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<p><a class="reference external" href="proxy.php?url=https%3A%2F%2Fgithub.com%2F%3Ca+href%3D"https://travis-ci.org/RyanKung/klefki"><img" rel="nofollow">https://travis-ci.org/RyanKung/klefki"><img alt="travis" src="proxy.php?url=https%3A%2F%2Fgithub.com%2F%3Ca+href%3D"https://travis-ci.org/RyanKung/klefki.svg?branch=master" rel="nofollow">https://travis-ci.org/RyanKung/klefki.svg?branch=master" /></a></p>
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<blockquote>
<div><p>Klefki (Japanese: クレッフィ Cleffy) is a dual-type Steel/Fairy Pokémon introduced in Generation VI. It is not known to evolve into or from any other Pokémon.</p>
</div></blockquote>
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<div class="section" id="tl-dr">
<h1>TL;DR<a class="headerlink" href="#tl-dr" title="Permalink to this headline">¶</a></h1>
<p><strong>Klefki is a playground for researching elliptic curve group based cryptocoins, such as Bitcoin and Ethereum. All data types & structures are based on mathematical defination of abstract algebra.</strong></p>
<div class="section" id="try-it">
<h2><a class="reference external" href="proxy.php?url=https%3A%2F%2Fgithub.com%2F%3Ca+href%3D"https://repl.it/@RyanKung/Klefki-Demo">Try" rel="nofollow">https://repl.it/@RyanKung/Klefki-Demo">Try it!</a><a class="headerlink" href="#try-it" title="Permalink to this headline">¶</a></h2>
</div>
<div class="section" id="for-installation-require-python-3-6">
<h2>For Installation (require python>=3.6):<a class="headerlink" href="#for-installation-require-python-3-6" title="Permalink to this headline">¶</a></h2>
<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>pip3 install klefki
klefki shell
</pre></div>
</div>
<p>Have Fun!!!!</p>
</div>
<div class="section" id="aat-abstract-algebra-type">
<h2>AAT(Abstract Algebra Type)<a class="headerlink" href="#aat-abstract-algebra-type" title="Permalink to this headline">¶</a></h2>
<p>With <code class="docutils literal notranslate"><span class="pre">AAT(Abstract</span> <span class="pre">Algebra</span> <span class="pre">Type)</span></code> you can easily implement the bitcoin <code class="docutils literal notranslate"><span class="pre">priv/pub</span> <span class="pre">key</span></code> and <code class="docutils literal notranslate"><span class="pre">sign/verify</span></code> algorithms like this:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span>
<span class="kn">import</span> <span class="nn">random</span>
<span class="kn">from</span> <span class="nn">klefki.utils</span> <span class="kn">import</span> <span class="n">to_sha256int</span>
<span class="kn">from</span> <span class="nn">klefki.types.algebra.concrete</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">JacobianGroupSecp256k1</span> <span class="k">as</span> <span class="n">JG</span><span class="p">,</span>
<span class="n">EllipticCurveCyclicSubgroupSecp256k1</span> <span class="k">as</span> <span class="n">CG</span><span class="p">,</span>
<span class="n">EllipticCurveGroupSecp256k1</span> <span class="k">as</span> <span class="n">ECG</span><span class="p">,</span>
<span class="n">FiniteFieldCyclicSecp256k1</span> <span class="k">as</span> <span class="n">CF</span>
<span class="p">)</span>
<span class="n">N</span> <span class="o">=</span> <span class="n">CG</span><span class="o">.</span><span class="n">N</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">CG</span><span class="o">.</span><span class="n">G</span>
<span class="k">def</span> <span class="nf">random_privkey</span><span class="p">()</span> <span class="o">-></span> <span class="n">CF</span><span class="p">:</span>
<span class="k">return</span> <span class="n">CF</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">pubkey</span><span class="p">(</span><span class="n">priv</span><span class="p">:</span> <span class="n">CF</span><span class="p">)</span> <span class="o">-></span> <span class="n">ECG</span><span class="p">:</span>
<span class="k">return</span> <span class="n">ECG</span><span class="p">(</span><span class="n">JG</span><span class="p">(</span><span class="n">G</span> <span class="o">@</span> <span class="n">priv</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">sign</span><span class="p">(</span><span class="n">priv</span><span class="p">:</span> <span class="n">CF</span><span class="p">,</span> <span class="n">m</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">:</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">CF</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">CF</span><span class="p">(</span><span class="n">to_sha256int</span><span class="p">(</span><span class="n">m</span><span class="p">))</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">CF</span><span class="p">((</span><span class="n">G</span> <span class="o">@</span> <span class="n">k</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># From Secp256k1Field to CyclicSecp256k1Field</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">z</span> <span class="o">/</span> <span class="n">k</span> <span class="o">+</span> <span class="n">priv</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">k</span>
<span class="k">return</span> <span class="n">r</span><span class="p">,</span> <span class="n">s</span>
<span class="k">def</span> <span class="nf">verify</span><span class="p">(</span><span class="n">pub</span><span class="p">:</span> <span class="n">ECG</span><span class="p">,</span> <span class="n">sig</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">,</span> <span class="n">mhash</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">sig</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">CF</span><span class="p">(</span><span class="n">mhash</span><span class="p">)</span>
