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 <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/openssl-0.10.54/src/ec.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>ec.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../openssl/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../openssl/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><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><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span>
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 </pre><pre class="rust"><code><span class="doccomment">//! Elliptic Curve
 //!
 //! Cryptography relies on the difficulty of solving mathematical problems, such as the factor
 //! of large integers composed of two large prime numbers and the discrete logarithm of a
 //! random elliptic curve.  This module provides low-level features of the latter.
 //! Elliptic Curve protocols can provide the same security with smaller keys.
 //!
 //! There are 2 forms of elliptic curves, `Fp` and `F2^m`.  These curves use irreducible
 //! trinomial or pentanomial.  Being a generic interface to a wide range of algorithms,
 //! the curves are generally referenced by [`EcGroup`].  There are many built-in groups
 //! found in [`Nid`].
 //!
 //! OpenSSL Wiki explains the fields and curves in detail at [Elliptic Curve Cryptography].
 //!
 //! [`EcGroup`]: struct.EcGroup.html
 //! [`Nid`]: ../nid/struct.Nid.html
 //! [Elliptic Curve Cryptography]: https://wiki.openssl.org/index.php/Elliptic_Curve_Cryptography
 </span><span class="kw">use </span>foreign_types::{ForeignType, ForeignTypeRef};
 <span class="kw">use </span>libc::c_int;
 <span class="kw">use </span>std::fmt;
 <span class="kw">use </span>std::ptr;

 <span class="kw">use </span><span class="kw">crate</span>::bn::{BigNum, BigNumContextRef, BigNumRef};
 <span class="kw">use </span><span class="kw">crate</span>::error::ErrorStack;
 <span class="kw">use </span><span class="kw">crate</span>::nid::Nid;
 <span class="kw">use </span><span class="kw">crate</span>::pkey::{HasParams, HasPrivate, HasPublic, Params, Private, Public};
 <span class="kw">use </span><span class="kw">crate</span>::util::ForeignTypeRefExt;
 <span class="kw">use crate</span>::{cvt, cvt_n, cvt_p, init};
 <span class="kw">use </span>openssl_macros::corresponds;

 <span class="doccomment">/// Compressed or Uncompressed conversion
 ///
 /// Conversion from the binary value of the point on the curve is performed in one of
 /// compressed, uncompressed, or hybrid conversions.  The default is compressed, except
 /// for binary curves.
 ///
 /// Further documentation is available in the [X9.62] standard.
 ///
 /// [X9.62]: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.202.2977&amp;rep=rep1&amp;type=pdf
 </span><span class="attribute">#[derive(Copy, Clone)]
 </span><span class="kw">pub struct </span>PointConversionForm(ffi::point_conversion_form_t);

 <span class="kw">impl </span>PointConversionForm {
     <span class="doccomment">/// Compressed conversion from point value.
     </span><span class="kw">pub const </span>COMPRESSED: PointConversionForm =
         PointConversionForm(ffi::point_conversion_form_t::POINT_CONVERSION_COMPRESSED);

     <span class="doccomment">/// Uncompressed conversion from point value.
     </span><span class="kw">pub const </span>UNCOMPRESSED: PointConversionForm =
         PointConversionForm(ffi::point_conversion_form_t::POINT_CONVERSION_UNCOMPRESSED);

     <span class="doccomment">/// Performs both compressed and uncompressed conversions.
     </span><span class="kw">pub const </span>HYBRID: PointConversionForm =
         PointConversionForm(ffi::point_conversion_form_t::POINT_CONVERSION_HYBRID);
 }

 <span class="doccomment">/// Named Curve or Explicit
 ///
 /// This type acts as a boolean as to whether the `EcGroup` is named or explicit.
 </span><span class="attribute">#[derive(Copy, Clone)]
 </span><span class="kw">pub struct </span>Asn1Flag(c_int);

 <span class="kw">impl </span>Asn1Flag {
     <span class="doccomment">/// Curve defined using polynomial parameters
     ///
     /// Most applications use a named EC_GROUP curve, however, support
     /// is included to explicitly define the curve used to calculate keys
     /// This information would need to be known by both endpoint to make communication
     /// effective.
     ///
     /// OPENSSL_EC_EXPLICIT_CURVE, but that was only added in 1.1.
     /// Man page documents that 0 can be used in older versions.
     ///
     /// OpenSSL documentation at [`EC_GROUP`]
     ///
     /// [`EC_GROUP`]: https://www.openssl.org/docs/manmaster/crypto/EC_GROUP_get_seed_len.html
     </span><span class="kw">pub const </span>EXPLICIT_CURVE: Asn1Flag = Asn1Flag(<span class="number">0</span>);

     <span class="doccomment">/// Standard Curves
     ///
     /// Curves that make up the typical encryption use cases.  The collection of curves
     /// are well known but extensible.
     ///
     /// OpenSSL documentation at [`EC_GROUP`]
     ///
     /// [`EC_GROUP`]: https://www.openssl.org/docs/manmaster/man3/EC_GROUP_order_bits.html
     </span><span class="kw">pub const </span>NAMED_CURVE: Asn1Flag = Asn1Flag(ffi::OPENSSL_EC_NAMED_CURVE);
 }

 <span class="macro">foreign_type_and_impl_send_sync! </span>{
     <span class="kw">type </span>CType = ffi::EC_GROUP;
     <span class="kw">fn </span>drop = ffi::EC_GROUP_free;

     <span class="doccomment">/// Describes the curve
     ///
     /// A curve can be of the named curve type.  These curves can be discovered
     /// using openssl binary `openssl ecparam -list_curves`.  Other operations
     /// are available in the [wiki].  These named curves are available in the
     /// [`Nid`] module.
     ///
     /// Curves can also be generated using prime field parameters or a binary field.
     ///
     /// Prime fields use the formula `y^2 mod p = x^3 + ax + b mod p`.  Binary
     /// fields use the formula `y^2 + xy = x^3 + ax^2 + b`.  Named curves have
     /// assured security.  To prevent accidental vulnerabilities, they should
     /// be preferred.
     ///
     /// [wiki]: https://wiki.openssl.org/index.php/Command_Line_Elliptic_Curve_Operations
     /// [`Nid`]: ../nid/index.html
     </span><span class="kw">pub struct </span>EcGroup;
     <span class="doccomment">/// Reference to [`EcGroup`]
     ///
     /// [`EcGroup`]: struct.EcGroup.html
     </span><span class="kw">pub struct </span>EcGroupRef;
 }

