Methodology of processing multi-digit numbers in asymmetric cryptosystems

Abstract

To date, an increase in the key length inevitably leads to an increase in computational volumes to protect information flows using asymmetric cryptosystems, where the most common operations there is the modular multiplication and modular exponentiation. Existing methods and algorithms for performing above-mention operations are based on positional numerical systems that are characterized by considerable time complexity due to the limited possibilities of parallelizing the computation process, which leads to a decrease in their performance. Using of new approaches, in particular, the vector-modular method of modular multiplication and exponential, as well as the system of residual classes, will allow expanding the functionality of computing systems to encrypt / decrypt information. To this goal, a methodology which allows to increase the speed of asymmetric cryptosystems is proposed, and the basic mechanism of which is grounded on the eight stages: the formation of a plurality of open-ended blocks, the formation of requirements for cryptosystem parameters and information security, the choice of an asymmetric cryptosystem, the formation of a set of basic operations, the choice of the method of operations execution , the choice of the form of the system of residual classes, the choice of methods for constructing perfect and modified perfect forms of the system of residual classes, the implementation of basic asymmetries cryptosystems based on these approaches. The proposed methodology can reduce the temporal complexity, increase the speed of algorithms, specialized software and hardware during the processing of multi-digit numbers in asymmetric cryptosystems.