Automatic synthesis of quantum circuits for point addition on ordinary   binary elliptic curves
  Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for GF(2)-linear operations by means of suitable graph colorings. 
Parshuram Budhathoki and Rainer Steinwandt
quant-ph