The function space F(D,V) becomes a vector space if we endow the space with an addition and scalar multiplication
such that the vector space axioms in Definition 6 are fulfilled.
However, the computation cost of the pairing is much higher than that of the scalar multiplication
over the elliptic curve group.
Graded Lie algebras and regular prehomogeneous vector spaces with one- dimensional scalar multiplication
The twelve selections that make up the main body of the text are devoted to pairing-based cryptography, parity-friendly elliptical curves, the arithmetic of finite fields, scalar multiplication
and exponentiation in pairing groups, final exponentiation, hashing into elliptic curves, and a wide variety of other related subjects.
It was shown in  how arithmetic operations of addition, subtraction, multiplication and scalar multiplication
could be performed on the set of neutrosophic quadruple numbers.
Actually, the neutrosophic scalar multiplication
is an extension of neutrosophic summation; in the last, one has [lambda] = 2.
m] is computation time for scalar multiplication
This addition and scalar multiplication
are called Blaschke addition and scalar multiplication
The relative computation cost of a pairing is approximately twenty times higher than that of the scalar multiplication
over elliptic curve group (CAO; KOU, 2011; CHEN et al.
Hariri and Reyhani-Masoleh  proposed a number of bit-serial and bit-parallel Montgomery multipliers and showed that MM can accelerate the ECC scalar multiplication
In this work, we want to reduce its computation by focusing on its bottleneck operation, scalar multiplication
G admits a scalar multiplication
, [direct sum], possessing the following properties.