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<title>Distributed key generation</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Distributed key generation</span></span>

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<p><b>Distributed key generation</b> (DKG) is a cryptographic process in which multiple parties contribute to the calculation of a shared public and private key set. Unlike most <a href="Public_key_infrastructure" title="Public key infrastructure">public key encryption</a> models, distributed key generation does not rely on <a href="Trusted_third_party" title="Trusted third party">Trusted Third Parties</a>.<sup id="cite_ref-Kate_1-0" class="reference"><a href="#cite_note-Kate-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Instead, the participation of a <a href="Threshold_cryptosystem" title="Threshold cryptosystem">threshold</a> of honest parties determines whether a key pair can be computed successfully.<sup id="cite_ref-Boldyreva_2-0" class="reference"><a href="#cite_note-Boldyreva-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Distributed key generation prevents single parties from having access to a private key. The involvement of many parties requires Distributed key generation to ensure secrecy in the presence of <a href="Adversary_(cryptography)" title="Adversary (cryptography)">malicious</a> contributions to the key calculation.<sup id="cite_ref-Kate_1-1" class="reference"><a href="#cite_note-Kate-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Distributed key generation is commonly used to decrypt shared <a href="Ciphertext" title="Ciphertext">ciphertexts</a> or create group <a href="Digital_signature" title="Digital signature">digital signatures</a>.<sup id="cite_ref-Boldyreva_2-1" class="reference"><a href="#cite_note-Boldyreva-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>Distributed key generation protocol was first specified by Torben Pedersen in 1991. This first model depended on the security of the Joint-Feldman Protocol for <a href="Verifiable_secret_sharing" title="Verifiable secret sharing">verifiable secret sharing</a> during the secret sharing process.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>In 1999, Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, and <a href="Tal_Rabin" title="Tal Rabin">Tal Rabin</a> produced a series of security proofs demonstrating that Feldman verifiable secret sharing was vulnerable to malicious contributions to Pedersen's distributed key generator that would leak information about the shared private key.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gennaro_5-0" class="reference"><a href="#cite_note-Gennaro-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The same group also proposed an updated distributed key generation scheme preventing malicious contributions from impacting the value of the private key.

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<div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2></div>

<p>The distributed key generation protocol specified by Gennaro, Jarecki, Krawczyk, and Rabin assumes that a group of players has already been established by an honest party prior to the key generation. It also assumes the communication between parties is <a href="Synchronization_(computer_science)" title="Synchronization (computer science)">synchronous</a>.<sup id="cite_ref-Gennaro_5-1" class="reference"><a href="#cite_note-Gennaro-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

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<ol><li>All parties use Pedersen's <a href="Verifiable_secret_sharing" title="Verifiable secret sharing">verifiable secret sharing</a> protocol to share the results of two random <a href="Polynomial#Polynomial_functions" title="Polynomial">polynomial functions</a>.</li>

<li>Every party then verifies all the shares they received. If verification fails, the recipient broadcasts a complaint for the party whose share failed. Each accused party then <a href="Broadcasting_(networking)" title="Broadcasting (networking)">broadcasts</a> their shares. Each party then has the opportunity to verify the broadcast shares or disqualify accused parties. All parties generate a common list of non-disqualified parties.</li>

<li>Each non-disqualified party broadcasts a set of values constructed by raising a common <a href="Subring#Subring_generated_by_a_set" title="Subring">generator</a> to the power of each value used in one polynomial in <b>Part 1</b>.</li>

<li>These broadcast values are verified by each party similarly to as in <b>Part 2</b>. When a verification fails, the party now broadcasts both the values received in <b>Part 1</b> and the values received in <b>Part 3</b>. For each party with verifiable complaints, all other parties reconstruct their own value sets in order to eliminate disqualified contributions.</li>

<li>The group computes the private key as the product of every qualified contribution (each qualified party's random polynomial evaluated at 0).<sup id="cite_ref-Gennaro_5-2" class="reference"><a href="#cite_note-Gennaro-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ol>

<div class="mw-heading mw-heading2"><h2 id="Avoiding_the_synchrony_assumption">Avoiding the synchrony assumption</h2></div>

<p>In 2009, Aniket Kate and Ian Goldberg presented a Distributed key generation protocol suitable for use over the Internet.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Unlike earlier constructions, this protocol does not require a broadcast channel or the synchronous communication assumption, and a <a rel="nofollow" class="external text" href="https://crysp.uwaterloo.ca/software/DKG/">ready-to-use library</a> is available.

