Simplified pairing computation and security implications

Journal of Mathematical Cryptology

Volumn 1, Issue 3, 2007, Pages 267-281

  Galbraith, Steven D ^a   Éigeartaigh, Colm Ó ^b   Sheedy, Caroline ^b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

Pairings

Indexed keywords

EID: 47849090365     PISSN: 18622976     EISSN: 18622984     Source Type: Journal    
DOI: 10.1515/JMC.2007.013     Document Type: Article

References (22)

1. L.M. Adleman, J. DeMarrais, and M.-D. Huang, A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields. ANTS-I (L.M. Adleman and M.-D. Huang, eds.), Lecture Notes in Computer Science 877, pp. 28-40. Springer, 1994.
2. G. Ars, J.-C. Faugère, H. Imai, M. Kawazoe, and M. Sugita, Comparison between XL and Gröbner basis algorithms. ASIACRYPT 2004 (P.-J. Lee, ed.), Lecture Notes in Computer Science 3329, pp. 338-353. Springer, 2004.
3. P. S. L. M. Barreto, S. D. Galbraith, C. Ó hÉ igeartaigh, and M. Scott, Efficient pairing computation on supersingular abelian varieties, Designs, Codes and Cryptography 42 (2007), pp. 239-271. (Pubitemid 46384645)
4. I. Blake, G. Seroussi, and N. P. Smart, Advances in elliptic curve cryptography. Cambridge University Press, 2005.
5. W. Bosma, J.J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Journal of Symbolic Computation 24 (1997), pp. 235-265. (Pubitemid 127167874)
6. H. Cohen and G. Frey (eds.), Handbook of elliptic and hyperelliptic curve cryptography. Chapman and Hall/CRC, 2006.
7. D. A. Cox, J. B. Little, and D. O'Shea, Ideals, varieties and algorithms: an introduction to computational algebraic geometry and commutative algebra, UTM. Springer, 1992.
8. p-x+d. ASIACRYPT 2003 (C.-S. Laih, ed.), Lecture Notes in Computer Science 2894, pp. 111-123. Springer, 2003.
9. G. Frey and H.-G. Rück, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Mathematics of Computation 62 (1994), pp. 865-874.
10. S. D. Galbraith, K. Harrison, and D. Soldera, Implementing the Tate pairing. ANTS-V, (C. Fieker and D. R. Kohel, eds.), Lecture Notes in Computer Science 2369, pp. 324-337. Springer, 2002.
11. R. Granger, F. Hess, R. Oyono, N. Thériault, and F. Vercauteren, Ate pairing on hyperellip-tic curves. EUROCRYPT 2007, (M. Naor, ed.), Lecture Notes in Computer Science 4515, pp. 430-447. Springer, 2007.
12. F. Hess, N. P. Smart, and F. Vercauteren, The eta pairing revisited, IEEE Transactions on Information Theory 52 (2006), pp. 4595-4602. (Pubitemid 46445294)
13. A. Joux, The Weil and Tate pairings as building blocks for public key cryptosystems. ANTS-V (C. Fieker and D.R. Kohel, eds.), Lecture Notes in Computer Science 2369, pp. 20-32. Springer, 2002.
14. B.-G. Kang and J.-H. Park, Powered Tate pairing computation, Cryptology ePrint Archive, Report 2005/260.
15. U.M. Maurer and S. Wolf, The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms, SIAM Journal on Computing 28 (1999), pp. 1689-1721. (Pubitemid 129304148)
16. V. S. Miller, Short programs for functions on curves, Unpublished manuscript, http://crypto.stanford.edu/miller/miller.pdf, 1986.
17. D. Page and F. Vercauteren, A fault attack on pairing based cryptography, IEEE Transactions on Computers 55 (2006), pp. 1075-1080. (Pubitemid 44263807)
18. T. Satoh, On degrees of polynomial interpolations related to elliptic curves. Proceedings of WCC 2005, Bergen, Norway, March 2005, Lecture Notes in Computer Science 3969, pp. 155-163. Springer, 2006. (Pubitemid 44165461)
19. -, On polynomial interpolations related to Verheul homomorphisms, LMS Journal of Computation and Mathematics 9 (2006), pp. 135-158.
20. J. H. Silverman, The arithmetic of elliptic curves, GTM 106. Springer, 1986.
21. E. Verheul, Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. EUROCRYPT 2001 (B. Pfitzmann, ed.), 2045, pp. 195-210. Springer, 2001. (Pubitemid 33275833)
22. -, Evidence that XTR is more secure than supersingular elliptic curve cryptosystems, Journal of Cryptology 17 (2004), pp. 277-296. (Pubitemid 41201460)