Arithmetic operators for pairing-based cryptography

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4727 LNCS, Issue , 2007, Pages 239-255

  Beuchat, Jean Luc ^a   Brisebarre, Nicolas ^b,c   Detrey, Jérémie ^c   Okamoto, Eiji ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b UNIVERSITÉ JEAN MONNET   (France)

^c UNIV LYON   (France)

Author keywords

Elliptic curve; Finite field arithmetic; FPGA; Hardware accelerator; T pairing

Indexed keywords

COMPUTER HARDWARE; CRYPTOGRAPHY; FIELD PROGRAMMABLE GATE ARRAYS (FPGA); PROGRAM PROCESSORS;

ELLIPTIC CURVES; FINITE FIELD ARITHMETIC; HARDWARE ACCELERATORS;

MATHEMATICAL OPERATORS;

EID: 38049036820     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-74735-2_17     Document Type: Conference Paper

References (32)

1. Barreto, P.S.L.M.: A note on efficient computation of cube roots in characteristic 3. Cryptology ePrint Archive, Report 2004/305 (2004)
2. Barreto, P.S.L.M., Galbraith, S., Ó hÉigeartaigh, C., Scott, M.: Efficient pairing computation on supersingular Abelian varieties. Cryptology ePrint Archive, Report 2004/375 (2004)
3. Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354-368. Springer, Heidelberg (2002)
4. Bertoni, G., Breveglieri, L., Fragneto, P., Pelosi, G.: Parallel hardware architectures for the cryptographie Tate pairing. In: Proceedings of the Third International Conference on Information Technology: New Generations (ITNG'06). IEEE Computer Society Press, Los Alamitos (2006)
5. m) arithmetic architectures for cryptographic applications. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 158-175. Springer, Heidelberg (2003)
6. T pairing in characteristic three. Cryptology ePrint Archive, Report 2007/045 (2007)
7. T pairing calculation in characteristic three and its hardware implementation. Cryptology ePrint Archive, Report 2006/327 (2006)
8. Cohen, H., Frey, G. (eds.): Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall/CRC (2005)
9. Dutta, R., Barua, R., Sarkar, P.: Pairing-based cryptographic protocols: A survey. Cryptology ePrint Archive, Report 2004/64 (2004)
10. p - x + d. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 111-123. Springer, Heidelberg (2003)
11. Frey, G., Rück, H.-G.: A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Mathematics of Computation 62(206), 865-874 (1994)
12. Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) Algorithmic Number Theory. LNCS, vol. 2369, pp. 324-337. Springer, Heidelberg (2002)
13. Grabher, P., Page, D.: Hardware acceleration of the Tate Pairing in characteristic three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 398-411. Springer, Heidelberg (2005)
14. Granger, R., Page, D., Smart, N.P.: High security pairing-based cryptography. Cryptology ePrint Archive, Report 2006/059 (2006)
15. m) using normal bases. Information and Computation 78, 171-177 (1988)
16. Joux, A.: A One Round Protocol for Tripartite Diffie-Hellman. In: Bosma, W. (ed.) Algorithmic Number Theory. LNCS, vol. 1838, pp. 385-394. Springer, Heidelberg (2000)
17. Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Efficient hardware for the Tate Pairing calculation in characteristic three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 412-426. Springer, Heidelberg (2005)
18. Kerins, T., Popovici, E., Marnane, W.: Algorithms and architectures for use in FPGA implementations of identity based encryption schemes. In: Becker, J., Platzner, M., Vernalde, S. (eds.) FPL 2004. LNCS, vol. 3203, pp. 74-83. Springer, Heidelberg (2004)
19. Knuth, D.E.: The Art of Computer Programming, 3rd edn., vol. 2. Addision-Wesley, Reading (1998)
20. Koblitz, N., Menezes, A.: Pairing-based cryptography at high security levels. In: Smart, N.P. (ed.) Cryptography and Coding. LNCS, vol. 3796, pp. 13-36. Springer, Heidelberg (2005)
21. Kwon, S.: Efficient Tate pairing computation for supersingular elliptic curves over binary fields. Cryptology ePrint Archive, Report 2004/303 (2004)
22. Menezes, A., Okamoto, T., Vanstone, S.A.: Reducing elliptic curves logarithms to logarithms in a finite field. IEEE Transactions on Information Theory 39(5), 1639-1646 (1993)
23. Rodríguez-Henríquez, F., Morales-Luna, G., Saqib, N.A., Cruz-Cortés, N.: A parallel version of the Itoh-Tsujii multiplicative inversion algorithm. In: Diniz, P.C., Marques, E., Berteis, K., Fernandes, M.M., Cardoso, J.M.P. (eds.) Reconfigurable Computing: Architectures, Tools and Applications - Proceedings of ARC 2007. LNCS, vol. 4419, pp. 226-237. Springer, Heidelberg (2007)
24. Rodríguez-Henríquez, F., Saqib, N.A., Pérez, A.D., Koç, Ç.K.: Cryptographic Algorithms on Reconfigurable Hardware. Springer, Heidelberg (2006)
25. T pairing in characteristic 3. Cryptology ePrint Archive, Report 2006/371(2006)
26. T pairing. Cryptology ePrint Archive, Report 2006/431 (2006)
27. Shu, C., Kwon, S., Gaj, K.: FPGA accelerated Tate pairing based cryptosystem over binary fields. Cryptology ePrint Archive, Report 2006/179 (2006)
28. Silverman, J.H.: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106. Springer, Heidelberg (1986)
29. Song, L., Parhi, K.K.: Low energy digit-serial/parallel finite field multipliers. Journal of VLSI Signal Processing 19(2), 149-166 (1998)
30. Thurber, E.G.: Efficient generation of minimal length addition chains. Journal on Computing 28(4), 1247-1263 (1999)
31. Verheul, E.R.: Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. Journal of Cryptology 17(4), 277-296 (2004)
32. von zur Gathen, J., Nöcker, M.: Computing special powers in finite fields. Mathematics of Computation 73(247), 1499-1523 (2003)