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<div class="mw-heading mw-heading2"><h2 id="Robustness">Robustness</h2></div>

<p>In many circumstances, a <a href="Robustness_(computer_science)" title="Robustness (computer science)">robust</a> distributed key generator is necessary. Robust generator protocols can reconstruct public keys in order to remove malicious shares even if malicious parties still remain in the qualified group during the reconstruction phase.<sup id="cite_ref-Gennaro_5-3" class="reference"><a href="#cite_note-Gennaro-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> For example, robust multi-party digital signatures can tolerate a number of malicious users roughly proportionate to the length of the modulus used during key generation.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Sparse-evaluated_DKG">Sparse-evaluated DKG</h2></div>

<p>Distributed key generators can implement a sparse evaluation matrix in order to improve efficiency during verification stages. Sparse evaluation can improve run time from <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(nt)}">

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<annotation encoding="application/x-tex">{\displaystyle O(nt)}</annotation>

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</math></span><img src="./dc2fdfea9882ba82dda67c942b400953ad26758f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.817ex; height:2.843ex;" alt="{\displaystyle O(nt)}" loading="lazy"></span> (where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

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<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

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</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> is the number of parties and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}">

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<annotation encoding="application/x-tex">{\displaystyle t}</annotation>

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</math></span><img src="./65658b7b223af9e1acc877d848888ecdb4466560.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}" loading="lazy"></span> is the threshold of malicious users) to <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(log^{3}n)}">

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<annotation encoding="application/x-tex">{\displaystyle O(log^{3}n)}</annotation>

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</math></span><img src="./eeb795412e01a889d9a3c35ec7d894159a60b5fe.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.971ex; height:3.176ex;" alt="{\displaystyle O(log^{3}n)}" loading="lazy"></span>. Instead of robust verification, sparse evaluation requires that a small set of the parties verify a small, randomly picked set of shares. This results in a small probability that the key generation will fail in the case that a large number of malicious shares are not chosen for verification.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<p>Distributed key generation and distributed key cryptography are rarely applied over the internet because of the reliance on synchronous communication.<sup id="cite_ref-Gennaro_5-4" class="reference"><a href="#cite_note-Gennaro-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Distributed key cryptography is useful in <a href="Key_escrow" title="Key escrow">key escrow</a> services where a company can meet a threshold to decrypt a ciphertext version of private key. This way a company can require multiple employees to recover a private key without giving the escrow service a plaintext copy.<sup id="cite_ref-Kate_1-2" class="reference"><a href="#cite_note-Kate-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Distributed key generation is also useful in <a href="Server-side" class="mw-redirect" title="Server-side">server-side</a> password <a href="Authentication_protocol" title="Authentication protocol">authentication</a>. If <a href="Cryptographic_hash_function#Password_verification" title="Cryptographic hash function">password hashes</a> are stored on a single server, a breach in the server would result in all the password hashes being available for attackers to <a href="Cryptanalysis" title="Cryptanalysis">analyze</a> offline. Variations of distributed key generation can authenticate user passwords across multiple servers and eliminate <a href="Single_point_of_failure#Computing" title="Single point of failure">single points of failure</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>Distributed key generation is more commonly used for group digital signatures. This acts as a form of voting, where a threshold of group members would have to participate in order for the group to digitally sign a document.<sup id="cite_ref-Boldyreva_2-2" class="reference"><a href="#cite_note-Boldyreva-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFKateGoldberg2010" class="citation book cs1">Kate, Aniket; Goldberg, Ian (2010). "Distributed Private-Key Generators for Identity-Based Cryptography". <i>Security and Cryptography for Networks</i>. Lecture Notes in Computer Science. Vol. 6280. pp. <span class="nowrap">436–</span>453. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.389.4486">10.1.1.389.4486</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-15317-4_27">10.1007/978-3-642-15317-4_27</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-642-15316-7</bdi>.</cite></span>

