Skew-Frobenius Maps on Hyperelliptic Curves

Shunji KOZAKI  Kazuto MATSUO  Yasutomo SHIMBARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.7   pp.1839-1843
Publication Date: 2008/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.7.1839
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
hyperelliptic curve cryptosystems,  scalar multiplications,  Frobenius expansions,  skew-Frobenius maps,  

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Scalar multiplication methods using the Frobenius maps are known for efficient methods to speed up (hyper)elliptic curve cryptosystems. However, those methods are not efficient for the cryptosystems constructed on fields of small extension degrees due to costs of the field operations. Iijima et al. showed that one can use certain automorphisms on the quadratic twists of elliptic curves for fast scalar multiplications without the drawback of the Frobenius maps. This paper shows an extension of the automorphisms on the Jacobians of hyperelliptic curves of arbitrary genus.