An Addition Algorithm in Jacobian of C_<34> Curve(Information Security)

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概要

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• This paper gives an efficient algorithm to compute addition in Jacobian of C_<34> curves, aiming at C_<34> curve cryptosystems. Using C_<34> curves for cryptosystems has two advantages. The first is safety and the second is the short size of the base field. In the paper, we modify the addition algorithm of [1] for C_<ab> curves in the specific manner to C_<34> curves. We classify all of the forms of the Groebner bases of ideals involved in the algorithm and eliminate the use of Buchberger algorithm from it. Our resulting algorithm computes the addition in Jacobian of C_<34> curves in about 3 times amount of computation of the one in elliptic curves, when the sizes of groups are set to be the same.

• 社団法人電子情報通信学会の論文
• 2005-06-01

著者

• ARITA Seigo

  Institute of Information Security

• Arita Seigo

  Inst. Information Security Yokohama‐shi Jpn

関連論文

• A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields(Discrete Mathematics and Its Applications)
• An Addition Algorithm in Jacobian of C_ Curve(Information Security)

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