<span class="n">u1</span> <span class="o">=</span> <span class="n">z</span> <span class="o">/</span> <span class="n">s</span>
<span class="n">u2</span> <span class="o">=</span> <span class="n">r</span> <span class="o">/</span> <span class="n">s</span>
<span class="n">rp</span> <span class="o">=</span> <span class="n">G</span> <span class="o">@</span> <span class="n">u1</span> <span class="o">+</span> <span class="n">pub</span> <span class="o">@</span> <span class="n">u2</span>
<span class="k">return</span> <span class="n">r</span> <span class="o">==</span> <span class="n">rp</span><span class="o">.</span><span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<p>Even proof the <code class="docutils literal notranslate"><span class="pre">Sign/Verify</span></code> algorithm mathematically.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">proof</span><span class="p">():</span>
<span class="n">priv</span> <span class="o">=</span> <span class="n">random_privkey</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="s1">'test'</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">CF</span><span class="p">(</span><span class="n">random_privkey</span><span class="p">())</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">CF</span><span class="p">(</span><span class="n">to_sha256int</span><span class="p">(</span><span class="n">m</span><span class="p">))</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">CF</span><span class="p">((</span><span class="n">G</span> <span class="o">@</span> <span class="n">k</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">z</span> <span class="o">/</span> <span class="n">k</span> <span class="o">+</span> <span class="n">priv</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">k</span>
<span class="k">assert</span> <span class="n">k</span> <span class="o">==</span> <span class="n">z</span> <span class="o">/</span> <span class="n">s</span> <span class="o">+</span> <span class="n">priv</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">s</span>
<span class="k">assert</span> <span class="n">G</span> <span class="o">@</span> <span class="n">k</span> <span class="o">==</span> <span class="n">G</span> <span class="o">@</span> <span class="p">(</span><span class="n">z</span> <span class="o">/</span> <span class="n">s</span> <span class="o">+</span> <span class="n">priv</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">s</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">G</span> <span class="o">@</span> <span class="n">k</span> <span class="o">==</span> <span class="n">G</span> <span class="o">@</span> <span class="p">(</span><span class="n">z</span> <span class="o">/</span> <span class="n">s</span><span class="p">)</span> <span class="o">+</span> <span class="n">G</span> <span class="o">@</span> <span class="n">priv</span> <span class="o">@</span> <span class="p">(</span><span class="n">r</span> <span class="o">/</span> <span class="n">s</span><span class="p">)</span>
<span class="n">pub</span> <span class="o">=</span> <span class="n">G</span> <span class="o">@</span> <span class="n">priv</span>
<span class="k">assert</span> <span class="n">pub</span> <span class="o">==</span> <span class="n">pubkey</span><span class="p">(</span><span class="n">priv</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">G</span> <span class="o">@</span> <span class="n">k</span> <span class="o">==</span> <span class="n">G</span> <span class="o">@</span> <span class="p">(</span><span class="n">z</span> <span class="o">/</span> <span class="n">s</span><span class="p">)</span> <span class="o">+</span> <span class="n">pub</span> <span class="o">@</span> <span class="p">(</span><span class="n">r</span> <span class="o">/</span> <span class="n">s</span><span class="p">)</span>
<span class="n">u1</span> <span class="o">=</span> <span class="n">z</span> <span class="o">/</span> <span class="n">s</span>
<span class="n">u2</span> <span class="o">=</span> <span class="n">r</span> <span class="o">/</span> <span class="n">s</span>
<span class="k">assert</span> <span class="n">G</span> <span class="o">@</span> <span class="n">k</span> <span class="o">==</span> <span class="n">G</span> <span class="o">@</span> <span class="n">u1</span> <span class="o">+</span> <span class="n">pub</span> <span class="o">@</span> <span class="n">u2</span>
</pre></div>
</div>
<p>Or transform your Bitcoin Private Key to EOS Private/Pub key (or back)</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">klefki.bitcoin.private</span> <span class="kn">import</span> <span class="n">decode_privkey</span>
<span class="kn">from</span> <span class="nn">klefki.eos.public</span> <span class="kn">import</span> <span class="n">gen_pub_key</span>
<span class="kn">from</span> <span class="nn">klefki.eos.private</span> <span class="kn">import</span> <span class="n">encode_privkey</span>
<span class="k">def</span> <span class="nf">test_to_eos</span><span class="p">(</span><span class="n">priv</span><span class="p">):</span>
<span class="n">key</span> <span class="o">=</span> <span class="n">decode_privkey</span><span class="p">(</span><span class="n">priv</span><span class="p">)</span>
<span class="n">eos_priv</span> <span class="o">=</span> <span class="n">encode_privkey</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<span class="n">eos_pub</span> <span class="o">=</span> <span class="n">gen_pub_key</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">eos_priv</span><span class="p">,</span> <span class="n">eos_pub</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="bijection">
<h2>Bijection<a class="headerlink" href="#bijection" title="Permalink to this headline">¶</a></h2>
<p>A morphism f : X → Y in a category is an isomorphism if it admits a two-sided inverse.</p>
