Efficient Tate pairing computation using double-base chains

Science in China, Series F: Information Sciences

Volumn 51, Issue 8, 2008, Pages 1096-1105

  Zhao, ChangAn ^a   Zhang, FangGuo ^a   Huang, JiWu ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Double base chains; Elliptic curves; Public key cryptography; Tate pairing

Indexed keywords

EID: 46749149989     PISSN: 10092757     EISSN: 18622836     Source Type: Journal    
DOI: 10.1007/s11432-008-0070-9     Document Type: Article

References (29)

1. Menezes A, Okamoto T, Vanstone S. Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans Inf Theory, 1993, 39: 1639-1646
2. Frey G, Rück H. A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math Comp, 1994, 52: 865-874
3. Joux A. A one round protocol for tripartite Diffie-Hellman. In: Goos G, Hartmanis J, Leeuwen V J, eds. Algorithm Number Theory Symposium-ANTS IV. Berlin/Heidelberg: Springer-Verlag, 2000, LNCS 1838: 385-394
4. Sakai R, Ohgishi K, Kasahara M. Cryptosystems based on pairing. In: Symposium on Cryptography and Information Security-SCIS'2000, Okinawa, Japan, Jan. 2000. 26-28
5. Boneh D, Franklin M. Identity-based encryption from the Weil pairing. In: Proceeding of Advances in Cryptology-Crypto'2001. Berlin/Heidelberg: Springer-Verlag, 2001. LNCS 2139: 213-229
6. Waters B. Efficient identity-based encryption without random oracles. In: Proceeding of Advances in Cryptology-Eurocrypt' 2005. Berlin/Heidelberg: Springer-Verlag, 2005, LNCS 3494: 114-127
7. Boneh D, Boyen X. Secure identity based encryption without random oracles. In: Proceeding of Advances in Cryptology-Crypto'2004. Berlin/Heidelberg: Springer-Verlag, 2004. LNCS 3152: 443-459
8. Boneh D, Lynn B, Shacham H. Short signatures from the Weil pairing. In: Advances in Cryptology-Asiacrypt'2001. Berlin/Heidelberg: Springer-Verlag, 2001, LNCS 2248: 514-532
9. Zhang F, Safavi-Naini R, Susilo W. An efficient signature scheme from bilinear pairings and its applications. In: Proceeding of PKC'2004. Berlin/Heidelberg: Springer-Verlag, 2004. LNCS 2947: 277-290
10. Boneh D, Boyen X. Short signatures without random oracles. In: Proceeding of Advances in Cryptology-Eurocrypt'2004. Berlin/Heidelberg: Springer-Verlag, 2004, LNCS 3027: 56-73
11. Boneh D, Boyen X, Shacham H. Short group signatures. In: Proceeding of Advances in Cryptology-Crypto'2004. Berlin/ Heidelberg: Springer-Verlag, 2004. LNCS 3152: 41-55
12. Miller V S. Short programs for functions on curves, unpublished manuscript, 1986
13. Barreto P S L M, Kim H Y, Lynn B, et al. Efficient algorithms for pairing-based cryptosystems. In: Proceeding of Advances in Cryptology- Crypto'2002. Berlin/Heidelberg: Springer-Verlag, 2002, LNCS 2442: 354-368
14. Galbraith S D, Harrison K, Soldera D. Implementing the Tate pairing. In: Proceeding of Algorithm Number Theory Symposium-ANTS V. Berlin/Heidelberg: Springer-Verlag, 2002, LNCS 2369: 324-337
15. p - x + d. In: Proceeding of Advances in Cryptology-Asiacrypt'2003. Berlin/Heidelberg: Springer-Verlag, 2003, LNCS 2894: 111-123
16. Eisenträer K, Lauter K, Montgomery P L. Fast elliptic curve arithmetic and improvedWeil pairing evaluation. In: Proceeding of CT-RSA'2003. Berlin/Heidelberg: Springer-Verlag, 2003, LNCS 2612: 343-354
17. Hu L, Dong J, Pei D. An implementation of cryptosystems based on Tate pairing. J Comp Sci Tech, 2005, 20: 264-269
18. Blake I, Murty K, Xu G. Refinements of Miller's algorithm for computing Weil/Tate pairing. J Algor, 2006, 58: 134-149
19. Izu T, Takagi T. Efficient computations of the Tate pairing for the large MOV degrees. In: proceeding of ICISC'02. Berlin/Heidelberg: Springer-Verlag, 2003. LNCS 2587: 283-297
20. Karatsuba A, Ofman Y. Multiplication on Many-Digittal Numbers by Automatic Computers. Sov Trans Phys-Doklady, 1963, 7: 595-596
21. Kobayashi T, Aoki K, Imai H. Efficient algorithms for Tate pairing. IEICE Trans Fundam, 2006, E89-A(1): 134-143
22. Barreto P S L M, Galbraith S, ÓhÉigeartaigh C. et al. Efficient pairing computation on supersingular abelian varieties. Des Cod Crypto, 2007, 42(3): 239-271
23. Hess F, Smart N P, Vercauteren F. The Eta pairing revisited. IEEE Trans Inf Theory, 2006, 52: 4595-4602
24. Muir J A, Stinson D R. On the low hamming weight discrete logarithm problem for nonadjacent representations. Appl Alg Eng, Commun Comput, 2006, 16: 461-472
25. Silverman J H. The Arithmetic of Elliptic Curves. New York: Springer-Verlag, 1986. 31-34
26. Dimitrov V S, Imbert L, Mishra P K. Efficient and secure elliptic curve point multiplication using double-base chains. In: Proceeding of Advances in Cryptology-Asiacrypt'2005. Berlin/Heidelberg: Springer-Verlag, 2005, LNCS 3788: 59-78
27. Galbraith S D. Pairings-Advances in Elliptic Curve Cryptography. Cambridge: Cambridge University Press, 2005
28. Ciet M, Joye M, Lauter K, et al. Trading inversions for multiplications in elliptic curve cryptography. Des Cod Crypto, 2006, 39(2): 189-206
29. k P based on Montgomery Trick. IEICE Trans Fund, 2006, E89-A(1): 334-339