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By Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.)

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"The publication includes 39 articles approximately computational algebraic quantity idea, mathematics geometry and cryptography. … The articles during this e-book replicate the huge curiosity of the organizing committee and the members. The emphasis lies at the mathematical thought in addition to on computational effects. we propose the publication to scholars and researchers who are looking to examine present study in quantity idea 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

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Pages 290–299. Springer, 2002. 13. Y. Choie, E. Jeong, and E. Lee. Supersingular hyperelliptic curve of genus 2 over finite fields. org, 2002. Number 2002/032. 14. C. Cocks. An identity based encryption scheme based on quadratic residues. Cryptography and Coding, 2001. pdf. 15. G. Frey, M. -G. R¨ uck. The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. IEEE Transactions on Information Theory, 45(5):1717–1718, 1999. 16. S. D. Galbraith. Supersingular curves in cryptography.

Kim and F. W. Roush, Diophantine undecidability of C(t1 , t2 ), J. Algebra 150 (1992), no. 1, 35–44. Mat70. Ju. V. Matijaseviˇc, The Diophantineness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279–282. Maz94. B. Mazur, Questions of decidability and undecidability in number theory, J. Symbolic Logic 59 (1994), no. 2, 353–371. MB. Laurent Moret-Bailly, paper in preparation, extending results presented in a lecture 18 June 2001 at a conference in honor of Michel Raynaud in Orsay, France.

33–42, 2002. c Springer-Verlag Berlin Heidelberg 2002 34 Bjorn Poonen For example, the subset Z≥0 := {0, 1, 2, . . } of Z is diophantine, since for a ∈ Z, we have a ∈ Z≥0 ⇐⇒ (∃x1 , x2 , x3 , x4 ∈ Z) x21 + x22 + x23 + x24 = a. One can show using “diagonal arguments” that there exists a listable subset L of Z whose complement is not listable. It follows that for this L, there is no algorithm that takes as input an integer a and decides in a finite amount of time whether a belongs to L; in other words, membership in L is undecidable.

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