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
(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  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.