Scaler multiplication on elliptic curves by Frobenius expansions

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Koblitz has suggested to use "anomalous" elliptic curves defined over F-2, which are non-supersingular and allow for efficient multiplication of a point by an integer. For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. In this paper, we propose an algorithm to speed up scalar multiplication on an elliptic curve defined over a small field. The proposed algorithm uses the same technique as Muller's to get an expansion by the Frobenius map, but its expansion length is half of Muller's due to the reduction step (Algorithm 1). Also, it uses a more efficient algorithm (Algorithm 3) to perform multiplication using the Frobenius expansion. Consequently, the proposed algorithm is two times faster than Mulier's. Moreover, it can be applied to an elliptic curve defined over a finite field with odd characteristic and does not require any precomputation or additional memory.
Publisher
ELECTRONICS TELECOMMUNICATIONS RESEARCH INST
Issue Date
1999-03
Language
English
Article Type
Article
Citation

ETRI JOURNAL, v.21, no.1, pp.27 - 38

ISSN
1225-6463
URI
http://hdl.handle.net/10203/68971
Appears in Collection
MA-Journal Papers(저널논문)
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