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Endomorphisms for faster elliptic curve cryptography on a large class of curves. (English) Zbl 1258.94036

Summary: Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. T. Iijima et al. (2002) gave such homomorphisms for a large class of elliptic curves by working over \(\mathbb{F}_{p^2}\). We extend their results and demonstrate that they can be applied to the GLV method.
In general we expect our method to require about \(0.75\) the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between \(0.70\) and \(0.83\) the time of the previous best methods for elliptic curve point multiplication on general curves.

MSC:

94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14G50 Applications to coding theory and cryptography of arithmetic geometry
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