Use of elliptic curves in cryptography

I will survey the checkered history of supersingular elliptic curves in cryptography, from their first consideration in the seminal papers of Koblitz and Miller, to their rejection after the discovery of the Weil and Tate pairing attacks on the discrete ...

Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert- Vanstone GLV method. We extend results of Iijima, Matsuo, Chao and Tsujii which give such homomorphisms for a large class of ...

We construct new families of 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 ...