scalar multiplication


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scalar multiplication

[′skā·lər ‚məl·tə·pli′kā·shən]
(mathematics)
The multiplication of a vector from a vector space by a scalar from the associated field; this usually contracts or expands the length of a vector.
References in periodicals archive ?
* Identity element of scalar multiplication: 1v = v, where 1 is the real number one.
In the NA[F.sub.k] algorithm, the converted NAF values are buffered in memory until scalar multiplication or modular exponentiation is completed.
Finally, we prove that scalar multiplication is continuous.
The proposed protocol requires more time in scalar multiplication and XOR operation.
The implementation of the scalar multiplication multiplyScalar() is straightforward as it corresponds to multiplying an arbitrary [C.sub.i]--we choose [C.sub.1] for simplicity--of the respective MPO by the scalar at hand.
The addition [[direct sum].sub.M] and scalar multiplication [[cross product].sub.M] for the set [parallel][V.sub.s][parallel] = {[+ or -][parallel]a[parallel]; a [member of] [V.sub.s]} in the axiom (VV) of gyrovector space are defined by the equations
It has been found that the cost of the bilinear parings is approximately 20 times more than that of the scalar multiplication over elliptic curve group [34].
The first scalar multiplication ([pp.sub.i] x [PS2.sub.j]) in [V.sub.ijk] can be pre-computed whenever the pseudonym is generated for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the current autonomous network as it saves one scalar multiplication during signature generation.
A linear topological space X over the real field R is said to be a paranormed space if there is a subadditive function g:X [member of] R such that g([theta]) = 0, g(x) = g(-x), and scalar multiplication is continuous, i.e., [absolute value of [[alpha].sub.n] - [alpha]] [right arrow] 0 and g([x.sub.n] - x) [right arrow] 0 imply g([[alpha].sub.n][x.sub.n] - ax) [right arrow] 0 for all x's in X and a's in R, where [theta] is the zero vector in the linear space X.
This addition and scalar multiplication are called Blaschke addition and scalar multiplication.
Temporary registers store intermediate results during the scalar multiplication. Add blockperforms finite field addition and subtraction, with simple XOR gates.
Therefore we can construct an IT2FNN-2 that computes all FBF expansion combinations with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the form of the proposed IT2FNN-2, and Y is closed under scalar multiplication.