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<p><img src="https://github.com/simplito/ecies-erl/actions/workflows/erlang.yml/badge.svg" alt="Build and Test" /> <a href="https://hex.pm/packages/ecies"><img src="https://img.shields.io/hexpm/v/ecies.svg" alt="Hex" /></a></p>
<h1 id="customizable-erlang-native-ecies-public-key-cryptography-library">Customizable Erlang native ECIES public-key cryptography library</h1>
<p>An Erlang native library implementing the ECIES (Elliptic Curve Integrated Encryption Scheme) public-key cryptography.<br />
It allows for configurable components such as DH key agreement, key derivation, data encryption, MAC algorithms and more.</p>
<p>Examples tailored to ECIES variants implemented in Electrum, Geth, and Bitcore are also provided.</p>
<h2 id="motivation">Motivation</h2>
<p>The Erlang OTP team decided to deprecate several <code>crypto</code> module functions in OTP 27 (See <a href="https://www.erlang.org/doc/deprecations.html#functions-deprecated-in-otp-27">functions deprecated in OTP 27</a>)<br />
Notably, no alternatives were provided for two of them <code>crypto:public_encrypt/4</code>, <code>crypto:private_decrypt/4</code>.<br />
It is worth mentioning that the above mentioned functions are RSA specific and cannot be used with Elliptic Curve cryptography anyway.</p>
<p>Some information about potential background of these deprecations can be found <a href="https://erlangforums.com/t/security-working-group-minutes/3451/6">here</a>.</p>
<p>In our projects we mainly use Elliptic Curve cryptography and we decided to share this small library for ECIES with the Erlang developers community.<br />
We will be happy if you find it useful and use in your project. If you find any ideas for improvements or notice any missing functionality, please open an issue here; even better propose a Pull Request.</p>
<h2 id="usage">Usage</h2>
<h3 id="basic">Basic</h3>
<p>The simplest variant without additionals params:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true"></a> <span class="co">% Bob generates keys</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true"></a> <span class="fu">{</span><span class="va">BobPublicKey</span><span class="fu">,</span> <span class="va">BobPrivateKey</span><span class="fu">}</span> <span class="op">=</span> <span class="fu">ecies:generate_key(),</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true"></a> <span class="co">% Alice knowing Bob's public key encrypts a message for him</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true"></a> <span class="va">Data</span> <span class="op">=</span> <span class="fu">ecies:public_encrypt(</span><span class="va">BobPublicKey</span><span class="fu">,</span> <span class="op"><<</span><span class="st">"top secret message"</span><span class="op">>></span><span class="fu">),</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true"></a> <span class="co">% Bob is able to decrypt the message using his private key</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true"></a> <span class="op"><<</span><span class="st">"top secret message"</span><span class="op">>></span> <span class="op">=</span> <span class="fu">ecies:private_decrypt(</span><span class="va">BobPrivateKey</span><span class="fu">,</span> <span class="va">Data</span><span class="fu">).</span></span></code></pre></div>
<p>In that case the default params are used (as returned by <code>ecies:default_params/0</code>):</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true"></a> <span class="fu">#{</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true"></a> <span class="ch">curve</span> <span class="op">=></span> <span class="ch">secp256k1</span><span class="fu">,</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true"></a> <span class="ch">cipher</span> <span class="op">=></span> <span class="ch">aes_256_cbc</span><span class="fu">,</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true"></a> <span class="ch">kdf</span> <span class="op">=></span> <span class="fu">{</span><span class="ch">kdf</span><span class="fu">,</span> <span class="ch">sha256</span><span class="fu">},</span> <span class="co">% ANSI-X9.63 key derivation</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true"></a> <span class="ch">mac</span> <span class="op">=></span> <span class="fu">{</span><span class="ch">hmac</span><span class="fu">,</span> <span class="ch">sha256</span><span class="fu">,</span> <span class="dv">256</span><span class="fu">}</span> <span class="co">% HMAC SHA256 with 256 bits (32 bytes) output</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true"></a> <span class="fu">}.</span></span></code></pre></div>
<h3 id="customisation">Customisation</h3>
<p>Specifying additional argument <code>Params</code> to the <code>generate_key</code>, <code>public_encrypt</code> and <code>privated_decrypt</code> function you can customize algorithms used in all steps of encryption / decryption.</p>
