EL-GAMAL’S CRYPTOGRAPHIC ALGORITHM: MATHEMATICAL FOUNDATIONS, APPLICATIONS AND ANALYSIS
D.S. Amirkhanova, O.Zh. Mamyrbayev · NEWS OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN · 2024
This paper is a comprehensive review of the El-Gamal cryptographic algorithm. The El-Gamal algorithm is a key algorithm in asymmetric encryption widely used in modern cryptography. It is main advantages include a high level of security due to the complexity of computing discrete logarithms and the ability to be used in digital signatures for authentication and non-repudiation.However, the El-Gamal algorithm is not without it is limitations. It is computational complexity can be quite high, especially when dealing with large numbers, which can lead to increased encryption and decryption times. Additionally, in some cases, the algorithm may be vulnerable to attacks based on mathematical analyses of the structure of the finite field. Overall, the El-Gamal algorithm remains an important tool in the field of cryptography, and it is application continues to expand across various platforms and industries. Moreover, asymmetric cryptography also facilitates the establishment of secure communication channels by using key exchange protocols, such as Diffie-Hellman, which allows two parties to agree upon a shared secret key without revealing it to any eavesdroppers. This is crucial in ensuring secure connections for various applications, including secure web browsing, online banking, and secure email communication. However, for maximum efficiency and security, it is necessary to consider both the advantages and limitations of this method, and apply it in accordance with the specific needs and requirements of each individual application. The paper details the mathematical foundations of the algorithm, including the computation of discrete logarithms, finite field operations, and cryptographic robustness evaluation. Encryption and digital signature algorithms based on El-Gamal's method are described. The advantages and disadvantages of the algorithm are analyzed, as well as its application in various fields such as e-commerce, email and cryptocurrencies. The paper contains a descriptive part explaining the concept of asymmetric cryptography and its advantages.