Title: Quantum circuits for binary elliptic curve arithmetic
Abstract: One of the prominent applications of quantum algorithms is the computation of discrete logarithms in finite cyclic groups. A task that naturally arises in this context is to implement the underlying group arithmetic. From a cryptographic point of view, cyclic subgroups of elliptic curves over finite fields are of particular interest, and this talk discusses quantum circuits to implement the point addition on binary elliptic curves. The main focus of the talk is how the choice of a particular representation of GF(2^n) or an elliptic curve affects the (gate) complexity of the resulting quantum circuit.
This talk is based on joint work with Brittanney Amento and Martin Roetteler.