Roger Penrose claimed in his new book The Emperor’s New Mind that all branches of mathematics have been taken in effect except number theory. But the following tens of years have witnessed that this antique theory have found its modern position in encryption with the galloping development of computers. In 1936 long before the earliest computer’s coming into life, Alan Turing had published his theory of the behaviour of Turing machines and meta-Turing machines, which were later implemented as computer programmes and computers. He left us a question whether P is equal to NP, namely, whether a problem can be solved in polynomial time as long as its solution can be checked in such time. The intangibility of P＝NP made us believe the opposite, which generated currently-used encryption algorithms, some of them based on big integers and number theoretical transform, guarding the information world. Now the ever-growing quantum computers aim to take the place of traditional encryption to construct the one without possibilities to be attacked.