Scalar multiplication” is a fancy way of saying multiplication by repeated additions

Huh, in every context I’ve seen it used, it has meant vector/scalar multiplication (as opposed to things like vector/vector multiplication). Thanks for defining terms.

I wonder what the origin of this “multiplication by repeated addition” definition is.

Actually it’s the same definition (though restricted to integer scalars): on the one hand you have a group element (could be a vector, could be an ECC point), for which an addition operation is defined. On the other hand you have a scalar, which can multiply the group element.

When the scalar is an integer n, adding the group element to itself n times gives exactly the same result as the vector/scalar multiplication you’re used to.

Huh, in every context I’ve seen it used, it has meant vector/scalar multiplication (as opposed to things like vector/vector multiplication). Thanks for defining terms.

I wonder what the origin of this “multiplication by repeated addition” definition is.

Actually it’s the same definition (though restricted to integer scalars): on the one hand you have a

group element(could be a vector, could be an ECC point), for which an addition operation is defined. On the other hand you have ascalar, which can multiply the group element.When the scalar is an integer

n, adding the group element to itselfntimes gives exactly the same result as the vector/scalar multiplication you’re used to.