The application of elementary number theory in cryptography
Yaxuan Ma · 2022
The cryptography has a history of thousands of years, and its development can be divided into three stages, classic cryptography, neoteric cryptography and modern cryptography. Nowadays, it has been further invigorated by 20th-century technology. Previous studies lack a systematic review, so the public has a relatively shallow understanding of the issue. Thus, to increase public awareness, the encryption and decryption are introduced in a easy to understand way. Through extensive reading, generalizing and combing, this paper introduced the number theory applied in some examples of classic, neoteric, and modern cryptography. It is found out that the knowledge of congruences, arithmetic, factorization in number theory are widely utilized in cryptographic algorithms, among them, congruences are the most secure and common type. It is also found out that the number theory can help create the algorithm to encrypt and decrypt messages.