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<li id="cite_note-Boldyreva-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Boldyreva_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Boldyreva_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Boldyreva_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFBoldyreva2003" class="citation book cs1">Boldyreva, Alexandra (2003). <a rel="nofollow" class="external text" href="http://iacr.org/archive/pkc2003/25670031/25670031.pdf">"Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme"</a> <span class="cs1-format">(PDF)</span>. <i>Public Key Cryptography — PKC 2003</i>. Lecture Notes in Computer Science. Vol. 2567. pp. <span class="nowrap">31–</span>46. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-36288-6_3">10.1007/3-540-36288-6_3</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-00324-3</bdi>.</cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{cite book}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (help)</span></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFGennaroJareckiKrawczykRabin1999" class="citation journal cs1">Gennaro, Rosario; Jarecki, Stanisław; Krawczyk, Hugo; Rabin, Tal (1999). <a rel="nofollow" class="external text" href="https://dl.acm.org/doi/10.5555/1756123.1756153">"Secure distributed key generation for discrete-log based cryptosystems"</a>. <i>Proceedings of the 17th International Conference on Theory and Application of Cryptographic Techniques</i>. EUROCRYPT'99. Berlin, Heidelberg: Springer-Verlag: <span class="nowrap">295–</span>310. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-65889-4</bdi>.</cite></span>

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<li id="cite_note-Gennaro-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gennaro_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gennaro_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Gennaro_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Gennaro_5-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Gennaro_5-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFGennaroJareckiKrawczykRabin2006" class="citation journal cs1">Gennaro, Rosario; Jarecki, Stanislaw; Krawczyk, Hugo; Rabin, Tal (24 May 2006). "Secure Distributed Key Generation for Discrete-Log Based Cryptosystems". <i>Journal of Cryptology</i>. <b>20</b> (1): <span class="nowrap">51–</span>83. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.6445">10.1.1.134.6445</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00145-006-0347-3">10.1007/s00145-006-0347-3</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3331212">3331212</a>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFKateGoldberg2006" class="citation conference cs1">Kate, Aniket; Goldberg, Ian (2006). "Distributed Key Generation for the Internet". <i>IEEE ICDCS</i>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICDCS.2009.21">10.1109/ICDCS.2009.21</a>.</cite></span>

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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFCastellucciaJareckiKimTsudik2006" class="citation journal cs1">Castelluccia, Claude; Jarecki, Stanisław; Kim, Jihye; Tsudik, Gene (2006). "Secure acknowledgment aggregation and multisignatures with limited robustness". <i>Computer Networks</i>. <b>50</b> (10): <span class="nowrap">1639–</span>1652. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.comnet.2005.09.021">10.1016/j.comnet.2005.09.021</a>.</cite></span>

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<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFCannySorkin2004" class="citation book cs1">Canny, John; Sorkin, Steve (2004). "Practical Large-Scale Distributed Key Generation". <a rel="nofollow" class="external text" href="http://www.cs.berkeley.edu/~jfc/papers/04/Eurocrypt/Eurocrypt04.pdf"><i>Advances in Cryptology - EUROCRYPT 2004</i></a> <span class="cs1-format">(PDF)</span>. Lecture Notes in Computer Science. Vol. 3027. pp. <span class="nowrap">138–</span>152. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.6028">10.1.1.69.6028</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-24676-3_9">10.1007/978-3-540-24676-3_9</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-21935-4</bdi>.</cite></span>

