Review of Modern Cryptography and Elliptic Curves, A Beginner's Guide by Thomas R. Shemanske

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 ...

We propose for the first time the computation of the Tate pairing on Jacobi intersection curves. For this, we use the geometric interpretation of the group law and the quadratic twist of Jacobi intersection curves to obtain a doubling step formula which ...

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 ...