The application of elementary number theory in cryptography

Yaxuan Ma

doi:10.1117/12.2635851

5 May 2022 The application of elementary number theory in cryptography

Yaxuan Ma

Proceedings Volume 12245, International Conference on Cryptography, Network Security, and Communication Technology (CNSCT 2022); 122450A (2022) https://doi.org/10.1117/12.2635851
Event: International Conference on Cryptography, Network Security, and Communication Technology (CNSCT 2022), 2022, Sanya, China

Abstract

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.

Citation Download Citation

Yaxuan Ma "The application of elementary number theory in cryptography", Proc. SPIE 12245, International Conference on Cryptography, Network Security, and Communication Technology (CNSCT 2022), 122450A (5 May 2022); https://doi.org/10.1117/12.2635851

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available