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</head><body class="rustdoc trait"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"><a href="#">CurveExt</a></h2><div class="sidebar-elems"><section><h3><a href="#required-associated-types">Required Associated Types</a></h3><ul class="block"><li><a href="#associatedtype.AffineExt">AffineExt</a></li><li><a href="#associatedtype.Base">Base</a></li><li><a href="#associatedtype.ScalarExt">ScalarExt</a></li></ul><h3><a href="#required-associated-consts">Required Associated Constants</a></h3><ul class="block"><li><a href="#associatedconstant.CURVE_ID">CURVE_ID</a></li></ul><h3><a href="#required-methods">Required Methods</a></h3><ul class="block"><li><a href="#tymethod.a">a</a></li><li><a href="#tymethod.b">b</a></li><li><a href="#tymethod.endo">endo</a></li><li><a href="#tymethod.hash_to_curve">hash_to_curve</a></li><li><a href="#tymethod.is_on_curve">is_on_curve</a></li><li><a href="#tymethod.jacobian_coordinates">jacobian_coordinates</a></li><li><a href="#tymethod.new_jacobian">new_jacobian</a></li></ul><h3><a href="#implementors">Implementors</a></h3></section><h2 class="location"><a href="index.html">In halo2_proofs::arithmetic</a></h2></div></nav><main><div class="width-limiter"><div class="sub-container"><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav></div><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn">Trait <a href="../index.html">halo2_proofs</a>::<wbr><a href="index.html">arithmetic</a>::<wbr><a class="trait" href="#">CurveExt</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="item-decl"><pre class="rust trait"><code>pub trait CurveExt: PrimeCurve<Affine = Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.AffineExt" title="type halo2_proofs::arithmetic::CurveExt::AffineExt">AffineExt</a>, Scalar = Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.ScalarExt" title="type halo2_proofs::arithmetic::CurveExt::ScalarExt">ScalarExt</a>> + Group + <a class="trait" href="https://doc.rust-lang.org/nightly/core/default/trait.Default.html" title="trait core::default::Default">Default</a> + <a class="trait" href="https://docs.rs/subtle/2.4.1/subtle/trait.ConditionallySelectable.html" title="trait subtle::ConditionallySelectable">ConditionallySelectable</a> + <a class="trait" href="https://docs.rs/subtle/2.4.1/subtle/trait.ConstantTimeEq.html" title="trait subtle::ConstantTimeEq">ConstantTimeEq</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><Self::Affine> + <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a><Scalar = Self::Scalar> {
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type <a href="#associatedtype.ScalarExt" class="associatedtype">ScalarExt</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a>;
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type <a href="#associatedtype.Base" class="associatedtype">Base</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a>;
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type <a href="#associatedtype.AffineExt" class="associatedtype">AffineExt</a>: <a class="trait" href="trait.CurveAffine.html" title="trait halo2_proofs::arithmetic::CurveAffine">CurveAffine</a><CurveExt = Self, ScalarExt = Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.ScalarExt" title="type halo2_proofs::arithmetic::CurveExt::ScalarExt">ScalarExt</a>, Output = Self, Output = Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.ScalarExt" title="type halo2_proofs::arithmetic::CurveExt::ScalarExt">ScalarExt</a>>;
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const <a href="#associatedconstant.CURVE_ID" class="constant">CURVE_ID</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a>;
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fn <a href="#tymethod.endo" class="fnname">endo</a>(&self) -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.jacobian_coordinates" class="fnname">jacobian_coordinates</a>(&self) -> (Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>);
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<span class="item-spacer"></span> fn <a href="#tymethod.hash_to_curve" class="fnname">hash_to_curve</a>(domain_prefix: &'a <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a>) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/boxed/struct.Box.html" title="struct alloc::boxed::Box">Box</a><dyn <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/function/trait.Fn.html" title="trait core::ops::function::Fn">Fn</a>(&[<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>]) + 'a, <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/alloc/struct.Global.html" title="struct alloc::alloc::Global">Global</a>>;
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<span class="item-spacer"></span> fn <a href="#tymethod.is_on_curve" class="fnname">is_on_curve</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.Choice.html" title="struct subtle::Choice">Choice</a>;
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<span class="item-spacer"></span> fn <a href="#tymethod.a" class="fnname">a</a>() -> Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>;
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<span class="item-spacer"></span> fn <a href="#tymethod.b" class="fnname">b</a>() -> Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>;
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<span class="item-spacer"></span> fn <a href="#tymethod.new_jacobian" class="fnname">new_jacobian</a>(x: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, y: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, z: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self>;
