Abstract
The new approach to accelerate the computational implementation of the basic for a wide range of cryptographic data protection mechanisms operation of exponentiation on Galois Fields have been proposed. The approach is based on the use of a specific property of a polynomial square and the Montgomery reduction. A new method of squaring reduces the amount of computation by 25% compared to the known ones. Based on the developed method, the exponentiation on Galois Fields procedure has been modified, which allows to reduce the amount of calculations by 20%.
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