Simplifying Shor’s Method

Our existing methods of key exchange and public key encryption are not secure within an era of quantum computers. Why? Because the hard problems they are based on, do not become hard problems anymore with quantum computers. For RSA, we create a public modulus (N) and which is the multiplication of two prime numbers (P and Q). If N is large enough (such as with 2,048 bits) and if random prime numbers are used, it is not computationally feasible to factor it (as it would take the energy to boil all the oceans on the planet, and still take billions and billions of years to crack a single key).

Shor imagined two sine waves, one of length P and the other of length Q. Assuming that P and Q are co-prime (that they do not share a common factor), he proposed a question of finding the point at which the harmony of P overlaps with Q, and then repeats itself. For this, we can project to a point N, and then find the point at which the phase of P and Q will be 0. In a quantum computer, this phase checking is a fairly easy task, and we can thus factorize N in terms of P and Q. All we need to do is to change the length of P and Q and find the point at which we determine they are in phase at point N.

So let’s say I pick P=2 and Q=3 (which are two prime numbers), and where I generate two sine waves with a length of 2 and a length of 3. When I plot the two together, you can see that the…