
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Robert Granger, Daniel Page, Martijn Stam, "Hardware and Software Normal Basis Arithmetic for PairingBased Cryptography in Characteristic Three," IEEE Transactions on Computers, vol. 54, no. 7, pp. 852860, July, 2005.  
BibTex  x  
@article{ 10.1109/TC.2005.120, author = {Robert Granger and Daniel Page and Martijn Stam}, title = {Hardware and Software Normal Basis Arithmetic for PairingBased Cryptography in Characteristic Three}, journal ={IEEE Transactions on Computers}, volume = {54}, number = {7}, issn = {00189340}, year = {2005}, pages = {852860}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2005.120}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Hardware and Software Normal Basis Arithmetic for PairingBased Cryptography in Characteristic Three IS  7 SN  00189340 SP852 EP860 EPD  852860 A1  Robert Granger, A1  Daniel Page, A1  Martijn Stam, PY  2005 KW  Index Terms Public key cryptosystems KW  computer arithmetic KW  highspeed arithmetic. VL  54 JA  IEEE Transactions on Computers ER   
[1] 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.
[2] P. Barreto, H. Kim, B. Lynn, and M. Scott, “Efficient Algorithms for PairingBased Cryptosystems,” Proc. CRYPTO '02, pp. 354368, 2002.
[3] G. Bertoni, J. Guajardo, S. Kumar, G. Orlando, C. Paar, and T. Wollinger, “Efficient $GF(p^m)$ Arithmetic Architectures for Cryptographic Applications,” Proc. Cryptographers TrackRSA '03, pp. 158175, 2003.
[4] D. Boneh and M. Franklin, “IdentityBased Encryption from the Weil Pairing,” SIAM J. Computing, vol. 32, no. 3, pp. 586615, 2003.
[5] I. Duursma and H. Lee, “Tate Pairing Implementation for Hyperelliptic Curves $y^2 = x^p  x + d$ ,” Proc. ASIACRYPT '03, pp. 111123, 2003.
[6] G. Frey and H. Ruck, “A Remark Concerning mDivisibility and the Discrete Logarithm Problem in the Divisor Class Group of Curves,” Math. Computation, vol. 62, pp. 865874, 1994.
[7] S. Galbraith, “Supersingular Curves in Cryptography,” Proc. ASIACRYPT '01, pp. 495513, 2001.
[8] S. Galbraith, K. Harrison, and D. Soldera, “Implementing the Tate Pairing,” Proc. Fifth Algorithmic Number Theory Symp. (ANTSV), pp. 324337, 2002.
[9] S. Gao, “Normal Bases over Finite Fields,” PhD thesis, Waterloo Univ., 1993.
[10] R. Granger, D. Page, and M. Stam, “On Small Characteristic Algebraic Tori in PairingBased Cryptography,” Cryptology ePrint Archive, Report 2004/132, 2004.
[11] K. Harrison, D. Page, and N.P. Smart, “Software Implementation of Finite Fields of Characteristic Three, for Use in Pairing Based Cryptosystems,” LMS J. Computation and Math., vol. 5, no. 1, pp. 181193, 2002.
[12] M.A. Hassan, M.Z. Wang, and V.K. Bhargava, “A Modified MasseyOmura Parallel Multiplier for a Class for Finite Fields,” IEEE Trans. Computers, vol. 42, no. 10, pp. 12781280, Oct. 1993.
[13] IEEEP 1363, “Standard Specifications for Public Key Cryptography,” IEEE Standards Dept., 1999.
[14] T. Itoh and S. Tsujii, “A Fast Algorithm for Computing Multiplicative Inverses in $GF(2^n)$ Using Normal Bases,” Information and Computation, vol. 78, pp. 171177, 1988.
[15] B.S. Kaliski Jr. and Y.L. Yin, “Storage Efficient Finite Field Basis Conversion,” Proc. Symp. Applied Computing (SAC '99), pp. 8193, 1999.
[16] A. Karatsuba and Y. Ofman, “Multiplication of ManyDigital Numbers by Automatic Computers,” Doklady Akad. Nauk SSSR, vol. 145, pp. 293294, 1962. Translation in PhysicsDoklady, vol. 7, pp. 595596, 1963.
[17] Ç.K. Koç and B. Sunar, “LowComplexity BitParallel Canonical and Normal Basis Multipliers for a Class for Finite Fields,” IEEE Trans. Computers, vol. 47, no. 3, pp. 353356, Mar. 1998.
[18] J. López and R. Dahab, “High Speed Software Multiplication in ${\hbox{\rlap{F}\kern 1.5pt{\hbox{F}}}}_{2^m}$ ,” Proc. INDOCRYPT '00, pp. 203212, 2000.
[19] A. Menezes, T. Okamoto, and S.A. Vanstone, “Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field,” IEEE Trans. Information Theory, vol. 39, pp. 16391646, 1993.
[20] P. Ning and Y.L. Yin, “Efficient Software Implementation for Finite Field Multiplication in Normal Basis,” Proc. Int'l Conf. Information and Comm. Security (ICICS '01), pp. 177188, 2001.
[21] M. Nöcker, “Data Structures for Parallel Exponentiation in Finite Fields,” PhD thesis, Universität Paderborn, 2001.
[22] D. Page and N.P. Smart, “Hardware Implementation of Finite Fields of Characteristic Three,” Proc. Workshop Cryptographic Hardware and Embedded Systems (CHES '02), pp. 529539, 2002.
[23] A. ReyhaniMasoleh and M.A. Hasan, “Fast Normal Basis Multiplication Using General Purpose Processors,” Proc. Symp. Applied Computing (SAC '01), pp. 230244, 2001.
[24] A. ReyhaniMasoleh and M.A. Hassan, “A New Construction of MasseyOmura Parallel Multiplier over $GF(2^m)$ ,” IEEE Trans. Computers, vol. 51, no. 5, pp. 511520, May 2002.
[25] R. Sakai, K. Ohgishi, and M. Kasahara, “Cryptosystems Based on Pairings,” Proc. Symp. Cryptography and Information Security (SCIS '00), 2000.
[26] M. Scott and P. Barreto, “Compressed Pairings,” Cryptology ePrint Archive, Report 2004/032, 2004.
[27] A. Shamir, “IdentityBased Cryptosystems and Signature Schemes,” Proc. CRYPTO '85, pp. 4753, 1985.
[28] J. Silverman, The Arithmetic of Elliptic Curves. Springer GTM 106, 1986.
[29] C.C. Wang, T.K. Truong, H.M. Shao, L.J. Deutsch, J.K. Omura, and I.S. Reed, “VLSI Architectures for Computing Multiplications and Inverses in $GF(2^m)$ ,” IEEE Trans. Computers, vol. 34, no. 8, pp. 709716, Aug. 1985.