FPGA and ASIC implementations of the ηT pairing in characteristic three

Computers and Electrical Engineering

Volumn 36, Issue 1, 2010, Pages 73-87

  Beuchat, Jean Luc ^a   Doi, Hiroshi ^b   Fujita, Kaoru ^c   Inomata, Atsuo ^d   Ith, Piseth ^a   Kanaoka, Akira ^a   Katouno, Masayoshi ^c   Mambo, Masahiro ^a   Okamoto, Eiji ^a   Okamoto, Takeshi ^e   Shiga, Takaaki ^f   Shirase, Masaaki ^g   Soga, Ryuji ^c   Takagi, Tsuyoshi ^g   Vithanage, Ananda ^f   Yamamoto, Hiroyasu ^c  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b INSTITUTE OF INFORMATION SECURITY   (Japan)

^c FDK Module System Technology Corporation   (Japan)

^d NARA INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^e TSUKUBA UNIVERSITY OF TECHNOLOGY   (Japan)

^f FDK CORPORATION   (Japan)

^g FUTURE UNIVERSITY HAKODATE   (Japan)

Author keywords

T pairing; Elliptic curve cryptography; Finite field arithmetic; Hardware accelerator; Tate pairing

Indexed keywords

CHARACTERISTIC THREE; CO-PROCESSORS; CRYPTOGRAPHIC APPLICATIONS; EFFICIENT IMPLEMENTATION; ELLIPTIC CURVE; ELLIPTIC CURVE CRYPTOGRAPHY; FINITE FIELD ARITHMETIC; HARDWARE ACCELERATORS; RESEARCH AREAS; SUPERSINGULAR ELLIPTIC CURVE; TATE PAIRING;

APPLICATION SPECIFIC INTEGRATED CIRCUITS; ELECTRIC POWER SUPPLIES TO APPARATUS; FIELD PROGRAMMABLE GATE ARRAYS (FPGA); GEOMETRY;

CRYPTOGRAPHY;

EID: 72449191229     PISSN: 00457906     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compeleceng.2009.05.001     Document Type: Article

References (49)

