Abstract
Problem statement: Modular exponentiation constitutes the basis of many well-known and widely used public key cryptosystems. Approach: A fast portable modular exponentiation algorithm considerably enhanced the speed and applicability of these systems, also an efficient implementation of this algorithm was the key to high performance of such system. Results: In this study, two main approaches for solving this problem were proposed. The proposed approaches involved calculations without usage of extra operational memory for saving constants and calculations with usage of preliminary calculated constants. Conclusion/Recommendations: The estimation of complexity of the speedup and effectiveness of proposed approaches for the data were presented.
Highlights
From this we have: Protection of information is one of the most important and complicated problems in computer equipment
The given problem can be decided with the help of fastening of exponentiation operation performance for numbers of high digit capacity
Diagram of dependence of the number of multiplication operations upon the value of frame of calculus s has the highest advantage in number of operations Parallel algorithm with frame of s=2t provides the minimum amount of multiplication operations and provides the greater effectiveness Fulfillment of exponentiation operation in case of representation of figure in Fibonacci Calculus (FC) requires the less amount of memory cells, than in case of representation of figures in calculus’s with frame of s = 2t
Summary
From this we have: Protection of information is one of the most important and complicated problems in computer equipment. Specialists face the task of creation of systems for transmission of information, which would maintain the high level of protection and security. Nowadays the speediest systems of confidential information transmission are the systems with open keys. The majority of these systems use operation of modular exponentiation xy mod z as basic for great numbers (Diffie and Hellman, 1976). The performance of given operation requires high expenses of machinery time. That is why the necessarily of this procedure optimization raises. The given problem can be decided with the help of fastening of exponentiation operation performance for numbers of high digit capacity
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