 <span class="kw">impl </span>EcGroup {
     <span class="doccomment">/// Returns the group of a standard named curve.
     ///
     /// # Examples
     ///
     /// ```
     /// # fn main() -&gt; Result&lt;(), Box&lt;dyn std::error::Error&gt;&gt; {
     /// use openssl::nid::Nid;
     /// use openssl::ec::{EcGroup, EcKey};
     ///
     /// let nid = Nid::X9_62_PRIME256V1; // NIST P-256 curve
     /// let group = EcGroup::from_curve_name(nid)?;
     /// let key = EcKey::generate(&amp;group)?;
     /// # Ok(()) }
     /// ```
     </span><span class="attribute">#[corresponds(EC_GROUP_new_by_curve_name)]
     </span><span class="kw">pub fn </span>from_curve_name(nid: Nid) -&gt; <span class="prelude-ty">Result</span>&lt;EcGroup, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             init();
             cvt_p(ffi::EC_GROUP_new_by_curve_name(nid.as_raw())).map(EcGroup)
         }
     }

     <span class="doccomment">/// Returns the group for given parameters
     </span><span class="attribute">#[corresponds(EC_GROUP_new_curve_GFp)]
     </span><span class="kw">pub fn </span>from_components(
         p: BigNum,
         a: BigNum,
         b: BigNum,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;EcGroup, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_GROUP_new_curve_GFp(
                 p.as_ptr(),
                 a.as_ptr(),
                 b.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(EcGroup)
         }
     }
 }

 <span class="kw">impl </span>EcGroupRef {
     <span class="doccomment">/// Places the components of a curve over a prime field in the provided `BigNum`s.
     /// The components make up the formula `y^2 mod p = x^3 + ax + b mod p`.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_curve_GFp)]
     </span><span class="kw">pub fn </span>components_gfp(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         p: <span class="kw-2">&amp;mut </span>BigNumRef,
         a: <span class="kw-2">&amp;mut </span>BigNumRef,
         b: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_GROUP_get_curve_GFp(
                 <span class="self">self</span>.as_ptr(),
                 p.as_ptr(),
                 a.as_ptr(),
                 b.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Places the components of a curve over a binary field in the provided `BigNum`s.
     /// The components make up the formula `y^2 + xy = x^3 + ax^2 + b`.
     ///
     /// In this form `p` relates to the irreducible polynomial.  Each bit represents
     /// a term in the polynomial.  It will be set to 3 `1`s or 5 `1`s depending on
     /// using a trinomial or pentanomial.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_curve_GF2m)]
     #[cfg(not(any(boringssl, osslconf = <span class="string">&quot;OPENSSL_NO_EC2M&quot;</span>)))]
     </span><span class="kw">pub fn </span>components_gf2m(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         p: <span class="kw-2">&amp;mut </span>BigNumRef,
         a: <span class="kw-2">&amp;mut </span>BigNumRef,
         b: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_GROUP_get_curve_GF2m(
                 <span class="self">self</span>.as_ptr(),
                 p.as_ptr(),
                 a.as_ptr(),
                 b.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Places the cofactor of the group in the provided `BigNum`.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_cofactor)]
     </span><span class="kw">pub fn </span>cofactor(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         cofactor: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_GROUP_get_cofactor(
                 <span class="self">self</span>.as_ptr(),
                 cofactor.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Returns the degree of the curve.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_degree)]
     </span><span class="kw">pub fn </span>degree(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; u32 {
         <span class="kw">unsafe </span>{ ffi::EC_GROUP_get_degree(<span class="self">self</span>.as_ptr()) <span class="kw">as </span>u32 }
     }

     <span class="doccomment">/// Returns the number of bits in the group order.
     </span><span class="attribute">#[corresponds(EC_GROUP_order_bits)]
     #[cfg(ossl110)]
     </span><span class="kw">pub fn </span>order_bits(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; u32 {
         <span class="kw">unsafe </span>{ ffi::EC_GROUP_order_bits(<span class="self">self</span>.as_ptr()) <span class="kw">as </span>u32 }
     }

     <span class="doccomment">/// Returns the generator for the given curve as an [`EcPoint`].
     </span><span class="attribute">#[corresponds(EC_GROUP_get0_generator)]
     </span><span class="kw">pub fn </span>generator(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>EcPointRef {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>ptr = ffi::EC_GROUP_get0_generator(<span class="self">self</span>.as_ptr());
             EcPointRef::from_const_ptr(ptr)
         }
     }

     <span class="doccomment">/// Sets the generator point for the given curve
     </span><span class="attribute">#[corresponds(EC_GROUP_set_generator)]
     </span><span class="kw">pub fn </span>set_generator(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         generator: EcPoint,
         order: BigNum,
         cofactor: BigNum,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_GROUP_set_generator(
                 <span class="self">self</span>.as_ptr(),
                 generator.as_ptr(),
                 order.as_ptr(),
                 cofactor.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Places the order of the curve in the provided `BigNum`.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_order)]
     </span><span class="kw">pub fn </span>order(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         order: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_GROUP_get_order(
                 <span class="self">self</span>.as_ptr(),
                 order.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Sets the flag determining if the group corresponds to a named curve or must be explicitly
     /// parameterized.
     ///
     /// This defaults to `EXPLICIT_CURVE` in OpenSSL 1.0.1 and 1.0.2, but `NAMED_CURVE` in OpenSSL
     /// 1.1.0.
     </span><span class="attribute">#[corresponds(EC_GROUP_set_asn1_flag)]
     </span><span class="kw">pub fn </span>set_asn1_flag(<span class="kw-2">&amp;mut </span><span class="self">self</span>, flag: Asn1Flag) {
         <span class="kw">unsafe </span>{
             ffi::EC_GROUP_set_asn1_flag(<span class="self">self</span>.as_ptr(), flag.<span class="number">0</span>);
         }
     }

