N.I. Chervyakov, M.V. Lobes

At the present stage the problem of security saving transferred information resources can be solved only on the basis of the use of cryptographic systems which basis are theoretic-numerical problems. So, for example, a guarantee of re-liability of one of the most applied on the Internet or in local networks cryptosystems with the open key are difficulties of the decision of problems factorization. The majority of existing theoretic-numerical problems contain numerous performance of such labor-consuming opera-tions, as modular exponentiation and division. At performance of these operations as operands the numbers exceeding a range of typical computers in one thousand - one million and more time act. In process of development of cryptographic methods and means of protection of the information ranges of recessive numbers continuously extend. Extensive classes of existing theoretic-numerical methods and algorithms within the limits of the speed provided by modern computers, practically cannot be realized. The great value at the decision of these problems is got with development of the parallel algorithms optimizing compu-ting process; development of parallel computers on which these algorithms could be effectively realized. For develop-ment of parallel computing algorithms huge opportunities are given with application of not item notations, most pers-pective of which is the system of residual classes. This system possesses advantages at natural распараллеливании calculations, small word length of the rests, high accuracy, reliability, ability to self-correction, and realizes a principle of conveyor processing of the information. Application claster systems gives new opportunities in development of the parallel computing algorithms based on JUICE. The article highlights the main shortcomings of algorithms for solving number-theoretic problems in terms of their application in cryptosystems. Main trends in the development of computer systems are introduced. An algorithm for parallel operation of modular exponentiation of large numbers is proposed. The concept of the cluster system as a platform for the implementation of the algorithm is defined.