Abstract
Hyperelliptic curve cryptosystems (HCC for short) is a generalization of ECC. It has been drawing the attention of more and more researchers in recent years. The problem of how to decrease the amount of addition and scalar multiplication on the Jacobians of hyperelliptic curves so that the implementation speed can be improved is very important for the practical use of HCC. In this paper, Using Frobenius endomorphism as a tool, we discuss the problem of faster scalar multiplication. A faster algorithm on Jacobian’s scalar multiplication of a family of specific hyperelliptic curves is proposed with its computational cost analyzed. Analysis reveals that our algorithms’s computational cost is less than that of Signed Binary Method.
This work was supported by the project 973 of China under the reference number G1999035804.
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Zhang, F., Zhang, F., Wang, Y. (2001). Fast Scalar Multiplication on the Jacobian of a Family of Hyperelliptic Curves. In: Qing, S., Okamoto, T., Zhou, J. (eds) Information and Communications Security. ICICS 2001. Lecture Notes in Computer Science, vol 2229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45600-7_9
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DOI: https://doi.org/10.1007/3-540-45600-7_9
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