A Compare between Shor´s quantum factoring algorithm and General Number Field Sieve

Factoring large integers has been one of the most difficult problems in the history of mathematics and computer science. There was no efficient solution of this problem until Shor´s algorithm emerged. Shor´s algorithm is a polynomial time factoring algorithm which works on a quantum computer. Quantum computing is a new paradigm of computing that uses quantum mechanical phenomena in solving problems. The computers we are using right now are called classical computer. The most efficient classical factoring algorithm is General Number Field Sieve (GNFS). GNFS also cannot factor integers in polynomial time. In this paper, we compared these two algorithms in factoring integer in a standalone system.