Also, note that this acceleration provided by Shor's algorithm is what people are talking about when they say "quantum breaks encryption". I don't like when people say that though because quantum computers don't break all encryption schemes. In fact, there is only one mainstream encryption scheme which is susceptible and that is RSA. Don't get me wrong, if RSA is comprised that would compromise a LOT of legacy systems. But we already have new public key ciphers, such as elliptic curves, which are ready to replace RSA once quantum computers become large enough to actually implement an attack against RSA.
Also, note that this acceleration provided by Shor's algorithm is what people are talking about when they say "quantum breaks encryption". I don't like when people say that though because quantum computers don't break all encryption schemes. In fact, there is only one mainstream encryption scheme which is susceptible and that is RSA. Don't get me wrong, if RSA is comprised that would compromise a LOT of legacy systems. But we already have new public key ciphers, such as elliptic curves, which are ready to replace RSA once quantum computers become large enough to actually implement an attack against RSA.