1. p. In: Proceedings of the 4th international conference on information technology: new generations (ITNG'08). IEEE Computer Society; 2008.
2. Barreto PSLM. A note on efficient computation of cube roots in characteristic 3. Cryptology ePrint archive, report 2004/305, 2004.
3. Barreto P.S.L.M., Galbraith S.D., ÓhÉigeartaigh C., and Scott M. Efficient pairing computation on supersingular Abelian varieties. Design Code Cryptogr 42 (2007) 239-271
4. Barreto P.S.L.M., Kim H.Y., Lynn B., and Scott M. Efficient algorithms for pairing-based cryptosystems. In: Yung M. (Ed). Advances in cryptology - CRYPTO 2002. Lecture notes in computer science vol. 2442 (2002), Springer 354-368
5. Bertoni G, Breveglieri L, Fragneto P, Pelosi G. Parallel hardware architectures for the cryptographic Tate pairing. In: Proceedings of the 3rd international conference on information technology: new generations (ITNG'06). IEEE Computer Society; 2006.
6. 3m. In: Galbraith S.D., and Paterson K.G. (Eds). Proceedings of pairing 2008, Lecture Notes in Computer Science Vol. 5209 (2008), Springer-Verlag, Berlin Heidelberg 297-315
7. T pairing in characteristic three. IEEE Trans Comput 57 11 (2008) 1454-1468
8. T pairing in characteristic three. In: Carlet C., and Sunar B. (Eds). Proceedings of Waifi 2007. Lecture notes in computer science vol. 4547 (2007), Springer 25-39
9. n): a survey. Int J Electron 95 7 (2008) 669-684
10. T pairing calculation in characteristic three and its hardware implementation. In: Kornerup P, Muller J-M, editors. Proceedings of the 18th IEEE symposium on computer arithmetic. IEEE Computer Society; 2007. p. 97-104.
11. Boneh D., and Franklin M. Identity-based encryption from the Weil pairing. In: Kilian J. (Ed). Advances in cryptology - CRYPTO 2001. Lecture notes in computer science vol. 2139 (2001), Springer 213-229
12. Boneh D., Gentry C., and Waters B. Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup V. (Ed). Advnces in cryptology - CRYPTO 2005. Lecture notes in computer science vol. 3621 (2005), Springer 258-275
13. Boneh D., Lynn B., and Shacham H. Short signatures from the Weil pairing. In: Boyd C. (Ed). Advances in cryptology - ASIACRYPT 2001. Lecture notes in computer science vol. 2248 (2001), Springer 514-532
14. Dutta R, Barua R, Sarkar P. Pairing-based cryptographic protocols: a survey. Cryptology ePrint archive, report 2004/64, 2004.
15. p - x + d. In: Laih C.S. (Ed). Advances in cryptology- ASIACRYPT 2003. Lecture notes in computer science vol. 2894 (2003), Springer 111-123
16. m). Acta Appl Math 93 1-3 (2006) 33-55
17. Fong K., Hankerson D., López J., and Menezes A. Field inversion and point halving revisited. IEEE Trans Comput 53 8 (2004) 1047-1059
18. Frey G., and Rück H.-G. A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math Comput 62 206 (1994) 865-874
19. Galbraith S.D., Harrison K., and Soldera D. Implementing the Tate pairing. In: Fieker C., and Kohel D.R. (Eds). Algorithmic number theory - ANTS V. Lecture notes in computer science vol. 2369 (2002), Springer 324-337
20. 36 m. In: Adams C., Miri A., and Wiener M. (Eds). Selected areas in cryptography - SAC 2007. Lecture notes in computer science vol. 4876 (2007), Springer 173-183
21. Grabher P., and Page D. Hardware acceleration of the Tate pairing in characteristic three. In: Rao J.R., and Sunar B. (Eds). Cryptographic hardware and embedded systems - CHES 2005. Lecture notes in computer science vol. 3659 (2005), Springer 398-411
22. Granger R., Page D., and Smart N.P. High security pairing-based cryptography revisited. In: Hess F., Pauli S., and Pohst M. (Eds). Algorithmic number theory - ANTS VII. Lecture notes in computer science vol. 4076 (2006), Springer 480-494
23. Granger R., Page D., and Stam M. On small characteristic algebraic tori in pairing-based cryptography. LMS J Comput Math 9 (2006) 64-85
24. Guajardo J., Güneysu T., Kumar S., Paar C., and Pelzl J. Efficient hardware implementation of finite fields with applications to cryptography. Acta Appl Math 93 1-3 (2006) 75-118
25. Hess F., Smart N., and Vercauteren F. The Eta pairing revisited. IEEE Trans Inform Theory 52 10 (2006) 4595-4602
26. m) using normal bases. Inform Comput 78 (1988) 171-177
27. Jiang J. Bilinear pairing (Eta_T pairing) IP core. Technical report, City University of Hong Kong, Department of Computer Science; May 2007.
28. Joux A. A one round protocol for tripartite Diffie-Hellman. In: Bosma W. (Ed). Algorithmic number theory - ANTS IV. Lecture notes in computer science vol. 1838 (2000), Springer 385-394
29. m) Tate pairing architecture. In: Bertels K., Cardoso J.M.P., and Vassiliadis S. (Eds). International workshop on applied reconfigurable computing (ARC 2006). Lecture notes in computer science vol. 3985 (2006), Springer 358-369
30. m). Comput Electr Eng 33 5-6 (2007) 392-406
31. Kerins T., Marnane W.P., Popovici E.M., and Barreto P.S.L.M. Efficient hardware for the Tate pairing calculation in characteristic three. In: Rao J.R., and Sunar B. (Eds). Cryptographic hardware and embedded systems - CHES 2005. Lecture notes in computer science vol. 3659 (2005), Springer 412-426
32. Koblitz N., and Menezes A. Pairing-based cryptography at high security levels. In: Smart N.P. (Ed). Cryptography and coding. Lecture notes in computer science vol. 3796 (2005), Springer 13-36
33. Kömürcü G, Savas E. An efficient hardware implementation of the Tate pairing in characteristic three. In: Prasolova-Førland E, Popescu M, editors. Proceedings of the 3rd international conference on systems - ICONS 2008. IEEE Computer Society; 2008. p. 23-8.
34. Kwon S. Efficient Tate pairing computation for elliptic curves over binary fields. In: Boyd C., and González Nieto J.M. (Eds). Information security and privacy - ACISP 2005. Lecture notes in computer science vol. 3574 (2005), Springer 134-145
35. Li H., Huang J., Sweany P., and Huang D. FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field. J Syst Archit 54 (2008) 1077-1088
36. Menezes A., Okamoto T., and Vanstone S.A. Reducing elliptic curves logarithms to logarithms in a finite field. IEEE Trans Infor Theory 39 5 (1993) 1639-1646
37. Miller VS. Short programs for functions on curves, 1986. Available from: http://crypto.stanford.edu/miller
38. Miller V.S. The Weil pairing, and its efficient calculation. J Cryptol 17 4 (2004) 235-261
39. Mitsunari S., Sakai R., and Kasahara M. A new traitor tracing. IEICE Trans Fund E85-A 2 (2002) 481-484
40. ÓhÉigeartaigh C. Pairing computation on hyperelliptic curves of genus 2. PhD thesis, Dublin City University; 2006.
41. T pairing. Int J High Perform Syst Archit 1 2 (2007) 79-88
42. Ronan R, ÓhÉigeartaigh C, Murphy C, Scott M, Kerins T. FPGA acceleration of the Tate pairing in characteristic 2. In: Proceedings of the IEEE international conference on field programmable technology - FPT 2006. IEEE; 2006. p. 213-20.
43. Ronan R., ÓhÉigeartaigh C., Murphy C., Scott M., and Kerins T. Hardware acceleration of the Tate pairing on a genus 2 hyperelliptic curve. J Syst Archit 53 (2007) 85-98
44. Sakai R, Ohgishi K, Kasahara M. Cryptosystems based on pairing. In: 2000 Symposium on cryptography and information security (SCIS2000). Okinawa, Japan; January 2000. p. 26-8.
45. Shu C, Kwon S, Gaj K. FPGA accelerated Tate pairing based cryptosystem over binary fields. In: Proceedings of the IEEE international conference on field programmable technology - FPT 2006. IEEE; 2006. p. 173-80.
46. Silverman J.H. The arithmetic of elliptic curves. Graduate texts in mathematics vol. 106 (1986), Springer-Verlag
47. Song L., and Parhi K.K. Low energy digit-serial/parallel finite field multipliers. J VLSI Signal Process 19 2 (1998) 149-166
48. Verheul E.R. Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. J Cryptol 17 4 (2004) 277-296
49. Washington L.C. Elliptic curves - number theory and cryptography. 2nd ed. (2008), CRC Press