Security and Communication Networks / 2020 / Article / Tab 1

Research Article

Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields

Table 1

Complexity comparison for -bit in different single algorithms.

MethodPoint operationsField operations (I = 10M)

Montgomery-D6mM + 10M + I1418M2474M
Montgomery-H3mM + m (2M + I)3495M6135M
Algorithm 2-D (-projective)10mM + 11M + I2351M4111M
Algorithm 2-D (twisted )9mM + 11M + I2118M3702M
Algorithm 1-H10mM + 11M + I2351M4111M

Montgomery-D = Montgomery double-and-add algorithm, Montgomery-H = Montgomery halve-and-add algorithm, Algorithm. 2-D (-Projective) = Algorithm 2 using the -projective coordinate system, Algorithm. 2-D (twisted ) = Algorithm 2 using the twisted coordinate system, Algorithm. 1-H = Algorithm 1 for halve-and-add.

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