mirror of https://github.com/zcash/halo2.git
Apply some suggestions from code review
Co-authored-by: str4d <thestr4d@gmail.com>
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Elliptic curves constructed over finite fields are another important cryptographic tool.
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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#Inverses_and_groups),
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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](fields#) is hard.
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There are several ways to define the curve equation, but for our purposes, let
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There are several ways to define the curve equation, but for our purposes, let
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@ -34,7 +34,7 @@ known as the discrete log of $H$ with respect to $G$, is considered computationa
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infeasible with classical computers. This is called the elliptic curve discrete log
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infeasible with classical computers. This is called the elliptic curve discrete log
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assumption.
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assumption.
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If an elliptic curve group $\mathbb{G}$ has prime order $q$ (like the ones used in Halo),
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If an elliptic curve group $\mathbb{G}$ has prime order $q$ (like the ones used in Halo 2),
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then it is a finite cyclic group. Recall from the section on [groups](fields.md#Groups)
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then it is a finite cyclic group. Recall from the section on [groups](fields.md#Groups)
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that this implies it is isomorphic to $\mathbb{Z}/q\mathbb{Z}$, or equivalently, to the
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that this implies it is isomorphic to $\mathbb{Z}/q\mathbb{Z}$, or equivalently, to the
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scalar field $\mathbb{F}_q$. Each possible generator $G$ fixes the isomorphism; then
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scalar field $\mathbb{F}_q$. Each possible generator $G$ fixes the isomorphism; then
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