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}</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>This trait is a common interface for dealing with elements of an elliptic
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curve group in a “projective” form, where that arithmetic is usually more
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efficient.</p>
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<p>Requires the <code>alloc</code> feature flag because of <code>hash_to_curve</code>.</p>
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</div></details><h2 id="required-associated-types" class="small-section-header">Required Associated Types<a href="#required-associated-types" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="associatedtype.ScalarExt" class="method has-srclink"><h4 class="code-header">type <a href="#associatedtype.ScalarExt" class="associatedtype">ScalarExt</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a></h4></section></summary><div class="docblock"><p>The scalar field of this elliptic curve.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="associatedtype.Base" class="method has-srclink"><h4 class="code-header">type <a href="#associatedtype.Base" class="associatedtype">Base</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a></h4></section></summary><div class="docblock"><p>The base field over which this elliptic curve is constructed.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="associatedtype.AffineExt" class="method has-srclink"><h4 class="code-header">type <a href="#associatedtype.AffineExt" class="associatedtype">AffineExt</a>: <a class="trait" href="trait.CurveAffine.html" title="trait halo2_proofs::arithmetic::CurveAffine">CurveAffine</a><CurveExt = Self, ScalarExt = Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.ScalarExt" title="type halo2_proofs::arithmetic::CurveExt::ScalarExt">ScalarExt</a>, Output = Self, Output = Self> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.ScalarExt" title="type halo2_proofs::arithmetic::CurveExt::ScalarExt">ScalarExt</a>></h4></section></summary><div class="docblock"><p>The affine version of the curve</p>
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</div></details></div><h2 id="required-associated-consts" class="small-section-header">Required Associated Constants<a href="#required-associated-consts" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="associatedconstant.CURVE_ID" class="method has-srclink"><h4 class="code-header">const <a href="#associatedconstant.CURVE_ID" class="constant">CURVE_ID</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a></h4></section></summary><div class="docblock"><p>CURVE_ID used for hash-to-curve.</p>
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</div></details></div><h2 id="required-methods" class="small-section-header">Required Methods<a href="#required-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.endo" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.endo" class="fnname">endo</a>(&self) -> Self</h4></section></summary><div class="docblock"><p>Apply the curve endomorphism by multiplying the x-coordinate
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by an element of multiplicative order 3.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.jacobian_coordinates" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.jacobian_coordinates" class="fnname">jacobian_coordinates</a>(&self) -> (Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>)</h4></section></summary><div class="docblock"><p>Return the Jacobian coordinates of this point.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.hash_to_curve" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.hash_to_curve" class="fnname">hash_to_curve</a>(domain_prefix: &'a <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a>) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/boxed/struct.Box.html" title="struct alloc::boxed::Box">Box</a><dyn <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/function/trait.Fn.html" title="trait core::ops::function::Fn">Fn</a>(&[<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>]) + 'a, <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/alloc/struct.Global.html" title="struct alloc::alloc::Global">Global</a>></h4></section></summary><div class="docblock"><p>Requests a hasher that accepts messages and returns near-uniformly
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distributed elements in the group, given domain prefix <code>domain_prefix</code>.</p>
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<p>This method is suitable for use as a random oracle.</p>
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<h5 id="example"><a href="#example">Example</a></h5>
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<div class="example-wrap"><pre class="rust rust-example-rendered"><code><span class="kw">use </span>pasta_curves::arithmetic::CurveExt;
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<span class="kw">fn </span>pedersen_commitment<C: CurveExt>(
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x: C::ScalarExt,
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r: C::ScalarExt,
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) -> C::Affine {
