Next, let us show that the addition and

scalar multiplication are continuous and multiplication is separately continuous in the topology [??].

In this section, we overview the well-known NAF conversion algorithms, which improve the [NAF.sub.W] algorithm in terms of memory efficiency and the NAF conversion speed in

scalar multiplication and so on.

We consider the cost of collision-resistant hash function, bilinear pairing,

scalar multiplication, exclusive-OR, and group exponent.

Graded Lie algebras and regular prehomogeneous vector spaces with one- dimensional

scalar multiplication Nagatoshi SASANO

(iv) the

scalar multiplication is continuous, that is,

* In session key computation, 2 pairings and 2 hashing operation,

scalar multiplication and exponentiation are required.

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.

Making use of these formulations, it is easy to show that basic operations such as

scalar multiplication, addition, and inner product as well as the multiplication of an MPS by an MPO or of two MPOs can be performed in the formalism.

The Mobius addition [[direct sum].sub.M] and the Mobius

scalar multiplication [[cross product].sub.M] are given by the equations

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.