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On the Isomorphism Classes of Elliptic Curves with 2-Torsion Points

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Network Computing and Information Security (NCIS 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 345))

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Abstract

This paper presents explicit formulas for the number of isomorphism classes of elliptic curves with 2-torsion points over finite fields. These results also can be used in the elliptic curve cryptosystems and classification problems.

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References

  1. Bernstein, D., Lange, T.: Explicit-Formula Database, http://www.hyperelliptic.org/EFD

  2. Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted Edwards Curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389–405. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Bernstein, D.J., Lange, T.: Faster Addition and Doubling on Elliptic Curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29–50. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Billet, O., Joye, M.: The Jacobi Model of an Elliptic Curve and Side-Channel Analysis. In: Fossorier, M.P.C., Høholdt, T., Poli, A. (eds.) AAECC 2003. LNCS, vol. 2643, pp. 34–42. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7, 385–434 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Edwards, H.M.: A normal form for elliptic curves. Bull. Amer. Math. Soc. 44, 393–422 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Feng, R., Nie, M., Wu, H.: Twisted Jacobi Intersections Curves. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds.) TAMC 2010. LNCS, vol. 6108, pp. 199–210. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Wu, H., Feng, R.: On the isomorphism classes of Legendre elliptic curves over finite fields. Sci. China Math. 54(9), 1885–1890 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers (1993)

    Google Scholar 

  10. Miller, V.S.: Use of Elliptic Curves in Cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)

    Google Scholar 

  11. Schoof, R.: Nonsigular plane cubic curves over finite field. J. Combine Theory Ser. A 46, 183–211 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  12. Silverman, J.H.: The Arithmetic of Elliptic Curves. GTM, vol. 106. Springer, Berlin (1986)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Sciences, North China University of Technology, Beijing, 100144, China

    Hongfeng Wu

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Rongquan Feng

Authors
  1. Hongfeng Wu
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  2. Rongquan Feng
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Editor information

Editors and Affiliations

  1. School of Computer and Information Engineering, Shanghai University of Electric Power, 200090, Shanghai, China

    Jingsheng Lei

  2. Caritas Institute of Higher Education, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

  3. School of Computer Engineering, Computer Science Division, Nanyang Technological University (NTU), 50 Nanyang Avenue, Singapore

    Mo Li

  4. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Yuan Luo

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© 2012 Springer-Verlag Berlin Heidelberg

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Wu, H., Feng, R. (2012). On the Isomorphism Classes of Elliptic Curves with 2-Torsion Points. In: Lei, J., Wang, F.L., Li, M., Luo, Y. (eds) Network Computing and Information Security. NCIS 2012. Communications in Computer and Information Science, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35211-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-35211-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35210-2

  • Online ISBN: 978-3-642-35211-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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