     <span class="doccomment">/// Returns the name of the curve, if a name is associated.
     </span><span class="attribute">#[corresponds(EC_GROUP_get_curve_name)]
     </span><span class="kw">pub fn </span>curve_name(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="prelude-ty">Option</span>&lt;Nid&gt; {
         <span class="kw">let </span>nid = <span class="kw">unsafe </span>{ ffi::EC_GROUP_get_curve_name(<span class="self">self</span>.as_ptr()) };
         <span class="kw">if </span>nid &gt; <span class="number">0 </span>{
             <span class="prelude-val">Some</span>(Nid::from_raw(nid))
         } <span class="kw">else </span>{
             <span class="prelude-val">None
         </span>}
     }
 }

 <span class="macro">foreign_type_and_impl_send_sync! </span>{
     <span class="kw">type </span>CType = ffi::EC_POINT;
     <span class="kw">fn </span>drop = ffi::EC_POINT_free;

     <span class="doccomment">/// Represents a point on the curve
     </span><span class="kw">pub struct </span>EcPoint;
     <span class="doccomment">/// A reference a borrowed [`EcPoint`].
     </span><span class="kw">pub struct </span>EcPointRef;
 }

 <span class="kw">impl </span>EcPointRef {
     <span class="doccomment">/// Computes `a + b`, storing the result in `self`.
     </span><span class="attribute">#[corresponds(EC_POINT_add)]
     </span><span class="kw">pub fn </span>add(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         a: <span class="kw-2">&amp;</span>EcPointRef,
         b: <span class="kw-2">&amp;</span>EcPointRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_add(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 a.as_ptr(),
                 b.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Computes `q * m`, storing the result in `self`.
     </span><span class="attribute">#[corresponds(EC_POINT_mul)]
     </span><span class="kw">pub fn </span>mul(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         q: <span class="kw-2">&amp;</span>EcPointRef,
         m: <span class="kw-2">&amp;</span>BigNumRef,
         <span class="comment">// FIXME should be &amp;mut
         </span>ctx: <span class="kw-2">&amp;</span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_mul(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 ptr::null(),
                 q.as_ptr(),
                 m.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Computes `generator * n`, storing the result in `self`.
     </span><span class="attribute">#[corresponds(EC_POINT_mul)]
     </span><span class="kw">pub fn </span>mul_generator(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         n: <span class="kw-2">&amp;</span>BigNumRef,
         <span class="comment">// FIXME should be &amp;mut
         </span>ctx: <span class="kw-2">&amp;</span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_mul(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 n.as_ptr(),
                 ptr::null(),
                 ptr::null(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Computes `generator * n + q * m`, storing the result in `self`.
     </span><span class="attribute">#[corresponds(EC_POINT_mul)]
     </span><span class="kw">pub fn </span>mul_full(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         n: <span class="kw-2">&amp;</span>BigNumRef,
         q: <span class="kw-2">&amp;</span>EcPointRef,
         m: <span class="kw-2">&amp;</span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_mul(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 n.as_ptr(),
                 q.as_ptr(),
                 m.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Inverts `self`.
     </span><span class="attribute">#[corresponds(EC_POINT_invert)]
     </span><span class="comment">// FIXME should be mutable
     </span><span class="kw">pub fn </span>invert(<span class="kw-2">&amp;mut </span><span class="self">self</span>, group: <span class="kw-2">&amp;</span>EcGroupRef, ctx: <span class="kw-2">&amp;</span>BigNumContextRef) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_invert(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Serializes the point to a binary representation.
     </span><span class="attribute">#[corresponds(EC_POINT_point2oct)]
     </span><span class="kw">pub fn </span>to_bytes(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         form: PointConversionForm,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;Vec&lt;u8&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>len = ffi::EC_POINT_point2oct(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 form.<span class="number">0</span>,
                 ptr::null_mut(),
                 <span class="number">0</span>,
                 ctx.as_ptr(),
             );
             <span class="kw">if </span>len == <span class="number">0 </span>{
                 <span class="kw">return </span><span class="prelude-val">Err</span>(ErrorStack::get());
             }
             <span class="kw">let </span><span class="kw-2">mut </span>buf = <span class="macro">vec!</span>[<span class="number">0</span>; len];
             <span class="kw">let </span>len = ffi::EC_POINT_point2oct(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 form.<span class="number">0</span>,
                 buf.as_mut_ptr(),
                 len,
                 ctx.as_ptr(),
             );
             <span class="kw">if </span>len == <span class="number">0 </span>{
                 <span class="prelude-val">Err</span>(ErrorStack::get())
             } <span class="kw">else </span>{
                 <span class="prelude-val">Ok</span>(buf)
             }
         }
     }

     <span class="doccomment">/// Creates a new point on the specified curve with the same value.
     </span><span class="attribute">#[corresponds(EC_POINT_dup)]
     </span><span class="kw">pub fn </span>to_owned(<span class="kw-2">&amp;</span><span class="self">self</span>, group: <span class="kw-2">&amp;</span>EcGroupRef) -&gt; <span class="prelude-ty">Result</span>&lt;EcPoint, ErrorStack&gt; {
         <span class="kw">unsafe </span>{ cvt_p(ffi::EC_POINT_dup(<span class="self">self</span>.as_ptr(), group.as_ptr())).map(EcPoint) }
     }

     <span class="doccomment">/// Determines if this point is equal to another.
     </span><span class="attribute">#[corresponds(EC_POINT_cmp)]
     </span><span class="kw">pub fn </span>eq(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         other: <span class="kw-2">&amp;</span>EcPointRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;bool, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>res = cvt_n(ffi::EC_POINT_cmp(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 other.as_ptr(),
                 ctx.as_ptr(),
             ))<span class="question-mark">?</span>;
             <span class="prelude-val">Ok</span>(res == <span class="number">0</span>)
         }
     }

