Mekush O. Modular arithmetic algorithms for long numbers

The thesis is devoted to analysis of algorithms aimed at modular arithmetic. New effective modular arithmetic algorithms are proposed, especially with using parallel computations. The effective iterative modular reduction algorithm is proposed, parallel modular exponentiation method based on linear forms of digital sequences was improved, new effective parallel multi-exponentiation methods based on modular exponentiation methods are proposed. These algorithms solve an important task - to speed up encryption-decryption of information in real time cryptography systems and have vital importance for developing software for current information security systems.