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Elliptic Twin Prime Conjecture

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Coding and Cryptology (IWCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5557))

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Abstract

Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime. In a work in progress theoretical extimates are obtained wherein the number of such points on both curves has a prescribed arithmetic structure.

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References

  1. Balog, A.: ‘The prime k-tuplets conjecture on average’, Analytic Number Theory. In: Progress in Mathematics, vol. 85, pp. 47–75. Birkhäuser, Basel (1990)

    Google Scholar 

  2. Birch, B.J.: How the number of points of an elliptic curve over a fixed prime field varies. J. Lond. Math. Soc. 43, 57–60 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chevassut, O., Fouque, P.-A., Gaudry, P., Pointcheval, D.: The twist-AUgmented technique for key exchange. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 410–426. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Deuring, M.: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper’. Abh. Math. Sem. Hansischen Univ. 14, 197–272 (1941)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lenstra, H.W.: Factoring integers with elliptic curves. Ann. Math. 126, 649–673 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Silverman, J.H.: The arithmetic of elliptic curves. Springer, Berlin (1995)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, Canada

    John B. Friedlander

  2. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

    Igor E. Shparlinski

Authors
  1. John B. Friedlander
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  2. Igor E. Shparlinski
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Editor information

Editors and Affiliations

  1. National Computer Systems, Center for Information Technology,, 73 Science Park Drive, S0511, Republic of Singapore

    Yeow Meng Chee  & San Ling  & 

  2. National University of Defense Technology, 411073, Changshu Hunan, China

    Chao Li

  3. National Computer Systems, Center for Information Technology, 73 Science Park Drive, S0511, Republic of Singapore

    Huaxiong Wang  & Chaoping Xing  & 

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© 2009 Springer-Verlag Berlin Heidelberg

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Friedlander, J.B., Shparlinski, I.E. (2009). Elliptic Twin Prime Conjecture. In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds) Coding and Cryptology. IWCC 2009. Lecture Notes in Computer Science, vol 5557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01877-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-01877-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01813-8

  • Online ISBN: 978-3-642-01877-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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