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Sublinear scalar multiplication on hyperelliptic Koblitz curves. (English) Zbl 1266.94023
Miri, Ali (ed.) et al., Selected areas in cryptography. 18th international workshop, SAC 2011, Toronto, ON, Canada, August 11–12, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-28495-3/pbk). Lecture Notes in Computer Science 7118, 399-411 (2012).
Summary: Recently, V. S. Dimitrov et. al. [IEEE Trans. Comput. 57, No. 11, 1469–1481 (2008; doi:10.1109/TC.2008.65)] proposed a novel algorithm for scalar multiplication of points on elliptic Koblitz curves that requires a provably sublinear number of point additions in the size of the scalar. Following some ideas used by this article, most notably double-base expansions for integers, we generalize their methods to hyperelliptic Koblitz curves of arbitrary genus over any finite field, obtaining a scalar multiplication algorithm requiring a sublinear number of divisor additions.
For the entire collection see [Zbl 1234.94005].
MSC:
94A60 Cryptography
14G50 Applications to coding theory and cryptography of arithmetic geometry
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