By Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.)
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"The e-book comprises 39 articles approximately computational algebraic quantity idea, mathematics geometry and cryptography. … The articles during this publication mirror the vast curiosity of the organizing committee and the individuals. The emphasis lies at the mathematical conception in addition to on computational effects. we suggest the ebook to scholars and researchers who are looking to examine present learn in quantity concept and mathematics geometry and its applications." (R. Carls, Nieuw Archief voor Wiskunde, Vol. 6 (3), 2005)
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Additional resources for Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 Proceedings
Chaum and T. P. Pedersen. Wallet databases with observers. In Ernest F. Brickell, editor, Advances in Cryptology - Crypto ’92, volume 740 of Lecture Notes in Comput. , pages 89–105, Berlin, 1992. Springer-Verlag. 11. D. Chaum and H. van Antwerpen. Undeniable signatures. In Gilles Brassard, editor, Advances in Cryptology - Crypto ’89, volume 435 of Lecture Notes in Comput. , pages 212–217, Berlin, 1989. Springer-Verlag. 12. Q. Cheng and S. Uchiyama. Nonuniform polynomial time algorithm to solve decisional Diﬃe–Hellman problem in ﬁnite ﬁelds under conjecture.
The discrete logarithm problem on elliptic curves of trace one. Journal of Cryptology, 12(3):193–196, 1999. 38. E. Verheul. Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. In B. Pﬁzmann, editor, Proceedings of EUROCRYPT’2001, volume 2045 of Lecture Notes in Comput. , pages 195–210. Springer, 2001. 39. E. Verheul. Self-blindable credential certiﬁcates from the Weil pairing. In C. Boyd, editor, Proceedings of ASIACRYPT’2001, volume 2248 of Lecture Notes in Comput.
As a consequence, using ﬁelds of small characteristic might be less secure than ﬁelds of large characteristic. This worry is expressed in the updated version of , where a solution is proposed. Since supersingular curves in large characteristic cannot have security parameter 6, Boneh, Lynn and Shacham propose to use complex multiplication in order to construct curves of cardinality l2 − l + 1 over Fq , with q = l2 + 1 prime. Assuming that is a large prime dividing l2 − l + 1, the –roots of unity can be embedded in Fq6 (and not in smaller extensions).
Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 Proceedings by Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.)