REDUCING INVERSION PROCESSES OF POINT ADDITION TO SPEED UP ELLIPTIC CURVE CRYPTOGRAPHY
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Abstract
In this paper, a modified algorithm for an affine coordinate system is proposed to speed up encryption and decryption processes in elliptic curve cryptography (ECC). In fact, inversion, squaring and multiplication are the main processes for both point addition and point doubling. For three different processes, the inversion process has the highest cost. In the related works, to find 8P where P is represented as a point on curve, at least two inversion processes are needed to perform this task. On the other hand, the proposed method requires only one inversion process to compute 8P. The experimental results show that the proposed method can perform the process faster than 2(4P) method. In general, the method is suitable for computing R = kP, where k = 8i + j and j is a small integer. Moreover, the proposed method also can be chosen to apply with Ternary/Binary Approach which is an improved point multiplication method to speed up ECC.
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References
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