<p>You can define your bijection encoder/decoder like this.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">klefki.types.algebra.isomorphism</span> <span class="kn">import</span> <span class="n">bijection</span><span class="p">,</span> <span class="n">do</span>
<span class="kn">from</span> <span class="nn">klefki.asn</span> <span class="kn">import</span> <span class="n">signature</span> <span class="k">as</span> <span class="n">sig</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
<span class="kn">import</span> <span class="nn">base58</span>
<span class="kn">from</span> <span class="nn">pyasn1.codec.der.encoder</span> <span class="kn">import</span> <span class="n">encode</span>
<span class="kn">from</span> <span class="nn">pyasn1.codec.der.decoder</span> <span class="kn">import</span> <span class="n">decode</span>
<span class="n">b58encoder</span> <span class="o">=</span> <span class="n">bijection</span><span class="p">(</span><span class="n">base58</span><span class="o">.</span><span class="n">b58decode</span><span class="p">)(</span><span class="n">base58</span><span class="o">.</span><span class="n">b58encode</span><span class="p">)</span>
<span class="n">asn1encoder</span> <span class="o">=</span> <span class="n">bijection</span><span class="p">(</span><span class="n">partial</span><span class="p">(</span><span class="n">decode</span><span class="p">,</span> <span class="n">asn1Spec</span><span class="o">=</span><span class="n">sig</span><span class="o">.</span><span class="n">ECDSA_Sig_Value</span><span class="p">()))(</span><span class="n">encode</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">sig</span><span class="o">.</span><span class="n">ECDSA_Sig_Value</span><span class="p">()</span>
<span class="n">data</span><span class="p">[</span><span class="s1">'r'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">123</span>
<span class="n">data</span><span class="p">[</span><span class="s1">'s'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">234</span>
<span class="n">process</span> <span class="o">=</span> <span class="n">do</span><span class="p">(</span><span class="n">asn1encoder</span><span class="p">,</span> <span class="n">b58encoder</span><span class="p">)</span>
<span class="n">process</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="o">>>></span> <span class="s1">'cTVygpHoWBNR'</span>
<span class="p">(</span><span class="o">~</span><span class="n">process</span><span class="p">)(</span><span class="n">process</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="o">>>></span> <span class="p">(</span><span class="n">ECDSA_Sig_Value</span><span class="p">()</span><span class="o">.</span><span class="n">setComponentByPosition</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">Integer</span><span class="p">(</span><span class="mi">123</span><span class="p">))</span><span class="o">.</span><span class="n">setComponentByPosition</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">Integer</span><span class="p">(</span><span class="mi">234</span><span class="p">)),</span>
<span class="sa">b</span><span class="s1">''</span><span class="p">)</span>
</pre></div>
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<ul class="current">
<li class="toctree-l1 current"><a class="current reference internal" href="#">TL;DR</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#try-it">Try it!</a></li>
<li class="toctree-l2"><a class="reference internal" href="#for-installation-require-python-3-6">For Installation (require python>=3.6):</a></li>
<li class="toctree-l2"><a class="reference internal" href="#aat-abstract-algebra-type">AAT(Abstract Algebra Type)</a></li>
<li class="toctree-l2"><a class="reference internal" href="#bijection">Bijection</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FNon-interactive%2520and%2520Reusable%2520Non-malleable%2520Commitment%2520Schemes.html">Non-interactive and Reusable Non-malleable Commitment Schemes</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FPedersen%2520Commitment.html">Pedersen Commitment</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FOn%2520Sigma%2520Protocols.html"><span class="math notranslate nohighlight">\(\Sigma\)</span> Protocols</a></li>
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<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FHomomorphic%2520Encryption.html">Homomorphic Encryption</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FFrom%2520ZK%2520to%2520Bulletproofs.html">From ZK to Bulletproofsproof via Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FPaillier%2527s%2520encryption%2520Scheme.html">Paillier’s encryption Scheme</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FElGamal.html">ElGamal</a></li>
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<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FShamir%2527s%2520secret%2520sharing%2520scheme.html">Shamir’s secret sharing scheme</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FTrapdoor%2520Commitment%2520Schemes.html">Discrete-Logarithm-Based Trapdoor Commitment Schemes</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FThreshold%2520ECDSA.html">Threshold ECDSA</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FPOD-Mini%2520and%2520POD-AS.html">POD-Mini and POD-AS</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FDamgard-Jurik%2520Scheme%2520of%2520Paillier.html">Damgard-Jurik Scheme of Paillier</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FThreshold%2520Paillier%2520Cryptosystem.html">Threshold Paillier Cryptosystem</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FR1CS%2520to%2520QAP.html">R1CS to QAP</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FMimbleWimble.html">Play MimbleWimble with klefki</a></li>
<li class="toctree-l1"><a class="reference internal" href="proxy.php?url=https%3A%2F%2Fgithub.com%2FGroth16.html">Groth16 in Klefki</a></li>
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