Simple Number Theorem Proof And Its Application

The modern scientific totally constitutes five basic categories which is natural science, social science, thinking science, philosophy and mathematical. As a big basic category , philosophy and mathematics are divided out because of their research objects and modern scientific development in the position and role of the decision. Mathmatics is particularly close contact with natural science. It is a tool of natural science research.Number theory refers to researching the nature of the integer. It is one of the important subject of mathematics branch. Gaussian once said a famous saying: "mathematics is the queen of the science of mathematics, while number theory is the queen". As an ancient based number theory, the mathematical subject in a very long time belongs to a kind of pure mathematics. Along with the development of modern science and the application in the whole scientific theory is very important.Cryptography is the study of the information encryption and decryption and deciphering technology subject. A remarkable characteristic of cryptography contains many mathmatical theories. There are a lot of number theory based content, such as division theory, congruence theory, and the Chinese remainder theorem, etc, in cryptography have important applications.The paper focus on basic knowlege of number theory and abroad about cryptography research status and research of cryptography, expounds the purpose and significance of the classical cryptography and modern cryptography and password system, RSA DES carry on the detailed analysis and discussion, will also with some examples expounding and more clearly explained.This paper introduced the elementary theory of number of basic theory and cryptography public‐key cryptosystem on number theory. On the basis of some special phenomenon, makes a deep analysis of observation, for the proposed new theory. Firstly, it introduced a new concept named Simple number, the minimalist Simple number and process of findng out Simple number.Based on the observation and analysis of the data, this paper summarizes the character and the number of Simple number and proof it. Based on this put forward a new theorem nameed Simple number theorem. The proposed, using the theorem of the content elementary theory of number after basic knowledge, will complete the proof process theorem of the show in the thesis. Additiongly, some special conclusion launch is introduced and proved in the process of proving Simple number theorem.Proposing the Simple number theorem creates a new idea in cryptography encryption and decryption process. Due to difference exist s in the simple numbers with different order in the process of finding out simple number ,ther is a not direct delicate relationship in the simple numbers with different order. It makes the simple number with uncertainty and fuzziness character. But it is clearly that for a given number, its minimalist Simple number is determined and irrelevant to find process. (Simple number theorem content).Then it wil look for its applications in cryptography. Trying to cryptography encryption and decryption technology explore new ideas, promote cryptography and information security technology development lastly.