Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves

When designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem, implementing the group arithmetic is a cost-critical task. We introduce a software tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. The resulting circuits reduce the number of T-gates by a factor 13/5 compared to the best previous construction, without increasing the number of qubits or T-depth. The software also optimizes the (CNOT) depth for F-2-linear operations by means of suitable graph colorings.