Reconfigurable computing approach for tate pairing cryptosystems over binary fields

IEEE Transactions on Computers

Volumn 58, Issue 9, 2009, Pages 1221-1237

  Shu, Chang ^a   Kwon, Soonhak ^b   Gaj, Kris ^c  

^a MARVELL SEMICONDUCTOR INC   (United States)

^b Sungkyunkwan University   (South Korea)

^c GEORGE MASON UNIVERSITY   (United States)

Author keywords

Elliptic curve; Field programmable gate arrays (FPGAs); Finite field; Reconfigurable computing; Tate pairing

Indexed keywords

ELLIPTIC CURVE; FIELD-PROGRAMMABLE GATE ARRAYS (FPGAS); FINITE FIELD; RECONFIGURABLE COMPUTING; TATE PAIRING;

ARCHITECTURAL DESIGN; COMPUTER SCIENCE; GEOMETRY; LOGIC GATES; PUBLIC KEY CRYPTOGRAPHY;

FIELD PROGRAMMABLE GATE ARRAYS (FPGA);

EID: 68949189663     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/TC.2009.64     Document Type: Article

References (32)

1. T. Kerins et al., "Efficient Hardware for the Tate Pairing Calculation in Characteristic Three," Proc. Cryptographic Hardware and Embedded Systems (CHES '05), pp. 412-426, 2005.
2. T. Kerins, E.M. Popovici, and W.P. Marnane, "Algorithms and Architectures for Use in FPGA Implementations of Identity Based Encryption Schemes," Proc. Field Programmable Logic and Applications (FPL '04), pp. 74-83, 2004.
3. P. Grabher and D. Page, "Hardware Acceleration of the Tate Pairing in Characteristic Three," Proc. Cryptographic Hardware and Embedded Systems (CHES '05), pp. 398-411, 2005.
4. R. Ronan, C.O. Eigeartaigh, C. Murphy, M. Scott, T. Kerins, and W.P. Marnane, "A Dedicated Processor for the Eta pairing," Cryptology ePrint Archive, http://eprint.iacr.org/2005/330.pdf, 2009.
5. G. Kömürcü and E. Savas, "An Efficient Hardware Implementation of the Tata Pairing in Characteristic Three," Proc. Third Int'l Conf. Systems (ICONS '08), pp. 23-28, 2008.
6. J.-L. Beuchat, N. Brisebarre, J. Detrey, E. Okamoto, M. Shirase, and T. Takagi, "Arithmetic Operators for Pairing-Based Cryptography," Proc. Cryptographic Hardware and Embedded Systems (CHES '07), pp. 239-255, 2007.
7. T Pairing in Characteristic Three," IEEE Trans. Computers, vol. 57, no. 11, Nov. 2008.
8. 3m," Proc. Int'l Conf. Pairing-Based Cryptography (Pairing '08), pp. 297-315, 2008.
9. R. Granger, D. Page, and M. Stam, "Hardware and Software Normal Basis Arithmetic for Pairing Based Cryptography in Characteristic Three," IEEE Trans. Computers, vol. 54, no. 7, Jul. 2005.
10. R. Granger, D. Page, and M. Stam, "On Small Characteristic Algebraic Tori in Pairing Based Cryptography," preprint, http://eprint.iacr.org/2004/132.pdf, 2004.
11. p - x + d," Proc. Int'l Conf. Theory and Application of Cryptology and Information Security (Asiacrypt '03), pp. 111-123, 2003.
12. P. Barreto, H. Kim, B. Lynn, and M. Scott, "Efficient Algorithms for Pairing Based Cryptosystems," Proc. Int'l Cryptology Conf. (Crypto '02), pp. 354-368, 2002.
13. P. Barreto, S. Galbraith, C. OhEigeartaigh, and M. Scott, "Efficient Pairing Computation on Supersingular Abelian Varieties," Design, Codes and Cryptography, vol. 42, no. 3, pp. 239-271, 2007.
14. S. Kwon, "Efficient Tate Pairing Computation for Supersingular Elliptic Curves Over Binary Fields," Proc. Australasian Conf. Information Security and Privacy (ACISP '05), pp. 134-145, 2005.
15. S. Galbraith, K. Harrison, and D. Soldera, "Implementing the Tate Pairing," Proc. Int'l Workshop ANT Algorithms (ANTS '02), pp. 324-337, 2002.
16. V. Miller, "Short Programs for Functions on Curves," unpublished manuscript, 1986.
17. F. Hess, N. Smart, and F. Vercauteren, "The Eta Pairing Revisited," IEEE Trans. Information Theory, vol. 52, no. 10, Oct. 2006.
18. A.J. Menezes, Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, 1993.
19. L.C. Washington, Elliptic Curves: Number Theory and Cryptography. CRC Press, Apr. 2008.
20. H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, and F. Vercauteren, Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, July 2005.
21. I.F. Blake, G. Seroussi, and N.P. Smart, Advances in Elliptic Curve Cryptography. Cambridge Univ. Press, 2005.
22. A. Shamir, "Identity-Based Cryptosystems and Signature Schemes," Proc. Int'l Cryptology Conf. (Crypto '85), vol. 196, pp. 47-53, 1985.
23. K. Fong, D. Hankerson, J. López, and A. Menezes, "Field Inversion and Point Halving Revisited," Technical Report CORR 2003-18, Univ. of Waterloo, 2003.
24. D. Boneh and M. Franklin, "Identity Based Encryption from the Weil Pairing," Proc. Int'l Cryptology Conf. (Crypto '01), pp. 213-229, 2001.
25. R. Sakai, K. Ohgishi, and M. Kasahara, "Cryptosystems Based on Pairing," Proc. Symp. Cryptography and Information Security (SICS '00), pp. 26-28, 2000.
26. A. Karatsuba and Y. Ofman, "Multiplication on Many-Digit Numbers by Automatic Computers," Translation in Physics-Doklady, vol. 7, pp. 595-596, 1963.
27. L. Song and K.K. Parhi, "Efficient Finite Field Serial/Parallel Multiplication," Proc. Int'l Conf. Application Specific Systems, Architectures and Processors (ASAP '96), pp. 72-82, 1996.
28. LiDIA, A C++ Library for Computational Number Theory, http:// www.informatik.tu-darmstadt.de/TI/LiDIA, 2009.
29. m) Using Normal Bases," Information and Computation, vol. 78, pp. 171-177, 1988.
30. Silicon Graphics, Inc., Reconfigurable Application-Specific Computer User's Guide. 2008.
31. Maplesoft, Inc., http://www.maplesoft.com, 2009.
32. A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1997.