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- W1786220217 abstract "We give a detailed account of the use of $$mathbb {Q}$$ -curve reductions to construct elliptic curves over $$mathbb {F}_{p^2}$$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Like GLS (which is a degenerate case of our construction), we offer the advantage over GLV of selecting from a much wider range of curves and thus finding secure group orders when $$p$$ is fixed for efficient implementation. Unlike GLS, we also offer the possibility of constructing twist-secure curves. We construct several one-parameter families of elliptic curves over $$mathbb {F}_{p^2}$$ equipped with efficient endomorphisms for every $$p > 3$$ , and exhibit examples of twist-secure curves over $$mathbb {F}_{p^2}$$ for the efficient Mersenne prime $$p = 2^{127}-1$$ ." @default.
- W1786220217 created "2016-06-24" @default.
- W1786220217 creator A5081112709 @default.
- W1786220217 date "2015-08-01" @default.
- W1786220217 modified "2023-10-12" @default.
- W1786220217 title "The $$mathbb {Q}$$ Q -curve Construction for Endomorphism-Accelerated Elliptic Curves" @default.
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- W1786220217 doi "https://doi.org/10.1007/s00145-015-9210-8" @default.
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