Efficient elliptic curve cryptosystems

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Darweesh Kamal; Saleh Mohammad

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2018 | Volume:9 | Issue:1 Page(s): 161-174

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Title

Efficient elliptic curve cryptosystems

Author(s)

Darweesh Kamal | Saleh Mohammad | Issue Writer Certificate

Keywords

cryptography

elliptic curves

affine coordinates

Abstract

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation, which allow e cient implementations of ECC. In this paper, we improve e cient algorithm for exponentiation on elliptic curves de ned over Fp in terms of a ne coordinates. The algorithm computes 2n2(2n1P +Q) directly from random points P and Q on an elliptic curve, without computing the intermediate points. Moreover, we apply the algorithm to exponentiation on elliptic curves with width{w Mutual Opposite Form (wMOF) and analyze their computational complexity. This algorithm can speed up the wMOF exponentiation of elliptic curves of size 160{bit about (21. 7%) as a result of its implementation with respect to a ne coordinates.

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APA: Copy

Darweesh, Kamal, & Saleh, Mohammad. (2018). Efficient elliptic curve cryptosystems. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 9(1), 161-174. SID. https://sid.ir/paper/340807/en

Vancouver: Copy

Darweesh Kamal, Saleh Mohammad. Efficient elliptic curve cryptosystems. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2018;9(1):161-174. Available from: https://sid.ir/paper/340807/en

IEEE: Copy

Kamal Darweesh, and Mohammad Saleh, “Efficient elliptic curve cryptosystems,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 9, no. 1, pp. 161–174, 2018, [Online]. Available: https://sid.ir/paper/340807/en

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