Breaking RSA Using Shor's Algorithm

Many of the optimization techniques that we use in this paper generalize to other contexts where arithmetic is performed. In particular, consider the Toffoli count for computing discrete logarithms over elliptic curves. It can likely be improved substantially by using windowed arithmetic. On the other hand, because of the need to compute modular inverses, it is not clear if the coset representation of modular integers is applicable. 

Which of our optimizations can be ported over, and which ones cannot? How much of an improvement would result? These are interesting questions for future research work.