Kolovanova I. Mathematical and computational methods of forecasting the number of GCM & GMAC weak keys

The thesis is devoted to the solution of important scientific and technical problem, which is to develop mathematical and computational methods for forecasting the number of GCM & GMAC weak keys, the justification of practical recommendations for its use in Ukraine. The thesis first developed the mathematical models and methods for estimating the number of GCM & GMAC weak keys. Analytical evaluations of the probability of weak keys, which leads to a degenerate work hashing function, were obtained. It was proved that the probability of occurrence of weak keys do not depend on their length, and is determined by back to the power of the blocks messages set. The thesis first developed the mathematical model of reduced (mini) version of GCM & GMAC based on the scaling symmetrical cryptotransformations preserving their algebraic structure. This allows to forecast the various cryptographic strength parameters of the full version mode when using originals ciphers. The computational method of forecasting the cryptographic properties of block symmetric ciphers was further developed. It designed to study collisional properties of formed message authentication codes with forecasting the corresponding characteristics when applying the full mode version and originals ciphers. Keywords: encryption mode, message authentication code, mini-version, hashing, forecasting, hash-code, weak key, counter, cryptotransformation.