Asynchronous cryptography is one of the most widely used cryptographic algorithms. Much research has been done to find other applications of this cryptography method. Modular exponentiation is one of the primitive operations in these algorithms. Since we need to perform multiplication, square and modular division, most aspects of these studies were based on optimizing each of these algorithms. Since access to faster software or hardware techniques was the objective of these studies, after studying optimized implementation methods of multiplication and division, we tried to take a step toward the application of methods of software implementation of some examples to decrease implementation time and increase the efficiency of algorithms of this type in this paper.
Key words: Reduction division, asynchronous cryptography, modular multiplication, Karatsuba-Ofman multiplication.
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