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2018•Unpublished venueRequires access

Applying Pell Numbers for Efficient Elliptic Curve Large Scalar Multiplication

Fudailah Duemong, Ladda Preechaveerakul

Open publisher page 2 citations

Abstract

One of the most effective techniques of cryptography is the Elliptic Curve Cryptography (ECC) which is currently used widely. The ECC provides a high level of security with a smaller key size and faster calculation. The scalar multiplication using points on a curve is the main process to generate the key in the ECC. However, the computation time to generate the key significantly increases with a number of arithmetic operations for a large scalar multiplication. Therefore, a new method applying with Pell numbers is presented. This proposed method outperforms traditional binary representation method regarding the computational efficiency for the large scalar multiplication.

About this research paper

What this paper is about

One of the most effective techniques of cryptography is the Elliptic Curve Cryptography (ECC) which is currently used widely. The ECC provides a high level of security with a smaller key size and faster calculation. The scalar multiplication using points on a curve is the main process to generate the key in the ECC. However, the computation time to generate the key significantly increases with a number of arithmetic operations for a large scalar multiplication. Therefore, a new method applying with Pell numbers is presented. This proposed method outperforms traditional binary representation method regarding the computational efficiency for the large scalar multiplication.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

One of the most effective techniques of cryptography is the Elliptic Curve Cryptography (ECC) which is currently used widely. The ECC provides a high level of security with a smaller key size and faster calculation. The scalar multiplication using points on a curve is the main process to generate the key in the ECC. However, the computation time to generate the key significantly increases with a number of arithmetic operations for a large scalar multiplication. Therefore, a new method applying with Pell numbers is presented. This proposed method outperforms traditional binary representation method regarding the computational efficiency for the large scalar multiplication.

Key concepts: Scalar multiplication, Elliptic curve cryptography, Elliptic curve point multiplication, Elliptic curve, Key size, Scalar (mathematics), Elliptic Curve Digital Signature Algorithm, Cryptography

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