With Mathematics as Key: A Path to Unlock the Secret Power of Cryptography

Abstract

In this paper, the core role of mathematics in cryptography is deeply discussed, and how the mathematical branches such as number theory, group theory and elliptic curve theory provide solid theoretical foundation and construction methods for cryptography algorithms is elaborated in detail. By analyzing the mathematical principles of classical and modern cryptosystems, this paper reveals the mathematical mysteries behind the technology from simple alternative encryption to advanced public key encryption, and shows the key applications of mathematical tools in ensuring information security, realizing secure communication, digital signature and key exchange, etc., providing in-depth insights from the mathematical perspective for further understanding and development of cryptography technology.