     <span class="doccomment">/// Places affine coordinates of a curve over a prime field in the provided
     /// `x` and `y` `BigNum`s.
     </span><span class="attribute">#[corresponds(EC_POINT_get_affine_coordinates)]
     #[cfg(ossl111)]
     </span><span class="kw">pub fn </span>affine_coordinates(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         x: <span class="kw-2">&amp;mut </span>BigNumRef,
         y: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_get_affine_coordinates(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 x.as_ptr(),
                 y.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Places affine coordinates of a curve over a prime field in the provided
     /// `x` and `y` `BigNum`s
     </span><span class="attribute">#[corresponds(EC_POINT_get_affine_coordinates_GFp)]
     </span><span class="kw">pub fn </span>affine_coordinates_gfp(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         x: <span class="kw-2">&amp;mut </span>BigNumRef,
         y: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_get_affine_coordinates_GFp(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 x.as_ptr(),
                 y.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Sets affine coordinates of a curve over a prime field using the provided
     /// `x` and `y` `BigNum`s
     </span><span class="attribute">#[corresponds(EC_POINT_set_affine_coordinates_GFp)]
     </span><span class="kw">pub fn </span>set_affine_coordinates_gfp(
         <span class="kw-2">&amp;mut </span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         x: <span class="kw-2">&amp;</span>BigNumRef,
         y: <span class="kw-2">&amp;</span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_set_affine_coordinates_GFp(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 x.as_ptr(),
                 y.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Places affine coordinates of a curve over a binary field in the provided
     /// `x` and `y` `BigNum`s
     </span><span class="attribute">#[corresponds(EC_POINT_get_affine_coordinates_GF2m)]
     #[cfg(not(any(boringssl, osslconf = <span class="string">&quot;OPENSSL_NO_EC2M&quot;</span>)))]
     </span><span class="kw">pub fn </span>affine_coordinates_gf2m(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         x: <span class="kw-2">&amp;mut </span>BigNumRef,
         y: <span class="kw-2">&amp;mut </span>BigNumRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_get_affine_coordinates_GF2m(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 x.as_ptr(),
                 y.as_ptr(),
                 ctx.as_ptr(),
             ))
             .map(|<span class="kw">_</span>| ())
         }
     }

     <span class="doccomment">/// Checks if point is infinity
     </span><span class="attribute">#[corresponds(EC_POINT_is_at_infinity)]
     </span><span class="kw">pub fn </span>is_infinity(<span class="kw-2">&amp;</span><span class="self">self</span>, group: <span class="kw-2">&amp;</span>EcGroupRef) -&gt; bool {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>res = ffi::EC_POINT_is_at_infinity(group.as_ptr(), <span class="self">self</span>.as_ptr());
             res == <span class="number">1
         </span>}
     }

     <span class="doccomment">/// Checks if point is on a given curve
     </span><span class="attribute">#[corresponds(EC_POINT_is_on_curve)]
     </span><span class="kw">pub fn </span>is_on_curve(
         <span class="kw-2">&amp;</span><span class="self">self</span>,
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;bool, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>res = cvt_n(ffi::EC_POINT_is_on_curve(
                 group.as_ptr(),
                 <span class="self">self</span>.as_ptr(),
                 ctx.as_ptr(),
             ))<span class="question-mark">?</span>;
             <span class="prelude-val">Ok</span>(res == <span class="number">1</span>)
         }
     }
 }

 <span class="kw">impl </span>EcPoint {
     <span class="doccomment">/// Creates a new point on the specified curve.
     </span><span class="attribute">#[corresponds(EC_POINT_new)]
     </span><span class="kw">pub fn </span>new(group: <span class="kw-2">&amp;</span>EcGroupRef) -&gt; <span class="prelude-ty">Result</span>&lt;EcPoint, ErrorStack&gt; {
         <span class="kw">unsafe </span>{ cvt_p(ffi::EC_POINT_new(group.as_ptr())).map(EcPoint) }
     }

     <span class="doccomment">/// Creates point from a binary representation
     </span><span class="attribute">#[corresponds(EC_POINT_oct2point)]
     </span><span class="kw">pub fn </span>from_bytes(
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         buf: <span class="kw-2">&amp;</span>[u8],
         ctx: <span class="kw-2">&amp;mut </span>BigNumContextRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;EcPoint, ErrorStack&gt; {
         <span class="kw">let </span>point = EcPoint::new(group)<span class="question-mark">?</span>;
         <span class="kw">unsafe </span>{
             cvt(ffi::EC_POINT_oct2point(
                 group.as_ptr(),
                 point.as_ptr(),
                 buf.as_ptr(),
                 buf.len(),
                 ctx.as_ptr(),
             ))<span class="question-mark">?</span>;
         }
         <span class="prelude-val">Ok</span>(point)
     }
 }

 <span class="macro">generic_foreign_type_and_impl_send_sync! </span>{
     <span class="kw">type </span>CType = ffi::EC_KEY;
     <span class="kw">fn </span>drop = ffi::EC_KEY_free;

     <span class="doccomment">/// Public and optional private key on the given curve.
     </span><span class="kw">pub struct </span>EcKey&lt;T&gt;;
     <span class="doccomment">/// A reference to an [`EcKey`].
     </span><span class="kw">pub struct </span>EcKeyRef&lt;T&gt;;
 }

 <span class="kw">impl</span>&lt;T&gt; EcKeyRef&lt;T&gt;
 <span class="kw">where
     </span>T: HasPrivate,
 {
     <span class="macro">private_key_to_pem! </span>{
         <span class="doccomment">/// Serializes the private key to a PEM-encoded ECPrivateKey structure.
         ///
         /// The output will have a header of `-----BEGIN EC PRIVATE KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_write_bio_ECPrivateKey)]
         </span>private_key_to_pem,
         <span class="doccomment">/// Serializes the private key to a PEM-encoded encrypted ECPrivateKey structure.
         ///
         /// The output will have a header of `-----BEGIN EC PRIVATE KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_write_bio_ECPrivateKey)]
         </span>private_key_to_pem_passphrase,
         ffi::PEM_write_bio_ECPrivateKey
     }

     <span class="macro">to_der! </span>{
         <span class="doccomment">/// Serializes the private key into a DER-encoded ECPrivateKey structure.
         </span><span class="attribute">#[corresponds(i2d_ECPrivateKey)]
         </span>private_key_to_der,
         ffi::i2d_ECPrivateKey
     }

     <span class="doccomment">/// Returns the private key value.
     </span><span class="attribute">#[corresponds(EC_KEY_get0_private_key)]
     </span><span class="kw">pub fn </span>private_key(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>BigNumRef {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>ptr = ffi::EC_KEY_get0_private_key(<span class="self">self</span>.as_ptr());
             BigNumRef::from_const_ptr(ptr)
         }
     }
 }

