Current Issue

Sardar Patel International Journal of Interdisciplinary Research & Innovation
ISSN: 3107-832X (Online)

Algebraic Methods in Cryptography and Information Security

ABSTRACT

Cryptography forms the backbone of modern information security, ensuring confidentiality, integrity, authentication, and non-repudiation in digital communication systems. At its core, cryptography relies heavily on algebraic structures such as groups, rings, fields, and lattices. These algebraic foundations enable the construction of secure encryption schemes, digital signatures, key exchange protocols, and cryptographic hash functions. This paper presents a detailed study of algebraic methods used in cryptography and information security. It explores classical and modern cryptographic systems from an algebraic perspective, highlighting the role of number theory, finite fields, group theory, and lattice theory. The paper also examines algebraic attacks and security assumptions, emphasizing how algebra both strengthens cryptographic designs and exposes vulnerabilities. Applications in public-key cryptography, elliptic curve cryptography, and post-quantum cryptography are discussed. The study demonstrates that algebraic methods are not merely mathematical tools but foundational elements that shape the security, efficiency, and future direction of cryptographic systems.

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