Study of Efficient Scalar Multiplication over Elliptic Curve


The process of repeatedly adding a point on a curve to itself is known as elliptic curve scalar multiplication [1]. In recent years, many cryptography researchers have been drawn to research on scalar multiplication over elliptic curves (EC) over finite fields to explore how elliptic curves cryptography (ECC) may be implemented and how to reduce its complexity [2]. The most efficient ways employed in Elliptic curve cryptography include elliptic curve scalar multiplication using the point-halving algorithm [3], then the double-base (DB) chain algorithm, and finally step multi-base representation (SMBR), however each technique has its own set of limitations. As a result, developing a novel approach that can be used to properly install ECC while simultaneously reducing its complexity is crucial. The Treble algorithm, which is a new approach, is introduced in the study for affine coordinates. To make the binary idea or double and add operation more efficient, we used the treble technique, which refers to the use of all input values in producing any form of output, including how much time and energy is required. The results show that our contribution can greatly improve EC scalar multiplication. Cryptography’s Elliptic Curve Scalar Multiplication is a fascinating topic.

Author (S) Details

Deepika Kamboj
MBM Engineering College, Jodhpur, Rajasthan, India.

Shivani Sharma
P.C.S Officer under Government of Uttar Pradesh, India.

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