementation of Pairings,” IdentityBased Cryptography, M. Joye and G. Neven, eds., IOS Press, 2008.
[17] D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography. Springer, 2003.
[18] F. Hess, “Generalising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem,” LMS J. Computation and Math., vol. 7, pp. 167192, 2004.
[19] I. Iijima, K. Matsuo, J. Chao, and S. Tsujii, “Construction of Frobenius Maps of Twists Elliptic Curves and Its Application to Elliptic Scalar Multiplication,” Proc. Symp. Cryptography and Information Security (SCIS '02), 2002.
[20] D. Jao, S. Miller, and R. Venkatesan, “Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?” Proc. Advances in Cryptology (ASIACRYPT '05), pp. 2140, 2005.
[21] K. Kim and S. Kim, “A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields,” Cryptology ePrint Archive: Report 2007/181, http://eprint.iacr.org/2007181, 2007.
[22] B. King, “An Improved Implementation of Elliptic Curves over $GF(2^n)$ When Using Projective Point Arithmetic,” Proc. Int'l Workshop Selected Areas in Cryptography (SAC '01), pp. 134150, 2001.
[23] B. King and B. Rubin, “Improvements to the Point Halving Algorithm,” Proc. Australasian Conf. Information Security and Privacy (ACISP '04), pp. 262276, 2004.
[24] E. Knudsen, “Elliptic Scalar Multiplication Using Point Halving,” Proc. Advances in Cryptology (ASIACRYPT '99), pp. 135149, 1999.
[25] N. Koblitz, “CMCurves with Good Cryptographic Properties,” Proc. Advances in Cryptology (CRYPTO '91), pp. 279287, 1991.
[26] T. Lange, “A Note on LópezDahab Coordinates,” Tatra Mountains Math. Publications, vol. 33, pp. 7581, http://eprint.iacr.org/2004323, 2006.
[27] C. Lim and H. Hwang, “Speeding Up Elliptic Scalar Multiplication with Precomputation,” Proc. Int'l Conf. Information Security and Cryptology, pp. 102119, 1999.
[28] J. López and R. Dahab, “Improved Algorithms for Elliptic Curve Arithmetic in $GF(2^n)$ ,” Proc. Int'l Workshop Selected Areas in Cryptography (SAC '98), pp. 201212, 1998.
[29] J. López and R. Dahab, “Highspeed software multiplication in ${\hbox{\rlap{I}\kern 2.0pt{\hbox{F}}}}_{2^m}$ ”, Progress in Cryptology Proc. First Int'l Conf. in Cryptology in India (INDOCRYPT '00), pp. 203212, 2000.
[30] M. Maurer, A. Menezes, and E. Teske, “Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree,” LMS J. Computation and Math., vol. 5, pp. 127174, 2002.
[31] A. Menezes and M. Qu, “Analysis of the Weil Descent Attack of Gaudry, Hess and Smart,” Proc. Topics in Cryptology: Cryptographers' Track at RSA (CTRSA '01), pp. 308318, 2001.
[32] A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography. CRC Press, 1996.
[33] B. Möller, “Algorithms for MultiExponentiation,” Proc. Int'l Workshop Selected Areas in Cryptography (SAC '01), pp. 165180, 2001.
[34] J. Muir and D. Stinson, “Minimality and Other Properties of the Width$w$ Nonadjacent Form,” Math. of Computation, vol. 75, pp.369384, 2006.
[35] R. Schroeppel, “Automatically Solving Equations in Finite Fields,” US patent 09/834,363, 2001.
[36] M. Scott, MIRACL—Multiprecision Integer and Rational Arithmetic C Library, http://www.computing.dcu.ie/~mikemiracl.html , 2008.
[37] J. Solinas, “Efficient Arithmetic on Koblitz Curves,” Designs, Codes and Cryptography, vol. 19, pp. 195249, 2000.