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 Nagatoshi SASANO

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 [3] 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 in [G.

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 [10] 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.