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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFMacKenzieShrimptonMarcus2006" class="citation journal cs1">MacKenzie, Philip; Shrimpton, Thomas; Marcus, Jakobsson (2006). "Threshold Password-authenticated Key Exchange". <i>Journal of Cryptology</i>. <b>19</b> (1): <span class="nowrap">27–</span>66. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.6403">10.1.1.101.6403</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00145-005-0232-5">10.1007/s00145-005-0232-5</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1732140">1732140</a>.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite id="CITEREFJareckiKiayiasKrawczyk2014" class="citation journal cs1">Jarecki, Stanislaw; Kiayias, Aggelos; Krawczyk, Hugo (2014). <a rel="nofollow" class="external text" href="https://eprint.iacr.org/2014/650.pdf">"Round-Optimal Password-Protected Secret Sharing and T-PAKE in the Password-Only model"</a> <span class="cs1-format">(PDF)</span>. <i>Cryptology ePrint Archive</i>. <b>650</b><span class="reference-accessdate">. Retrieved <span class="nowrap">5 November</span> 2014</span>.</cite></span>

</li>

</ol></div></div>

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<ul><li><a href="Benaloh_cryptosystem" title="Benaloh cryptosystem">Benaloh</a></li>

<li><a href="Blum%E2%80%93Goldwasser_cryptosystem" title="Blum–Goldwasser cryptosystem">Blum–Goldwasser</a></li>

<li><a href="Cayley%E2%80%93Purser_algorithm" title="Cayley–Purser algorithm">Cayley–Purser</a></li>

<li><a href="Damg%C3%A5rd%E2%80%93Jurik_cryptosystem" title="Damgård–Jurik cryptosystem">Damgård–Jurik</a></li>

<li><a href="Goldwasser%E2%80%93Micali_cryptosystem" title="Goldwasser–Micali cryptosystem">Goldwasser–Micali</a></li>

<li><a href="Naccache%E2%80%93Stern_cryptosystem" title="Naccache–Stern cryptosystem">Naccache–Stern</a></li>

<li><a href="Paillier_cryptosystem" title="Paillier cryptosystem">Paillier</a></li>

<li><a href="Rabin_signature" class="mw-redirect" title="Rabin signature">Rabin</a></li>

<li><a href="Okamoto%E2%80%93Uchiyama_cryptosystem" title="Okamoto–Uchiyama cryptosystem">Okamoto–Uchiyama</a></li>

<li><a href="Schmidt-Samoa_cryptosystem" title="Schmidt-Samoa cryptosystem">Schmidt–Samoa</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%"><a href="Discrete_logarithm" title="Discrete logarithm">Discrete logarithm</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Cramer%E2%80%93Shoup_cryptosystem" title="Cramer–Shoup cryptosystem">Cramer–Shoup</a></li>

<li><a href="Elliptic_Curve_Digital_Signature_Algorithm" title="Elliptic Curve Digital Signature Algorithm">ECDSA</a></li>

<li><a href="EdDSA" title="EdDSA">EdDSA</a>

<li><a href="ECMQV" class="mw-redirect" title="ECMQV">ECMQV</a></li>

<li><a href="ElGamal_encryption" title="ElGamal encryption">ElGamal</a>

<ul><li><a href="ElGamal_signature_scheme" title="ElGamal signature scheme">signature scheme</a></li></ul></li>

<li><a href="Schnorr_signature" title="Schnorr signature">Schnorr</a></li>

<li><a href="SPEKE" title="SPEKE">SPEKE</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%"><a href="Lattice-based_cryptography" title="Lattice-based cryptography">Lattice/SVP/CVP</a>/<wbr><a href="Learning_with_errors" title="Learning with errors">LWE</a>/<wbr><a href="Short_integer_solution_problem" title="Short integer solution problem">SIS</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BLISS_signature_scheme" title="BLISS signature scheme">BLISS</a></li>

<li><a href="Kyber" title="Kyber">Kyber</a></li>

<li><a href="NewHope" title="NewHope">NewHope</a></li>

<li><a href="NTRUEncrypt" title="NTRUEncrypt">NTRUEncrypt</a></li>

<li><a href="NTRUSign" title="NTRUSign">NTRUSign</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group wraplinks" style="width:1%">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="CEILIDH" title="CEILIDH">CEILIDH</a></li>

<li><a href="Lamport_signature" title="Lamport signature">Lamport</a></li>

<li><a href="McEliece_cryptosystem" title="McEliece cryptosystem">McEliece</a></li>

<li><a href="Merkle%E2%80%93Hellman_knapsack_cryptosystem" title="Merkle–Hellman knapsack cryptosystem">Merkle–Hellman</a></li>

