Vol. 1 No. 8 (2025), Articles
Vol. 1 No. 8 (2025)

MATHEMATICAL FOUNDATIONS OF CRYPTOGRAPHIC ALGORITHMS: AN INTRODUCTION TO NUMBER THEORY

Articles
Published 2025-04-21
Yoqubova Husniya Abdixalil qizi
University of Information Technology and Management Digital Technologies faculty, 2rd year student.
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Keywords

cryptography, number theory, prime numbers, modular arithmetic, RSA algorithm, Diffie-Hellman, elliptic curve cryptography, encryption, mathematical foundation.

Abstract

This article explores the mathematical foundations of cryptographic algorithms, focusing on the role of number theory in modern encryption techniques. It introduces key concepts such as prime numbers, modular arithmetic, and the properties of large integers, which are critical for the development and security of cryptographic systems. The paper explains how number theory underpins algorithms such as RSA, Diffie-Hellman, and elliptic curve cryptography, which form the backbone of secure communication in digital systems. The connection between theoretical mathematics and practical cryptography is examined, shedding light on the importance of number theory in creating robust encryption protocols.

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References

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2. Stinson, D. R. (2005). Cryptography: Theory and Practice (3rd ed.). CRC Press.

3. Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (2001). Handbook of Applied Cryptography. CRC Press.

4. Koblitz, N. (1987). Elliptic Curve Cryptosystems. Springer-Verlag.

5. Shoup, V. (2009). A Computational Introduction to Number Theory and Algebra. Cambridge University Press.