Breaking RSA Using Shor's Algorithm

In this section, we consider how the security of RSA, and of cryptographic schemes based on the intractability of the DLP in finite fields, is affected when the optimized construction previously described is used to implement the currently most efficient derivatives of Shor's algorithms. 

Our goal throughout this section is to minimize the overall expected spacetime volume, includ- ing expected repetitions, when factoring RSA integers or computing discrete logarithms. That is to say, we minimize the spacetime volume in each run of the quantum algorithm times the expected number of runs required.