Abstract
The Frobenius expansion has been used to speed up scalar multiplication in hyperelliptic curves as it is used in elliptic curves. In this paper we propose a new Frobenius expansion method for hyperelliptic curves that have efficiently computable endomorphisms used in Park, Jeong and Lim [1]. When our method is applied to scalar multiplication for hyperelliptic curves, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6–28.3% over the previous algorithm, when the algorithms are implemented over finite fields of odd characteristics.
Keywords
This work was supported by the MOST grant M6-0203-00-0039.
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Park, TJ., Lee, MK., Park, K. (2004). Efficient Scalar Multiplication in Hyperelliptic Curves Using A New Frobenius Expansion. In: Lim, JI., Lee, DH. (eds) Information Security and Cryptology - ICISC 2003. ICISC 2003. Lecture Notes in Computer Science, vol 2971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24691-6_13
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DOI: https://doi.org/10.1007/978-3-540-24691-6_13
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