 <span class="kw">impl</span>&lt;T&gt; EcKeyRef&lt;T&gt;
 <span class="kw">where
     </span>T: HasPublic,
 {
     <span class="doccomment">/// Returns the public key.
     </span><span class="attribute">#[corresponds(EC_KEY_get0_public_key)]
     </span><span class="kw">pub fn </span>public_key(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>EcPointRef {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>ptr = ffi::EC_KEY_get0_public_key(<span class="self">self</span>.as_ptr());
             EcPointRef::from_const_ptr(ptr)
         }
     }

     <span class="macro">to_pem! </span>{
         <span class="doccomment">/// Serializes the public key into a PEM-encoded SubjectPublicKeyInfo structure.
         ///
         /// The output will have a header of `-----BEGIN PUBLIC KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_write_bio_EC_PUBKEY)]
         </span>public_key_to_pem,
         ffi::PEM_write_bio_EC_PUBKEY
     }

     <span class="macro">to_der! </span>{
         <span class="doccomment">/// Serializes the public key into a DER-encoded SubjectPublicKeyInfo structure.
         </span><span class="attribute">#[corresponds(i2d_EC_PUBKEY)]
         </span>public_key_to_der,
         ffi::i2d_EC_PUBKEY
     }
 }

 <span class="kw">impl</span>&lt;T&gt; EcKeyRef&lt;T&gt;
 <span class="kw">where
     </span>T: HasParams,
 {
     <span class="doccomment">/// Returns the key&#39;s group.
     </span><span class="attribute">#[corresponds(EC_KEY_get0_group)]
     </span><span class="kw">pub fn </span>group(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>EcGroupRef {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>ptr = ffi::EC_KEY_get0_group(<span class="self">self</span>.as_ptr());
             EcGroupRef::from_const_ptr(ptr)
         }
     }

     <span class="doccomment">/// Checks the key for validity.
     </span><span class="attribute">#[corresponds(EC_KEY_check_key)]
     </span><span class="kw">pub fn </span>check_key(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="prelude-ty">Result</span>&lt;(), ErrorStack&gt; {
         <span class="kw">unsafe </span>{ cvt(ffi::EC_KEY_check_key(<span class="self">self</span>.as_ptr())).map(|<span class="kw">_</span>| ()) }
     }
 }

 <span class="kw">impl</span>&lt;T&gt; ToOwned <span class="kw">for </span>EcKeyRef&lt;T&gt; {
     <span class="kw">type </span>Owned = EcKey&lt;T&gt;;

     <span class="kw">fn </span>to_owned(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; EcKey&lt;T&gt; {
         <span class="kw">unsafe </span>{
             <span class="kw">let </span>r = ffi::EC_KEY_up_ref(<span class="self">self</span>.as_ptr());
             <span class="macro">assert!</span>(r == <span class="number">1</span>);
             EcKey::from_ptr(<span class="self">self</span>.as_ptr())
         }
     }
 }

 <span class="kw">impl </span>EcKey&lt;Params&gt; {
     <span class="doccomment">/// Constructs an `EcKey` corresponding to a known curve.
     ///
     /// It will not have an associated public or private key. This kind of key is primarily useful
     /// to be provided to the `set_tmp_ecdh` methods on `Ssl` and `SslContextBuilder`.
     </span><span class="attribute">#[corresponds(EC_KEY_new_by_curve_name)]
     </span><span class="kw">pub fn </span>from_curve_name(nid: Nid) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Params&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             init();
             cvt_p(ffi::EC_KEY_new_by_curve_name(nid.as_raw())).map(|p| EcKey::from_ptr(p))
         }
     }

     <span class="doccomment">/// Constructs an `EcKey` corresponding to a curve.
     </span><span class="attribute">#[corresponds(EC_KEY_set_group)]
     </span><span class="kw">pub fn </span>from_group(group: <span class="kw-2">&amp;</span>EcGroupRef) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Params&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_KEY_new())
                 .map(|p| EcKey::from_ptr(p))
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_group(key.as_ptr(), group.as_ptr())).map(|<span class="kw">_</span>| key)
                 })
         }
     }
 }

 <span class="kw">impl </span>EcKey&lt;Public&gt; {
     <span class="doccomment">/// Constructs an `EcKey` from the specified group with the associated [`EcPoint`]: `public_key`.
     ///
     /// This will only have the associated `public_key`.
     ///
     /// # Example
     ///
     /// ```
     /// # fn main() -&gt; Result&lt;(), Box&lt;dyn std::error::Error&gt;&gt; {
     /// use openssl::bn::BigNumContext;
     /// use openssl::ec::*;
     /// use openssl::nid::Nid;
     /// use openssl::pkey::PKey;
     ///
     /// let group = EcGroup::from_curve_name(Nid::SECP384R1)?;
     /// let mut ctx = BigNumContext::new()?;
     ///
     /// // get bytes from somewhere
     /// let public_key = // ...
     /// # EcKey::generate(&amp;group)?.public_key().to_bytes(&amp;group,
     /// # PointConversionForm::COMPRESSED, &amp;mut ctx)?;
     ///
     /// // create an EcKey from the binary form of a EcPoint
     /// let point = EcPoint::from_bytes(&amp;group, &amp;public_key, &amp;mut ctx)?;
     /// let key = EcKey::from_public_key(&amp;group, &amp;point)?;
     /// key.check_key()?;
     /// # Ok(()) }
     /// ```
     </span><span class="attribute">#[corresponds(EC_KEY_set_public_key)]
     </span><span class="kw">pub fn </span>from_public_key(
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         public_key: <span class="kw-2">&amp;</span>EcPointRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Public&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_KEY_new())
                 .map(|p| EcKey::from_ptr(p))
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_group(key.as_ptr(), group.as_ptr())).map(|<span class="kw">_</span>| key)
                 })
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_public_key(
                         key.as_ptr(),
                         public_key.as_ptr(),
                     ))
                     .map(|<span class="kw">_</span>| key)
                 })
         }
     }

