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      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.

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        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.