The $$\mathbb {Q}$$ Q -curve Construction for Endomorphism-Accelerated Elliptic Curves

We give a detailed account of the use of $$\mathbb {Q}$$ Q -curve reductions to construct elliptic curves over $$\mathbb {F}_{p^2}$$ 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… CONTINUE READING