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Selection of secure hyperelliptic curves ofg=2 based on a subfield

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Abstract

In the implementation of hyperelliptic curve cryptosystems, a siginificant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed. In this paper, we discuss the hyperelliptic curves ofg=2 such asv 2+uv=f andv 2+v=f(u) defined onGF(2r). The curves defined onGF(4) andGF(8) are expanded to the curves defined onGF(4)k andGF(8)t respectively, where 38<k<70, 25<t<50. We also find out all the secure curves ofg=2 that are suitable for establishing cryptosystems.

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Authors and Affiliations

  1. P. O. Box 119 Key Laboratory on ISN, Xidian University, 710071, Xi’an, P. R. China

    Zhang Fangguo, Zhang Futai & Wang Yumin

  2. College of Mathematics and Computer Science, Nanjing Normal University, 210097, Nanjing, P. R. China

    Zhang Futai

Authors
  1. Zhang Fangguo
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  2. Zhang Futai
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  3. Wang Yumin
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Corresponding author

Correspondence to Zhang Fangguo.

Additional information

This work is supported by the National NKBRSF ‘973’ Program of China (Grant No.G1999035804).

ZHANG Fangguo was born in 1972. He received the B.S. degree in mathematics from Yantai Teachers’ University in 1996 and the M.S. degree in applied mathematics from Tongji University in 1999. He is currently a Ph.D. candidate in cryptography at Xidian University. His research interests are electronic commerce, elliptic curve cryptography and hyperelliptic curve cryptography.

ZHANG Futai was born in 1965. He received the M.S. degree in fundamental mathematics from Shanxi Normal University in 1990. He is currently a Ph.D. candidate in cryptography at Xidian University. His research interests are information security, cryptography and electronic commerce.

WANG Yumin was born in 1936. He is now a professor, a Ph.D. supervisor in Xidian University, and a member of IEEE. His research interests are the philosophy of communication, information theory, coding and cryptography.

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Zhang, F., Zhang, F. & Wang, Y. Selection of secure hyperelliptic curves ofg=2 based on a subfield. J. Compt. Sci. & Technol. 17, 836–842 (2002). https://doi.org/10.1007/BF02960774

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  • DOI: https://doi.org/10.1007/BF02960774

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