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<span class="kw">let </span>hasher = C::hash_to_curve(<span class="string">"z.cash:example_pedersen_commitment"</span>);
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<span class="kw">let </span>g = hasher(<span class="string">b"g"</span>);
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<span class="kw">let </span>h = hasher(<span class="string">b"h"</span>);
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(g * x + <span class="kw-2">&</span>(h * r)).to_affine()
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}</code></pre></div>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.is_on_curve" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.is_on_curve" class="fnname">is_on_curve</a>(&self) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.Choice.html" title="struct subtle::Choice">Choice</a></h4></section></summary><div class="docblock"><p>Returns whether or not this element is on the curve; should
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always be true unless an “unchecked” API was used.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.a" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.a" class="fnname">a</a>() -> Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a></h4></section></summary><div class="docblock"><p>Returns the curve constant a.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.b" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.b" class="fnname">b</a>() -> Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a></h4></section></summary><div class="docblock"><p>Returns the curve constant b.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.new_jacobian" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.new_jacobian" class="fnname">new_jacobian</a>(x: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, y: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>, z: Self::<a class="associatedtype" href="trait.CurveExt.html#associatedtype.Base" title="type halo2_proofs::arithmetic::CurveExt::Base">Base</a>) -> <a class="struct" href="https://docs.rs/subtle/2.4.1/subtle/struct.CtOption.html" title="struct subtle::CtOption">CtOption</a><Self></h4></section></summary><div class="docblock"><p>Obtains a point given Jacobian coordinates $X : Y : Z$, failing
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if the coordinates are not on the curve.</p>
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</div></details></div><h2 id="implementors" class="small-section-header">Implementors<a href="#implementors" class="anchor"></a></h2><div id="implementors-list"><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-CurveExt-for-Ep" class="impl has-srclink"><a href="#impl-CurveExt-for-Ep" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.CurveExt.html" title="trait halo2_proofs::arithmetic::CurveExt">CurveExt</a> for Ep</h3></section></summary><div class="impl-items"><section id="associatedtype.ScalarExt-1" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.ScalarExt-1" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.ScalarExt" class="associatedtype">ScalarExt</a> = Fq</h4></section><section id="associatedtype.Base-1" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Base-1" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Base" class="associatedtype">Base</a> = Fp</h4></section><section id="associatedtype.AffineExt-1" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.AffineExt-1" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.AffineExt" class="associatedtype">AffineExt</a> = EpAffine</h4></section><section id="associatedconstant.CURVE_ID-1" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.CURVE_ID-1" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.CURVE_ID" class="constant">CURVE_ID</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a> = "pallas"</h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-CurveExt-for-Eq" class="impl has-srclink"><a href="#impl-CurveExt-for-Eq" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.CurveExt.html" title="trait halo2_proofs::arithmetic::CurveExt">CurveExt</a> for Eq</h3></section></summary><div class="impl-items"><section id="associatedtype.ScalarExt-2" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.ScalarExt-2" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.ScalarExt" class="associatedtype">ScalarExt</a> = Fp</h4></section><section id="associatedtype.Base-2" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Base-2" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Base" class="associatedtype">Base</a> = Fq</h4></section><section id="associatedtype.AffineExt-2" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.AffineExt-2" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.AffineExt" class="associatedtype">AffineExt</a> = EqAffine</h4></section><section id="associatedconstant.CURVE_ID-2" class="associatedconstant trait-impl has-srclink"><a href="#associatedconstant.CURVE_ID-2" class="anchor"></a><h4 class="code-header">const <a href="#associatedconstant.CURVE_ID" class="constant">CURVE_ID</a>: &'static <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.str.html">str</a> = "vesta"</h4></section></div></details></div><script src="../../implementors/pasta_curves/arithmetic/curves/trait.CurveExt.js" data-ignore-extern-crates="pasta_curves" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="halo2_proofs" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (06f049a35 2022-10-17)" ></div></body></html> |