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Elliptic curves constructed over finite fields are another important cryptographic tool.
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We use elliptic curves because they provide a cryptographic [group](fields.md#Groups),
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i.e. a group in which the [discrete logarithm problem](fields#) is hard.
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i.e. a group in which the discrete logarithm problem (discussed below) is hard.
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There are several ways to define the curve equation, but for our purposes, let
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$\mathbb{F}_p$ be a large (255-bit) field, and then let the set of solutions $(x, y)$ to
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