@inbook{1dd6cc93e8444afc994295a062b36470,

title = "Faster scalar multiplication on koblitz curves combining point halving with the frobenius endomorphism",

abstract = "Let E be an elliptic curve defined over F2n. The inverse operation of point doubling, called point halving, can be done up to three times as fast as doubling. Some authors have therefore proposed to perform a scalar multiplication by an {"}halve-and-add{"} algorithm, which is faster than the classical double-and-add method. If the coefficients of the equation defining the curve lie in a small subfield of F2n, one can use the Frobenius endomorphism τ of the field extension to replace doublings. Since the cost of τ is negligible if normal bases are used, the scalar multiplication is written in {"}base τ{"} and the resulting {"}τ-and-add{"} algorithm gives very good performance. For elliptic Koblitz curves, this work combines the two ideas for the first time to achieve a novel decomposition of the scalar. This gives a new scalar multiplication algorithm which is up to 14.29% faster than the Frobenius method, without any additional precomputation.",

keywords = "Integer decomposition, Koblitz curves, Point halving, Scalar multiplication, τ-adic expansion",

author = "Avanzi, {Roberto Maria} and Mathieu Ciet and Francesco Sica",

year = "2004",

doi = "10.1007/978-3-540-24632-9_3",

language = "English",

isbn = "3540210180",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "28--40",

editor = "Feng Bao and Robert Deng and Jianying Zhou",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "Germany",

}