Aim of research is analysis of existing, improvement and development of methods of new construction of authentication codes messages that would have greater compared with existing, speed while maintaining a given level of security. The object of the study is to process authentication data, based on the use of universal hashing functions based on polynomial value computation over finite fields and rings. The subject of research is the authentication methods of data with a given level of resistance based on polynomial value computation over finite fields and rings that allow to fulfill the requirements for message authentication codes, including the required collision resistance, difficulty finding preimage and second preimage, high performance, ease of implementation. Research methods: the methods of game theory and information theory in the study of the mathematical model with data authentication and substantiation requirements for data authentication methods, methods of field theory and group methods of probability theory and mathematical statistics in determining the probability of weak keys and the methods of the theory of parallel computing in constructing and evaluation of the properties of parallel algorithms for hashing, methods of system analysis when compared to existing methods of authentication messages; software modeling in the implementation process of universal hashing. Theoretical and practical research results 1. The improvement of method of universal hashing based on polynomial value computation over a finite field, which is different from the prototype that involves hashing messages n in parallel streams superblock with n blocks with some key x followed by hashing the received intermediate hash-value of key x ^ n, which allowed to increase performance in n times, where n - number of threads, was proposed. 2. For the first time the method of universal hashing, which is based on calculating the value of a polynomial in the ring of integers modulo 2 ^ l, thus allowing for the probability of collisions 1 / (2 ^ (l-1)) regardless of the length of the message, increase the speed of approximately 2, 5 times as compared with the function hashing based on polynomial value computation over a finite field, provide invulnerability to attacks observation time performance, was proposed. 3. For the first time the method of universal hashing, which is based on compositional cascade scheme and hashing based on polynomial value computation in the ring of integers modulo 2 ^ l in both stages, which allows a greater number of keys that do not belong to the class of weak keys, in comparison with universal hashing method based on polynomial value computation in the ring of integers modulo 2 ^ l, was proposed. 4. For the first time algorithm of parallel universal hashing based on polynomial value computation over a finite field, involving hashing messages n parallel streams superblock with n blocks with some key x followed by hashing the received intermediate hash-value of key x ^ n, was proposed. 5. For the first time universal hashing algorithm based on calculating the value of a polynomial in the ring of integers modulo 2 ^ l, which uses only the transformation over the ring of integers modulo instead of changes in the fields, was proposed. 6. For the first time parallel algorithm universal hashing, realizing compositional cascade scheme and hashing based on polynomial value computation in the ring of integers modulo 2 ^ l in both stages, was proposed. 7. Software that implement the methods of universal hashing in the ring of integers modulo 2 ^ l was developed. 8. Some analytical relationships, which allows to estimate the probability of choosing weak keys for universal hashing functions based on polynomial value computation over finite fields and over the ring of integers modulo 2 ^ l, were developed. Scientific novelty. 1. The improvement of method of universal hashing based on polynomial value computation over a finite field, which is different from the prototype that involves hashing messages n in parallel streams superblock with n blocks with some key x followed by hashing the received intermediate hash-value of key x ^ n, which allowed to increase performance in n times, where n - number of threads, was proposed. 2. For the first time the method of universal hashing, which is based on calculating the value of a polynomial in the ring of integers modulo 2 ^ l, thus allowing for the probability of collisions 1 / (2 ^ (l-1)) regardless of the length of the message, increase the speed of approximately 2, 5 times as compared with the function hashing based on polynomial value computation over a finite field, provide invulnerability to attacks observation time performance, was proposed. 3. For the first time the method of universal hashing, which is based on compositional cascade scheme and hashing based on polynomial value computation in the ring of integers modulo 2 ^ l in both stages, which allows a greater number of keys that do not belong to the class of weak keys, in comparison with universal hashing method based on polynomial value computation in the ring of integers modulo 2 ^ l, was proposed. Scientific theoretical and practical results of the thesis can be used in the design of high-speed protection of information in computer systems and networks
