Integer variable x-based ate pairing

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

Volumn 5209 LNCS, Issue , 2008, Pages 178-191

  Nogami, Yasuyuki ^a   Akane, Masataka ^b   Sakemi, Yumi ^a   Kato, Hidehiro ^a   Morikawa, Yoshitaka ^a  

^a OKAYAMA UNIVERSITY   (Japan)

^b MITSUBISHI ELECTRIC CORPORATION   (Japan)

Author keywords

Ate pairing; Miller's algorithm

Indexed keywords

CONTROL THEORY;

ATE PAIRING; INTERNATIONAL CONFERENCES; LOWER BOUNDS; MILLER'S ALGORITHM; NUMBER OF ITERATIONS; PAIRING-BASED CRYPTOGRAPHY;

CRYPTOGRAPHY;

EID: 52449098485     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85538-5_13     Document Type: Conference Paper

References (19)

1. Akane, M., Kato, H., Okimoto, T., Nogami, Y., Morikawa, Y.: An Improvement of Miller's Algorithm in Ate Pairing with Barreto-Naehrig Curve. In: Proc. of Computer Security Symposium 2007 (CSS 2007), pp. 489-494 (2007)
2. Akane, M., Kato, H., Okimoto, T., Nogami, Y., Morikawa, Y.: Efficient Parameters for Ate Pairing Computation with Barreto-Naehrig Curve. In: Proc. of Computer Security Symposium 2007 (CSS 2007), pp. 495-500 (2007)
3. Barreto, P.S.L.M., Naehrig, M.: Pairing-Friendly. Elliptic Curves of Prime Order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319-331. Springer, Heidelberg (2006)
4. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514-532. Springer, Heidelberg (2001)
5. Cohen, H., Frey, G.: Handbook of Elliptic and Hyperelliptic Curve Cryptography, Discrete Mathematics and Its Applications. Chapman & Hall CRC (2005)
6. Devegili, A.J., Scott, M., Dahab, R.: Implementing Cryptographic Pairings over Barreto-Naehrig Curves. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 197-207. Springer, Heidelberg (2007)
7. Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves (preprint, 2006), http://math.berkeley.edu/∼dfreeman/papers/ taxonomy.pdf
8. Galbraith, S.D., Scott, M.: Exponentiation in pairing-friendly groups using homomorphisms. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS. Springer, Heidelberg (to appear, 2008)
9. GNU MP, http://gmplib.org/
10. Hess, F., Smart, N., Vercauteren, F.: The Eta Pairing Revisited. IEEE Trans. Information Theory, 4595-4602 (2006)
11. m) Using Normal Bases. Inf. and Comp. 78, 171-177 (1988)
12. Kato, H., Nogami, Y., Yoshida, T., Morikawa, Y.: Cyclic Vector Multiplication Algorithm Based on a Special Class of Gauss Period Normal Basis. ETRI Journal 29(6), 769-778 (2007),http://etrij.etri.re.kr/Cyber/servlet/ BrowseAbstract?paperid=RP0702-0040
13. Knuth, D.: The Art of Computer Programming. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1981)
14. Lee, E., Lee, H., Park, C.: Efficient and Generalized Pairing Computation on Abelien Varieties, IACR ePrint archive, http://eprint.iacr.org/2008/040
15. Matsuda, S., Kanayama, N., Hess, F., Okamoto, E.: Optimised Versions of the Ate and Twisted Ate Pairings. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 302-312. Springer, Heidelberg (2007)
16. Nakanishi, T., Funabiki, N.: Verifier-Local Revocation Group Signature Schemes with Backward Unlinkability from Bilinear Maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 443-454. Springer, Heidelberg (2005)
17. p8. Memoirs of the Faculty of Engineering Okayama University 37(2), 73-88 (2003)
18. Sakemi, Y., Kato, H., Akane, M., Okimoto, T., Nogami, Y., Morikawa, Y.: An Improvement of Twisted Ate Pairing Using Integer Variable with Small Hamming Weight. In: The 2008 Symposium on Cryptography and Information Security (SCIS 2008), January 22-25 (2008)
19. Vercauteren, F.: Optimal Pairings, IACR ePrint archive, http://eprint.iacr.org/2008/096