Compressed Pairings

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

Volumn 3152, Issue , 2004, Pages 140-156

  Scott, Michael ^a   Barreto, Paulo S L M ^b  

^a DUBLIN CITY UNIVERSITY   (Ireland)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Efficient implementation; Pairing based cryptosystem

Indexed keywords

PUBLIC KEY CRYPTOGRAPHY;

EFFICIENT IMPLEMENTATION; ELLIPTIC CURVE; EXPONENTIATIONS; PAIRING BASED CRYPTOSYSTEMS; PAIRING-BASED CRYPTOSYSTEM; POINT COMPRESSION; SPEED UP; WEIL PAIRING;

CRYPTOGRAPHY;

EID: 35048849890     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-28628-8_9     Document Type: Article

References (32)

1. 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 354-368, Santa Barbara, USA, 2002. Springer-Verlag.
2. 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, Amalfi, Italy, 2002. Springer-Verlag.
3. P. S. L. M. Barreto, B. Lynn, and M. Scott. On the selection of pairing-friendly groups. In Selected Areas in Cryptography - SAC'2003, Ottawa, Canada, 2003. to appear.
4. D. Bleichenbacher, W. Bosma, and A. K. Lenstra. Some remarks on lucas-based cryptosystems. In Advances in Cryptology - Crypto'95, volume 963 of Lecture Notes in Computer Science, pages 386-396, Santa Barbara, USA, 1995. Springer-Verlag.
5. D. Boneh and M. Franklin. Identity-based encryption from the Weil pairing. SIAM Journal of Computing, 32(3):586-615, 2003.
6. 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, Gold Coast, Australia, 2002. Springer-Verlag.
7. 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.
8. A. E. Brouwer, R. Pellikaan, and E. R. Verheul. Doing more with fewer bits. In Advances in Cryptology - Asiacrypt'99, volume 1716 of Lecture Notes in Computer Science, pages 321-332, Singapore, 1999. Springer-Verlag.
9. L. Carlitz. Recurrences of the third order and related combinatorial identities. Fibonacci Quarterly, 16(1):11-18, 1978.
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. Available from http://eprint.iacr.org/2002/094.
11. p-x+d. In Advances in Cryptology - Asiacrypt'2003, volume 2894 of Lecture Notes in Computer Science, pages 111-123, Taipei, Taiwan, 2003. Springer-Verlag.
12. S. Galbraith, K. Harrison, and D. Soldera. Implementing the Tate pairing. In Algorithmic Number Theory Symposium - ANTS V, volume 2369 of Lecture Notes in Computer Science, pages 324-337, Sydney, Australia, 2002. Springer-Verlag.
13. S. Galbraith, K. Harrison, and D. Soldera. Using primitive subgroups to do more with fewer bits. In Algorithmic Number Theory Symposium - ANTS VI, volume 3076 of Lecture Notes in Computer Science, pages 18-41, Annapolis, USA, 2004. Springer-Verlag.
14. S. Galbraith, H. Hopkins, and I. Shparlinski. Secure bilinear diffie-hellman bits. Cryptology ePrint Archive, Report 2002/155, 2002. Available from http: //eprint.iacr.org/2002/155.
15. D. Gordon. A survey of fast exponentiation methods. Journal of Algorithms, 27:129-146, 2002.
16. K. Huffman and R. Kunze. Linear Algebra. Prentice Hall, New Jersey, USA, 2nd edition, 1971.
17. A. Joux. A one-round protocol for tripartite Diffie-Hellman. In Algorithmic Number Theory Symposium - ANTS IV, volume 1838 of Lecture Notes in Computer Science, pages 385-394, Leiden, The Netherlands, 2000. Springer-Verlag.
18. M. Joye and J. J. Quisquater. Efficient computation of full Lucas sequences. Electronics Letters, 32(6):537-538, 1996.
19. 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.
20. D. H. Lehmer. Computer technology applied to the theory of numbers. In W. J. LeVeque, editor, Studies in Number Theory, volume 6 of MAA Studies in Mathematics, pages 117-151. Math. Assoc. Amer, (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1969.
21. A. K. Lenstra and E. R. Verheul. The xtr public key system. In Advances in Cryptology - Crypto'2000, volume 1880 of Lecture Notes in Computer Science, pages 1-19, Santa Barbara, USA, 2000. Springer-Verlag.
22. R. Lidl and H. Niederreiter. Finite Fields. Number 20 in Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, UK, 2nd edition, 1997.
23. A. Menezes. Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, 1993.
24. V. S. Miller. Short programs for functions on curves. Unpublished manuscript, 1986. Available from http://crypto.stanford.edu/miller/miller.pdf.
25. V. S. Miller. Use of elliptic curves in cryptography. In Advances in Cryptology - Crypto'85, volume 218 of Lecture Notes in Computer Science, pages 417-426, Santa Barbara, USA, 1986. Springer-Verlag.
26. 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.
27. P. L. Montgomery. Speeding the pollard and elliptic curve methods of factorization. Mathematics of Computation, 48(177):243-264, 1987.
28. D. Nalla and K. C. Reddy. Signcryption scheme for identity-based cryptosystems. Cryptology ePrint Archive, Report 2003/066, 2002. Available from http: //eprint.iacr.org/2003/066.
29. J. H. Silverman. The Arithmetic of Elliptic Curves. Number 106 in Graduate Texts in Mathematics. Springer-Verlag, Berlin, Germany, 1986.
30. N. P. Smart. An identity based authenticated key agreement protocol based on the weil pairing. Electronics Letters, 38:630-632, 2002.
31. M. Stam and A. K. Lenstra. Speeding up XTR. In Advances in Cryptology -Asiacrypt'2001, volume 2248 of Lecture Notes in Computer Science, pages 125-143, Gold Coast, Australia, 2001. Springer-Verlag.
32. S. M. Yen and C. S. Laih. Fast algorithms for LUG digital signature computation. IEE Proceedings on Computers and Digital Techniques, 142(2): 165-169, 1995.