     <span class="doccomment">/// Constructs a public key from its affine coordinates.
     </span><span class="attribute">#[corresponds(EC_KEY_set_public_key_affine_coordinates)]
     </span><span class="kw">pub fn </span>from_public_key_affine_coordinates(
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         x: <span class="kw-2">&amp;</span>BigNumRef,
         y: <span class="kw-2">&amp;</span>BigNumRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Public&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_KEY_new())
                 .map(|p| EcKey::from_ptr(p))
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_group(key.as_ptr(), group.as_ptr())).map(|<span class="kw">_</span>| key)
                 })
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_public_key_affine_coordinates(
                         key.as_ptr(),
                         x.as_ptr(),
                         y.as_ptr(),
                     ))
                     .map(|<span class="kw">_</span>| key)
                 })
         }
     }

     <span class="macro">from_pem! </span>{
         <span class="doccomment">/// Decodes a PEM-encoded SubjectPublicKeyInfo structure containing a EC key.
         ///
         /// The input should have a header of `-----BEGIN PUBLIC KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_read_bio_EC_PUBKEY)]
         </span>public_key_from_pem,
         EcKey&lt;Public&gt;,
         ffi::PEM_read_bio_EC_PUBKEY
     }

     <span class="macro">from_der! </span>{
         <span class="doccomment">/// Decodes a DER-encoded SubjectPublicKeyInfo structure containing a EC key.
         </span><span class="attribute">#[corresponds(d2i_EC_PUBKEY)]
         </span>public_key_from_der,
         EcKey&lt;Public&gt;,
         ffi::d2i_EC_PUBKEY
     }
 }

 <span class="kw">impl </span>EcKey&lt;Private&gt; {
     <span class="doccomment">/// Generates a new public/private key pair on the specified curve.
     ///
     /// # Examples
     ///
     /// ```
     /// # fn main() -&gt; Result&lt;(), Box&lt;dyn std::error::Error&gt;&gt; {
     /// use openssl::bn::BigNumContext;
     /// use openssl::nid::Nid;
     /// use openssl::ec::{EcGroup, EcKey, PointConversionForm};
     ///
     /// let nid = Nid::X9_62_PRIME256V1; // NIST P-256 curve
     /// let group = EcGroup::from_curve_name(nid)?;
     /// let key = EcKey::generate(&amp;group)?;
     ///
     /// let mut ctx = BigNumContext::new()?;
     ///
     /// let public_key = &amp;key.public_key().to_bytes(
     ///     &amp;group,
     ///     PointConversionForm::COMPRESSED,
     ///     &amp;mut ctx,
     /// )?;
     /// assert_eq!(public_key.len(), 33);
     /// assert_ne!(public_key[0], 0x04);
     ///
     /// let private_key = key.private_key().to_vec();
     /// assert!(private_key.len() &gt;= 31);
     /// # Ok(()) }
     /// ```
     </span><span class="attribute">#[corresponds(EC_KEY_generate_key)]
     </span><span class="kw">pub fn </span>generate(group: <span class="kw-2">&amp;</span>EcGroupRef) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Private&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_KEY_new())
                 .map(|p| EcKey::from_ptr(p))
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_group(key.as_ptr(), group.as_ptr())).map(|<span class="kw">_</span>| key)
                 })
                 .and_then(|key| cvt(ffi::EC_KEY_generate_key(key.as_ptr())).map(|<span class="kw">_</span>| key))
         }
     }

     <span class="doccomment">/// Constructs an public/private key pair given a curve, a private key and a public key point.
     </span><span class="attribute">#[corresponds(EC_KEY_set_private_key)]
     </span><span class="kw">pub fn </span>from_private_components(
         group: <span class="kw-2">&amp;</span>EcGroupRef,
         private_number: <span class="kw-2">&amp;</span>BigNumRef,
         public_key: <span class="kw-2">&amp;</span>EcPointRef,
     ) -&gt; <span class="prelude-ty">Result</span>&lt;EcKey&lt;Private&gt;, ErrorStack&gt; {
         <span class="kw">unsafe </span>{
             cvt_p(ffi::EC_KEY_new())
                 .map(|p| EcKey::from_ptr(p))
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_group(key.as_ptr(), group.as_ptr())).map(|<span class="kw">_</span>| key)
                 })
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_private_key(
                         key.as_ptr(),
                         private_number.as_ptr(),
                     ))
                     .map(|<span class="kw">_</span>| key)
                 })
                 .and_then(|key| {
                     cvt(ffi::EC_KEY_set_public_key(
                         key.as_ptr(),
                         public_key.as_ptr(),
                     ))
                     .map(|<span class="kw">_</span>| key)
                 })
         }
     }

     <span class="macro">private_key_from_pem! </span>{
         <span class="doccomment">/// Deserializes a private key from a PEM-encoded ECPrivateKey structure.
         ///
         /// The input should have a header of `-----BEGIN EC PRIVATE KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_read_bio_ECPrivateKey)]
         </span>private_key_from_pem,

         <span class="doccomment">/// Deserializes a private key from a PEM-encoded encrypted ECPrivateKey structure.
         ///
         /// The input should have a header of `-----BEGIN EC PRIVATE KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_read_bio_ECPrivateKey)]
         </span>private_key_from_pem_passphrase,

         <span class="doccomment">/// Deserializes a private key from a PEM-encoded encrypted ECPrivateKey structure.
         ///
         /// The callback should fill the password into the provided buffer and return its length.
         ///
         /// The input should have a header of `-----BEGIN EC PRIVATE KEY-----`.
         </span><span class="attribute">#[corresponds(PEM_read_bio_ECPrivateKey)]
         </span>private_key_from_pem_callback,
         EcKey&lt;Private&gt;,
         ffi::PEM_read_bio_ECPrivateKey
     }

     <span class="macro">from_der! </span>{
         <span class="doccomment">/// Decodes a DER-encoded elliptic curve private key structure.
         </span><span class="attribute">#[corresponds(d2i_ECPrivateKey)]
         </span>private_key_from_der,
         EcKey&lt;Private&gt;,
         ffi::d2i_ECPrivateKey
     }
 }

 <span class="kw">impl</span>&lt;T&gt; Clone <span class="kw">for </span>EcKey&lt;T&gt; {
     <span class="kw">fn </span>clone(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; EcKey&lt;T&gt; {
         (<span class="kw-2">**</span><span class="self">self</span>).to_owned()
     }
 }