<p>Example:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true"></a> <span class="co">% Alice and Bob agrees on the following params</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true"></a> <span class="va">Params</span> <span class="op">=</span> <span class="fu">#{</span> <span class="ch">curve</span> <span class="op">=></span> <span class="ch">x25519</span><span class="fu">,</span> <span class="ch">kdf</span> <span class="op">=></span> <span class="fu">{</span><span class="ch">hkdf</span><span class="fu">,</span> <span class="ch">sha256</span><span class="fu">},</span> <span class="ch">cipher</span> <span class="op">=></span> <span class="ch">aes_256_ctr</span><span class="fu">,</span> <span class="ch">mac</span> <span class="op">=></span> <span class="fu">{</span><span class="ch">hmac</span><span class="fu">,</span> <span class="ch">sha256</span><span class="fu">,</span> <span class="dv">96</span><span class="fu">}</span> <span class="fu">},</span></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true"></a> <span class="co">% Bob generates keys</span></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true"></a> <span class="fu">{</span><span class="va">BobPublicKey</span><span class="fu">,</span> <span class="va">BobPrivateKey</span><span class="fu">}</span> <span class="op">=</span> <span class="fu">ecies:generate_key(</span><span class="va">Params</span><span class="fu">),</span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true"></a> <span class="co">% Alice knowing Bob's public key encrypts a message for him</span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true"></a> <span class="va">Data</span> <span class="op">=</span> <span class="fu">ecies:public_encrypt(</span><span class="va">BobPublicKey</span><span class="fu">,</span> <span class="op"><<</span><span class="st">"top secret message"</span><span class="op">>></span><span class="fu">,</span> <span class="va">Params</span><span class="fu">),</span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true"></a> <span class="co">% Bob is able to decrypt the message using his private key</span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true"></a> <span class="op"><<</span><span class="st">"top secret message"</span><span class="op">>></span> <span class="op">=</span> <span class="fu">ecies:private_decrypt(</span><span class="va">BobPrivateKey</span><span class="fu">,</span> <span class="va">Data</span><span class="fu">,</span> <span class="va">Params</span><span class="fu">).</span></span></code></pre></div>
<p>The list of all supported elliptic curves (<code>curve</code> param), ciphers (<code>cipher</code> param) and hash functions used by KDF and MAC algorithms can be obtained using <code>ecies:supports/1</code> function:</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true"></a><span class="op">-</span><span class="ch">spec</span> <span class="fu">supports(</span><span class="ch">hashs</span><span class="fu">)</span> <span class="op">-></span> <span class="fu">[digest_type()];</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true"></a> <span class="fu">(</span><span class="ch">curves</span><span class="fu">)</span> <span class="op">-></span> <span class="fu">[named_curve()];</span></span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true"></a> <span class="fu">(</span><span class="ch">ciphers</span><span class="fu">)</span> <span class="op">-></span> <span class="fu">[cipher()];</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true"></a> <span class="fu">(</span><span class="ch">cmac_ciphers</span><span class="fu">)</span> <span class="op">-></span> <span class="fu">[cmac_cipher()];</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true"></a> <span class="fu">(</span><span class="ch">aead_ciphers</span><span class="fu">)</span> <span class="op">-></span> <span class="fu">[aead_cipher()].</span></span></code></pre></div>
<p>NOTE: For Edwards Curves 25519 and 448 do use <code>x25519</code> and <code>x448</code>.</p>
<p>For key derivation (<code>kdf</code> param) you can use:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true"></a><span class="op">-</span><span class="ch">type</span> <span class="fu">kdf_type()</span> <span class="fu">::</span> <span class="fu">{</span><span class="ch">hkdf</span><span class="fu">,</span> <span class="fu">digest_type()}</span> <span class="fu">|</span> <span class="co">% HMAC-based Extract-and-Expand Key Derivation Function (HKDF)</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true"></a> <span class="fu">{</span><span class="ch">kdf</span><span class="fu">,</span> <span class="fu">digest_type()}</span> <span class="fu">|</span> <span class="co">% ANSI-X9.63 KDF</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true"></a> <span class="fu">{</span><span class="ch">concat_kdf</span><span class="fu">,</span> <span class="fu">digest_type()}</span> <span class="fu">|</span> <span class="co">% NIST SP 800-56 Concatenation Key Derivation Function (see section 5.8.1).</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true"></a> <span class="fu">kdf_fun().