Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
Elliptic Net Scalar Multiplication upon Koblitz Curves
Muslim, N., Yunos, F., Razali, Z., and Said, M. R. M.
Corresponding Email: faridahy@upm.edu.my
Received date: 30 March 2020
Accepted date: 20 August 2020
Abstract:
Elliptic net scalar multiplication (ENSM) is a recent trend in cryptography. The first ENSM was constructed using short Weierstrass's division
polynomials over a prime field. However, the ENSM over binary field is unknown. Hence, this study proposes a scalar multiplication via elliptic net upon Koblitz curves over binary field. The objectives outlined in this study are to investigate the relationships between division polynomials, elliptic divisibility sequences, and two types of Koblitz curve over binary field. Additionally, this study looked into the new relationship established between elliptic net and its scalar multiplication. The explicit formulae for ENSM are proposed and their computational costs of field operations are evaluated and discussed.
Keywords: Binary field, elliptic net, point, scalar multiplication, Weierstrass curve
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