# 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 ?
A] that is smaller than [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and then compute the scalar multiplication [D.
As the above shown, each of Alice and Bob compute two scalar multiplications and the scalar multiplication is the unique operation that involved in HECDH.
A natural algorithm to compute the scalar multiplication mD is (signed) binary method.
The [tau]-expansion's length of any algebraic integral number is optimized in Section 5, An efficient scalar multiplication algorithm is proposed in Section 6, and the last section gives the conclusion.
According to the above discussion, we can obtain an efficient scalar multiplication algorithm.
n] be a map such that E(K) is closed under addition and positive scalar multiplication and E(K) [?
Since E(K) is closed under addition and positive scalar multiplication, [lambda]E(x)+(1-[lambda])E(y)[member of]E(K) that implies [lambda]E(x)+(1-[lambda])E(y)[member of]K.
In the ID-AK-1 protocol each user needs to compute 4 Weil pairings and 1 scalar multiplication.
Regarding efficiency, in each protocol run the following operations have to be computed: 4 pairing operation, 5 scalar multiplication and 1 exponentiations.
According to the authors, their protocol requires the following computational operations: 8 pairing operation, 4 scalar multiplication, 8 exponentiations.
In the second protocol, 1D-AK-2, each user is required to compute 2 scalar multiplications and 3 Weil pairings.
It requires each participant to compute 2 additions, 4 scalar multiplications, and 4 Well pairings.

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