Abstract: The most popular tasks in cryptography are information encryption\decryption tasks, the calculation of a digital signature, the calculation of the greatest common divisor for several numbers, the creation of safe (cryptographically resistant) data transmission protocols and so on. The protocols use the asymmetric cryptography for keys authentication, the symmetric encryption for confidentiality preservation, the message authentication codes to ensure the message integrity. But at the same time with the increase of local network capacity as well as internet traffic, the role of cryptographic protocol performance increases. Many cryptographic algorithms are performed over a field, so the acceleration of the basic arithmetic operations implementation (addition, multiplication, exponential calculation) will speed up the implementation of the whole algorithm. This study describes the effective versions of multiplication, exponent calculation and modular reduction algorithms for a wide range of cryptography issues. The detailed description of these algorithms is provided, combined with mathematical transformations necessary for their analysis, the field of their use is described, their comparative analysis is performed on the basis of which we may obtain for example, a more efficient version of asymmetric cryptography algorithms such as RSA, El Gamal and others and thus develop some faster protocols.