IMPLEMENTATION OF A CRYPTOGRAPHICALLY STRONG ALGORITHM WITH A SIMPLE ENCRYPTION AND DECRYPTION PROCEDURE BASED ON ELLIPTIC CURVES

Abstract

The work considers various methods and advantages of using cryptographic algorithms based on the theory of elliptic curves. Examples of implementation of electronic digital signature schemes based on these algorithms are also given. One of the key advantages of algorithms based on elliptic curves is to provide a high level of security with smaller key sizes compared to other cryptographic systems. The work examines in detail which elliptic curves can be used in various cryptographic schemes. A comparison with other algorithms such as RSA or DSA is also given, noting the advantages of using elliptic curves. The paper gives examples of implementation of electronic digital signature schemes using elliptic curves. Digital signatures are an important mechanism for authentication and data integrity in cryptography, and the use of elliptic curves can improve the effectiveness and security of such signatures. During testing, a linear dependence of time on the number of algorithm runs was revealed. The execution time of the RSA algorithm is approximately equal to the execution time of the DSA algorithm. This is primarily due to the linear launch of the algorithms. When it comes to schemes based on elliptic curves, they allow you to achieve the desired level of security with a much smaller key length than in the case of the RSA scheme. When using elliptic curves, it is possible to provide the same level of information protection by using smaller keys compared to traditional methods such as RSA. The work helps to understand the use of the theory of elliptic curves in cryptography, providing information on various methods and applications of these algorithms, in particular, in electronic digital signature schemes.