# Scalar Multiplication A point-scalar multiplication for an elliptic curve is defined as follows: $$ kP = k\*(x,y) $$ Here, $$k$$ is a scalar or base field element of an elliptic curve and $$P$$ or $$(x,y)$$ is a point on an elliptic curve. Optimizing point-scalar multiplication for elliptic curve points is of significant interest. As point addition proves very cheap, we must reduce point multiplications into a series of point additions instead. The simplest and most naive method to achieve this is the [Double-and-add](/intro/primitives/abstract-algebra/elliptic-curve/scalar-multiplication/double-and-add.md) method. Perhaps the more significant problem to solve is the [MSM problem](/intro/primitives/abstract-algebra/elliptic-curve/msm.md) where the question of how to most efficiently optimize scalar multiplication is generalized to how to most efficiently optimize the sum of multiple scalar multiplications. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://fractalyze.gitbook.io/intro/primitives/abstract-algebra/elliptic-curve/scalar-multiplication.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.