Ramzi A. High-efficiency implementation of the data protection protocols based on modular arithmetic operations

The proposed approach to solving of this problem is base on of assumption that in practice the keys of the most public-keys data protection systems such as RSA and Digital Signature Standard, are changing rarely. So the modulus is changing a rather rarely too. This fact allows to speed up of modular operations implementation by using of precomputations which are depend on modulus only. The new precomputation modular multiplication algorithms are presented for modular multiplication for a fixed modulus. One of them is base on classical modular multiplication scheme and second is the modification of Montgomery algorithm. It has been shown that performance of proposed algorithms approximately twice high in compare to Montgomery algorithm and the amount of required storage is moderate. The new algorithms for modular squaring and multiplication by fixed number based on reduction of Montgomery have been proposed. By including of excess operations and using of precomputations the computational complexityof the proposed algorithm is less in compare to Montgomery modular multiplication algorithm.