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

Authors:
Fangguo Zhang;Futai Zhang;Yumin Wang
Affiliations:
P.O.Box 119 Key Laboratory on ISN, Xidian University, Xi'an 710071, P.R. China;P.O.Box 119 Key Laboratory on ISN, Xidian University, Xi'an 710071, P.R. China and College of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P.R. China;P.O.Box 119 Key Laboratory on ISN, Xidian University, Xi'an 710071, P.R. China
Venue:
Journal of Computer Science and Technology
Year:
2002

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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 of g = 2 such as v2 + uv = f and v2 + v = f(u) defined on GF(2r). The curves defined on GF(4) and GF(8) are expanded to the curves defined on GF(4)k and GF(8)t respectively, where 38 k t g = 2 that are suitable for establishing cryptosystems.