Computing the Tate pairing

Lecture Notes in Computer Science

Volumn 3376, Issue , 2005, Pages 293-304

  Scott, Michael ^a  

^a DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

Elliptic curves; Pairing based cryptosystems

Indexed keywords

COMPUTATION THEORY; OPTIMIZATION;

ELLIPTIC CURVES; PAIRING-BASED CRYPTOSYSTEMS; TATE PAIRING;

CRYPTOGRAPHY;

EID: 24144479376     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-30574-3_20     Document Type: Conference Paper

References (29)

1. P. S. L. M. Barreto. The pairing-based crypto lounge, 2004. http://planeta.terra.com.br/informatica/paulobarreto/pblounge.html.
2. P.S.L.M. Barreto, H.Y. Kim, B. Lynn, and M. Scott. Efficient algorithms for pairing-based cryptosystems. In Advances in Cryptology - Crypto'2002, volume 2442 of Lecture Notes in Computer Science, pages 354-68. Springer-Verlag, 2002.
3. P.S.L.M. Barreto, B. Lynn, and M. Scott. Constructing elliptic curves with prescribed embedding degrees. In Security in Communication Networks - SCN'2002, volume 2576 of Lecture Notes in Computer Science, pages 263-273. Springer-Verlag, 2002.
4. P.S.L.M. Barreto, B. Lynn, and M. Scott. On the selection of pairing-friendly groups. In Selected Areas in Cryptography - SAC 2003, volume 3006 of Lecture Notes in Computer Science, pages 17-25. Springer-Verlag, 2003.
5. I. F. Blake, G. Seroussi, and N. P. Smart, editors. Advances in Elliptic Curve Cryptography, Volume 2. Cambridge University Press, 2005.
6. D. Boneh and M. Franklin. Identity-based encryption from the Weil pairing. SIAM Journal of Computing, 32(3):586-615, 2003.
7. D. Boneh, B. Lynn, and H. Shacham. Short signatures from the Weil pairing. In Advances in Cryptology - Asiacrypt'2001, volume 2248 of Lecture Notes in Computer Science, pages 514-532. Springer-Verlag, 2002.
8. F. Brezing and A. Weng. Elliptic curves suitable for pairing based cryptography. Cryptology ePrint Archive, Report 2003/143, 2003. Available from http://eprint.iacr.org/2003/143.
9. E. F. Brickell, D. M. Gordon, K. S. McCurley, and D. B. Wilson. Fast exponentiation with precomputation: Algorithms and lower bounds. In Advances in Cryptology - Eurocrypt'92, volume 658 of Lecture Notes in Computer Science, pages 200-207. Springer-Verlag, 1993.
10. R. Dupont, A. Enge, and F. Morain. Building curves with arbitrary small MOV degree over finite prime fields. Cryptology ePrint Archive, Report 2002/094, 2002. http://sprint.iacr.org/2002/094.
11. R. Dutta, R. Barua, and P. Sarkar. Pairing-based cryptography: A survey. Cryptology ePrint Archive, Report 2004/064, 2004. http://eprint.iacr.org/2004/064.
12. I. Duursma and H.-S. Lee. Tate-pairing implementations for tripartite key agreement. In Advances in Cryptology - Asiacrypt 2003, volume 2894 of Lecture Notes in Computer Science, pages 111-123. Springer-Verlag, 2003.
13. S. Galbraith, K. Harrison, and D. Soldera. Implementing the Tate pairing. In Algorithm Number Theory Symposium - ANTS V, volume 2369 of Lecture Notes in Computer Science, pages 324-337. Springer-Verlag, 2002.
14. IEEE Std 1363-2000. Standard specifications for public-key cryptography. IEEE P1363 Working Group, 2000.
15. T. Izu and T. Takagi. Efficient computations of the Tate pairing for the large MOV degrees. In ICISC 2002, volume 2587 of Lecture Notes in Computer Science, pages 283-297, 2003.
16. M. Joye and S. Yen. The Montgomery powering ladder. In Cryptographic Hardware and Embedded Systems - CHES 2002, volume 2523 of Lecture Notes in Computer Science, pages 291-302, Berlin, Germany, 2003. Springer-Verlag.
17. P. Kocher, J. Jaffe, and B. Jun. Introduction to differential power analysis and related attacks, 1998. http://www.cryptography.com/dpa/technical.
18. W. Mao and K. Harrison. Divisors, bilinear pairings, and pairing enabled cryptographic applications, 2003. http://hplbwww.hpl.hp.com/people/wm/research/pairing.pdf.
19. N. McCullagh. Personal Communication, 2004.
20. A. Menezes. Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, 1993.
21. A. Miyaji, M. Nakabayashi, and S. Takano. New explicit conditions of elliptic curve traces for FR-reduction. IEICE Transactions on Fundamentals, E84-A(5):1234-1243, 2001.
22. R. Sakai and M. Kasahara. ID based cryptosystems with pairing on elliptic curve. Cryptography ePrint Archive, Report 2003/054, 2003. http://eprint.iacr.org/2003/054.
23. M. Scott, 2002. http://ftp.compapp.dcu.ie/pub/crypto/cm.exe.
24. M. Scott, 2002. http://www.computing.dcu.ie/~mike/tate.html.
25. M. Scott and P. Barreto. Compressed pairings. In Advances in Cryptology - Crypto' 2004, volume 3152 of Lecture Notes in Computer Science, pages 140-156. Springer-Verlag, 2004. Also available from http://eprint.iacr.org/2004/032/.
26. M. Scott and P. Barreto. Generating more MNT elliptic curves. Cryptology ePrint Archive, Report 2004/058, 2004. Available from http://eprint.iacr.org/2004/058/.
27. I. Semaev. Summation polynomials and the discrete logarithm problem on elliptic curves. Cryptography ePrint Archive, Report 2004/031, 2003. http://eprint.iacr.org/2004/031/.
28. N. P. Smart. An identity based authenticated key agreement protocol based on the Weil pairing. Electronics Letters, 38:630-632, 2002.
29. J. Solinas. ID-based digital signature algorithms, 2003. http://www.cacr.math.uwaterloo.ca/conferences/2003/ecc2003/solinas.pdf.