</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true"></a><span class="co">% Custom KDF function</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true"></a><span class="op">-</span><span class="ch">type</span> <span class="fu">kdf_fun()</span> <span class="fu">::</span> <span class="kw">fun</span><span class="fu">((</span><span class="va">SharedKey</span> <span class="fu">::</span> <span class="fu">binary(),</span> <span class="va">Info</span> <span class="fu">::</span> <span class="fu">binary(),</span> <span class="va">Length</span> <span class="fu">::</span> <span class="fu">pos_integer())</span> <span class="op">-></span> <span class="va">Result</span> <span class="fu">::</span> <span class="fu">binary()).</span></span></code></pre></div>
<p>For message authentication (<code>mac</code> param):</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true"></a><span class="op">-</span><span class="ch">type</span> <span class="fu">mac_type()</span> <span class="fu">::</span> <span class="fu">{</span><span class="ch">hmac</span><span class="fu">,</span> <span class="fu">digest_type(),</span> <span class="fu">mac_bits()}</span> <span class="fu">|</span> <span class="co">% HMAC for given digest function with specified output bits</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true"></a> <span class="fu">{</span><span class="ch">cmac</span><span class="fu">,</span> <span class="fu">cmac_cipher(),</span> <span class="fu">mac_bits()}</span> <span class="fu">|</span> <span class="co">% CMAC with AES-*-CBC cipher and given output bits</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true"></a> <span class="fu">{</span><span class="ch">aead</span><span class="fu">,</span> <span class="fu">mac_bits()}.</span> <span class="co">% Special case when AES CCM/GCM ciphers are used to just specify tag output bits </span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true"></a><span class="op">-</span><span class="ch">type</span> <span class="fu">mac_bits()</span> <span class="fu">::</span> <span class="fu">pos_integer()</span> <span class="fu">|</span> <span class="ch">default</span><span class="fu">.</span> <span class="co">% default atom means output size equal to given mac key length</span></span></code></pre></div>
<p>Additionally we provide default params used in bitcore<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a>, geth<a href="#fn2" class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a>, electrum<a href="#fn3" class="footnote-ref" id="fnref3" role="doc-noteref"><sup>3</sup></a>.</p>
<p>Example usage:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode erlang"><code class="sourceCode erlang"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true"></a> <span class="va">Params</span> <span class="op">=</span> <span class="fu">ecies_electrum:default_params(),</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true"></a> <span class="va">PrivateKey</span> <span class="op">=</span> <span class="fu">binary:decode_hex(</span><span class="op"><<</span><span class="st">"ee3231b5deea48b619814d72a6e1aa04a9f521df281afad5ada89f5393941b1c"</span><span class="op">>></span><span class="fu">),</span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true"></a> <span class="va">MessageBase64</span> <span class="op">=</span> <span class="op"><<</span><span class="st">"QklFMQJdmY+9Ys1WjqANreLwXaau62N01r9lebJ9Rp7Az+XRMdNAVgg3J8EEVhni5gn2v+WOD59uDMDp0zY/xPT3IElReQo6XUCSMmgRgRtYl+TUEw=="</span><span class="op">>></span><span class="fu">,</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true"></a> <span class="op"><<</span><span class="st">"hello world"</span><span class="op">>></span> <span class="op">=</span> <span class="fu">ecies:private_decrypt(</span><span class="va">PrivateKey</span><span class="fu">,</span> <span class="va">MessageBase64</span><span class="fu">,</span> <span class="va">Params</span><span class="fu">).</span></span></code></pre></div>
<p>NOTE: Unfortunately Electrum uses full compressed point from Diffie-Hellman step of calculating shared key instead of usual x coordinate, and erlang’s <code>crypto:compute_key</code> is not enough to calculate this. For using electrum compatible params you need to add <code>libsecp256k1</code> to your dependencies, otherwise <code>error(unsupported)</code> will be thrown.</p>
<p>More advanced usage cases will be described later.</p>
<section class="footnotes" role="doc-endnotes">
<hr />
<ol>
<li id="fn1" role="doc-endnote"><p><a href="https://www.researchgate.net/publication/251958691_A_comparison_of_the_standardized_versions_of_ECIES">A comparison of the standardized versions of ECIES.</a><a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn2" role="doc-endnote"><p>https://github.com/bitpay/bitcore-ecies<a href="#fnref2" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn3" role="doc-endnote"><p>https://github.com/ethereum/go-ethereum/blob/master/crypto/ecies/ecies.go<a href="#fnref3" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
</ol>
</section>
</body>
</html>
