A Research On Certain Questions Related To Factorization Of Large Numbers In History

Primality testing and integer factorization are of great value not only in theory but also in practice. This thesis is mainly based on the former researches and systematically summarizes the development of the primality testing and integer factorization. Further, this thesis also briefly introduces the application of integer factorization in the cryptography. The main content of the thesis is listed as follows:The first part expounds the systematical research of the integer problem in ancient China, which mainly includes the two aspects:Chinese remainder theory and greatest common divisor.The second part expounds the origin of the number theory in western math. This chapter not only includes the number theory researches conducted by Pythagoras and Euclid, but also includes the brief introduction of Gauss’s basic theorem of arithmetic.The third part detailed investigates the basic theory of prime Numbers. Combing some method for determination of prime Numbers, and shows how to implement on computer prime number determination.The fourth part not only elaborates the evolution of the integer factorization since ancient times but also introduces some of the typical and historic decomposition methods in details.The last part researches the cryptography and integer factorization. This chapter not only expounds every phase of the cryptography since ancient times but also introduces the RSA public key system which is designed on the basis of the difficulty of integer factorization.