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- W2951667790 abstract "We construct new families of elliptic curves over (FF_{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. Our construction is based on reducing (QQ)-curves-curves over quadratic number fields without complex multiplication, but with isogenies to their Galois conjugates-modulo inert primes. As a first application of the general theory we construct, for every (p > 3), two one-parameter families of elliptic curves over (FF_{p^2}) equipped with endomorphisms that are faster than doubling. Like GLS (which appears as 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. Unlike GLS, we also offer the possibility of constructing twist-secure curves. Among our examples are prime-order curves equipped with fast endomorphisms, with almost-prime-order twists, over (FF_{p^2}) for (p = 2^{127}-1) and (p = 2^{255}-19)." @default.
- W2951667790 created "2019-06-27" @default.
- W2951667790 creator A5081112709 @default.
- W2951667790 date "2013-05-23" @default.
- W2951667790 modified "2023-09-27" @default.
- W2951667790 title "Families of fast elliptic curves from Q-curves" @default.
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