 <span class="kw">impl</span>&lt;T&gt; fmt::Debug <span class="kw">for </span>EcKey&lt;T&gt; {
     <span class="kw">fn </span>fmt(<span class="kw-2">&amp;</span><span class="self">self</span>, f: <span class="kw-2">&amp;mut </span>fmt::Formatter&lt;<span class="lifetime">&#39;_</span>&gt;) -&gt; fmt::Result {
         <span class="macro">write!</span>(f, <span class="string">&quot;EcKey&quot;</span>)
     }
 }

 <span class="attribute">#[cfg(test)]
 </span><span class="kw">mod </span>test {
     <span class="kw">use </span>hex::FromHex;

     <span class="kw">use super</span>::<span class="kw-2">*</span>;
     <span class="kw">use </span><span class="kw">crate</span>::bn::{BigNum, BigNumContext};
     <span class="kw">use </span><span class="kw">crate</span>::nid::Nid;

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>key_new_by_curve_name() {
         EcKey::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>generate() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>ec_group_from_components() {
         <span class="comment">// parameters are from secp256r1
         </span><span class="kw">let </span>p = BigNum::from_hex_str(
             <span class="string">&quot;FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>a = BigNum::from_hex_str(
             <span class="string">&quot;FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>b = BigNum::from_hex_str(
             <span class="string">&quot;5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();

         <span class="kw">let </span>_curve = EcGroup::from_components(p, a, b, <span class="kw-2">&amp;mut </span>ctx).unwrap();
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>ec_point_set_affine() {
         <span class="comment">// parameters are from secp256r1
         </span><span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>gen_point = EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span>gen_x = BigNum::from_hex_str(
             <span class="string">&quot;6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>gen_y = BigNum::from_hex_str(
             <span class="string">&quot;4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5&quot;</span>,
         )
         .unwrap();
         gen_point
             .set_affine_coordinates_gfp(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>gen_x, <span class="kw-2">&amp;</span>gen_y, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();
         <span class="macro">assert!</span>(gen_point.is_on_curve(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>ec_group_set_generator() {
         <span class="comment">// parameters are from secp256r1
         </span><span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>p = BigNum::from_hex_str(
             <span class="string">&quot;FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>a = BigNum::from_hex_str(
             <span class="string">&quot;FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>b = BigNum::from_hex_str(
             <span class="string">&quot;5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B&quot;</span>,
         )
         .unwrap();

         <span class="kw">let </span><span class="kw-2">mut </span>group = EcGroup::from_components(p, a, b, <span class="kw-2">&amp;mut </span>ctx).unwrap();

         <span class="kw">let </span><span class="kw-2">mut </span>gen_point = EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span>gen_x = BigNum::from_hex_str(
             <span class="string">&quot;6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>gen_y = BigNum::from_hex_str(
             <span class="string">&quot;4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5&quot;</span>,
         )
         .unwrap();
         gen_point
             .set_affine_coordinates_gfp(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>gen_x, <span class="kw-2">&amp;</span>gen_y, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();

         <span class="kw">let </span>order = BigNum::from_hex_str(
             <span class="string">&quot;FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551&quot;</span>,
         )
         .unwrap();
         <span class="kw">let </span>cofactor = BigNum::from_hex_str(<span class="string">&quot;01&quot;</span>).unwrap();
         group.set_generator(gen_point, order, cofactor).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>constructed_order = BigNum::new().unwrap();
         group.order(<span class="kw-2">&amp;mut </span>constructed_order, <span class="kw-2">&amp;mut </span>ctx).unwrap();

         <span class="kw">let </span>named_group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>named_order = BigNum::new().unwrap();
         named_group.order(<span class="kw-2">&amp;mut </span>named_order, <span class="kw-2">&amp;mut </span>ctx).unwrap();

         <span class="macro">assert_eq!</span>(
             constructed_order.ucmp(<span class="kw-2">&amp;</span>named_order),
             std::cmp::Ordering::Equal
         );
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>cofactor() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>cofactor = BigNum::new().unwrap();
         group.cofactor(<span class="kw-2">&amp;mut </span>cofactor, <span class="kw-2">&amp;mut </span>ctx).unwrap();
         <span class="kw">let </span>one = BigNum::from_u32(<span class="number">1</span>).unwrap();
         <span class="macro">assert_eq!</span>(cofactor, one);
     }

     <span class="attribute">#[test]
     #[allow(clippy::redundant_clone)]
     </span><span class="kw">fn </span>dup() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
         drop(key.clone());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>point_new() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>point_bytes() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span>point = key.public_key();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>bytes = point
             .to_bytes(<span class="kw-2">&amp;</span>group, PointConversionForm::COMPRESSED, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();
         <span class="kw">let </span>point2 = EcPoint::from_bytes(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>bytes, <span class="kw-2">&amp;mut </span>ctx).unwrap();
         <span class="macro">assert!</span>(point.eq(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>point2, <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>point_owned() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span>point = key.public_key();
         <span class="kw">let </span>owned = point.to_owned(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="macro">assert!</span>(owned.eq(<span class="kw-2">&amp;</span>group, point, <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>mul_generator() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>public_key = EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
         public_key
             .mul_generator(<span class="kw-2">&amp;</span>group, key.private_key(), <span class="kw-2">&amp;</span>ctx)
             .unwrap();
         <span class="macro">assert!</span>(public_key.eq(<span class="kw-2">&amp;</span>group, key.public_key(), <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>generator() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>gen = group.generator();
         <span class="kw">let </span>one = BigNum::from_u32(<span class="number">1</span>).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ecp = EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
         ecp.mul_generator(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>one, <span class="kw-2">&amp;</span>ctx).unwrap();
         <span class="macro">assert!</span>(ecp.eq(<span class="kw-2">&amp;</span>group, gen, <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>key_from_public_key() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>bytes = key
             .public_key()
             .to_bytes(<span class="kw-2">&amp;</span>group, PointConversionForm::COMPRESSED, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();

         drop(key);
         <span class="kw">let </span>public_key = EcPoint::from_bytes(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>bytes, <span class="kw-2">&amp;mut </span>ctx).unwrap();
         <span class="kw">let </span>ec_key = EcKey::from_public_key(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>public_key).unwrap();
         <span class="macro">assert!</span>(ec_key.check_key().is_ok());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>key_from_private_components() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>key = EcKey::generate(<span class="kw-2">&amp;</span>group).unwrap();

