"A quantum algorithm used for integer factorisation. It's important because it can, in theory, be used to break the widely used public-key cryptography scheme known as RSA. RSA is based on the assumption that factoring large numbers is computationally infeasible. This assumption is valid for classical computers; no classical algorithm is known that can factor in polynomial time."
In order to gain control of Destiny, Rush planned to somehow use the algorithm to crack the ship's master code. However, he was unsuccessful. (SGU: "Human")
Shor's algorithm can be (theoretically) used to crack RSA-based encryption codes, which work on the assumption that finding the two prime factors of an extremely large integer is intractable to a classical computer. The Tau'ri scientist Peter Shor proved that on a quantum computer it would be possible to crack any RSA-based encryption code.
When Michael Kenmore invaded Atlantis, his Lead Hybrid stated that Atlantis' encryption code contained extremely large integers; however, the hybrid was eventually able to crack the code. Since a classical computer would take more units of time than the age of the known universe to crack such a code, it may be possible that Michael was in possession of a quantum computer of some sort that ran a Wraith variant of Shor's algorithm. (SGA: "The Prodigal")