         <span class="kw">let </span>dup_key =
             EcKey::from_private_components(<span class="kw-2">&amp;</span>group, key.private_key(), key.public_key()).unwrap();
         dup_key.check_key().unwrap();

         <span class="macro">assert!</span>(key.private_key() == dup_key.private_key());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>key_from_affine_coordinates() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>x = Vec::from_hex(<span class="string">&quot;30a0424cd21c2944838a2d75c92b37e76ea20d9f00893a3b4eee8a3c0aafec3e&quot;</span>)
             .unwrap();
         <span class="kw">let </span>y = Vec::from_hex(<span class="string">&quot;e04b65e92456d9888b52b379bdfbd51ee869ef1f0fc65b6659695b6cce081723&quot;</span>)
             .unwrap();

         <span class="kw">let </span>xbn = BigNum::from_slice(<span class="kw-2">&amp;</span>x).unwrap();
         <span class="kw">let </span>ybn = BigNum::from_slice(<span class="kw-2">&amp;</span>y).unwrap();

         <span class="kw">let </span>ec_key = EcKey::from_public_key_affine_coordinates(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>xbn, <span class="kw-2">&amp;</span>ybn).unwrap();
         <span class="macro">assert!</span>(ec_key.check_key().is_ok());
     }

     <span class="attribute">#[cfg(ossl111)]
     #[test]
     </span><span class="kw">fn </span>get_affine_coordinates() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>x = Vec::from_hex(<span class="string">&quot;30a0424cd21c2944838a2d75c92b37e76ea20d9f00893a3b4eee8a3c0aafec3e&quot;</span>)
             .unwrap();
         <span class="kw">let </span>y = Vec::from_hex(<span class="string">&quot;e04b65e92456d9888b52b379bdfbd51ee869ef1f0fc65b6659695b6cce081723&quot;</span>)
             .unwrap();

         <span class="kw">let </span>xbn = BigNum::from_slice(<span class="kw-2">&amp;</span>x).unwrap();
         <span class="kw">let </span>ybn = BigNum::from_slice(<span class="kw-2">&amp;</span>y).unwrap();

         <span class="kw">let </span>ec_key = EcKey::from_public_key_affine_coordinates(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>xbn, <span class="kw-2">&amp;</span>ybn).unwrap();

         <span class="kw">let </span><span class="kw-2">mut </span>xbn2 = BigNum::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ybn2 = BigNum::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>ec_key_pk = ec_key.public_key();
         ec_key_pk
             .affine_coordinates(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;mut </span>xbn2, <span class="kw-2">&amp;mut </span>ybn2, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();
         <span class="macro">assert_eq!</span>(xbn2, xbn);
         <span class="macro">assert_eq!</span>(ybn2, ybn);
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>get_affine_coordinates_gfp() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span>x = Vec::from_hex(<span class="string">&quot;30a0424cd21c2944838a2d75c92b37e76ea20d9f00893a3b4eee8a3c0aafec3e&quot;</span>)
             .unwrap();
         <span class="kw">let </span>y = Vec::from_hex(<span class="string">&quot;e04b65e92456d9888b52b379bdfbd51ee869ef1f0fc65b6659695b6cce081723&quot;</span>)
             .unwrap();

         <span class="kw">let </span>xbn = BigNum::from_slice(<span class="kw-2">&amp;</span>x).unwrap();
         <span class="kw">let </span>ybn = BigNum::from_slice(<span class="kw-2">&amp;</span>y).unwrap();

         <span class="kw">let </span>ec_key = EcKey::from_public_key_affine_coordinates(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>xbn, <span class="kw-2">&amp;</span>ybn).unwrap();

         <span class="kw">let </span><span class="kw-2">mut </span>xbn2 = BigNum::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ybn2 = BigNum::new().unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>ec_key_pk = ec_key.public_key();
         ec_key_pk
             .affine_coordinates_gfp(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;mut </span>xbn2, <span class="kw-2">&amp;mut </span>ybn2, <span class="kw-2">&amp;mut </span>ctx)
             .unwrap();
         <span class="macro">assert_eq!</span>(xbn2, xbn);
         <span class="macro">assert_eq!</span>(ybn2, ybn);
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>is_infinity() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>g = group.generator();
         <span class="macro">assert!</span>(!g.is_infinity(<span class="kw-2">&amp;</span>group));

         <span class="kw">let </span><span class="kw-2">mut </span>order = BigNum::new().unwrap();
         group.order(<span class="kw-2">&amp;mut </span>order, <span class="kw-2">&amp;mut </span>ctx).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>inf = EcPoint::new(<span class="kw-2">&amp;</span>group).unwrap();
         inf.mul_generator(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;</span>order, <span class="kw-2">&amp;</span>ctx).unwrap();
         <span class="macro">assert!</span>(inf.is_infinity(<span class="kw-2">&amp;</span>group));
     }

     <span class="attribute">#[test]
     #[cfg(not(any(boringssl, osslconf = <span class="string">&quot;OPENSSL_NO_EC2M&quot;</span>)))]
     </span><span class="kw">fn </span>is_on_curve() {
         <span class="kw">let </span>group = EcGroup::from_curve_name(Nid::X9_62_PRIME256V1).unwrap();
         <span class="kw">let </span><span class="kw-2">mut </span>ctx = BigNumContext::new().unwrap();
         <span class="kw">let </span>g = group.generator();
         <span class="macro">assert!</span>(g.is_on_curve(<span class="kw-2">&amp;</span>group, <span class="kw-2">&amp;mut </span>ctx).unwrap());

         <span class="kw">let </span>group2 = EcGroup::from_curve_name(Nid::X9_62_PRIME239V3).unwrap();
         <span class="macro">assert!</span>(!g.is_on_curve(<span class="kw-2">&amp;</span>group2, <span class="kw-2">&amp;mut </span>ctx).unwrap());
     }
 }
 </code></pre></div>
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