<li><span class="wraplinks"><a href="Naccache%E2%80%93Stern_knapsack_cryptosystem" title="Naccache–Stern knapsack cryptosystem">Naccache–Stern knapsack cryptosystem</a></span></li>

<li><a href="Three-pass_protocol" title="Three-pass protocol">Three-pass protocol</a></li>

<li><a href="SQIsign" title="SQIsign">SQIsign</a></li>

<li><a href="SPHINCS%2B" title="SPHINCS+">SPHINCS<sup>+</sup></a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Discrete_logarithm#Cryptography" title="Discrete logarithm">Discrete logarithm cryptography</a></li>

<li><a href="Elliptic-curve_cryptography" title="Elliptic-curve cryptography">Elliptic-curve cryptography</a></li>

<li><a href="Hash-based_cryptography" title="Hash-based cryptography">Hash-based cryptography</a></li>

<li><a href="Non-commutative_cryptography" title="Non-commutative cryptography">Non-commutative cryptography</a></li>

<li><a href="RSA_problem" title="RSA problem">RSA problem</a></li>

<li><a href="Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Standardization</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="CRYPTREC" title="CRYPTREC">CRYPTREC</a></li>

<li><a href="NESSIE" title="NESSIE">NESSIE</a></li>

<li><a href="NSA_Suite_B_Cryptography" title="NSA Suite B Cryptography">NSA Suite B</a></li>

<li><a href="NIST_Post-Quantum_Cryptography_Standardization" title="NIST Post-Quantum Cryptography Standardization">Post-Quantum Cryptography</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Digital_signature" title="Digital signature">Digital signature</a></li>

<li><a href="Public_key_fingerprint" title="Public key fingerprint">Fingerprint</a></li>

<li><a href="Web_of_trust" title="Web of trust">Web of trust</a></li>

<li><a href="Identity-based_cryptography" title="Identity-based cryptography">Identity-based cryptography</a></li>

<li><a href="Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li>

<li><a href="OpenPGP_card" title="OpenPGP card">OpenPGP card</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Cryptography149" style="font-size:114%;margin:0 4em"><a href="Cryptography" title="Cryptography">Cryptography</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_cryptography" title="History of cryptography">History of cryptography</a></li>

<li><a href="Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li>

<li><a href="Classical_cipher" title="Classical cipher">Classical cipher</a></li>

<li><a href="Cryptographic_protocol" title="Cryptographic protocol">Cryptographic protocol</a>

<ul><li><a href="Authentication_protocol" title="Authentication protocol">Authentication protocol</a></li></ul></li>

<li><a href="Cryptographic_primitive" title="Cryptographic primitive">Cryptographic primitive</a></li>

<li><a href="Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a></li>

<li><a href="Cryptocurrency" title="Cryptocurrency">Cryptocurrency</a></li>

<li><a href="Cryptosystem" title="Cryptosystem">Cryptosystem</a></li>

<li><a href="Cryptographic_nonce" title="Cryptographic nonce">Cryptographic nonce</a></li>

<li><a href="Cryptovirology" title="Cryptovirology">Cryptovirology</a></li>

<li><a href="Hash_function" title="Hash function">Hash function</a>

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Key_derivation_function" title="Key derivation function">Key derivation function</a></li>

<li><a href="Secure_Hash_Algorithms" title="Secure Hash Algorithms">Secure Hash Algorithms</a></li></ul></li>

<li><a href="Digital_signature" title="Digital signature">Digital signature</a></li>

<li><a href="Kleptography" title="Kleptography">Kleptography</a></li>

<li><a href="Key_(cryptography)" title="Key (cryptography)">Key (cryptography)</a></li>

<li><a href="Key_exchange" title="Key exchange">Key exchange</a></li>

<li><a href="Key_generator" title="Key generator">Key generator</a></li>

<li><a href="Key_schedule" title="Key schedule">Key schedule</a></li>

<li><a href="Key_stretching" title="Key stretching">Key stretching</a></li>

<li><a href="Keygen" title="Keygen">Keygen</a></li>

<li>Machines</li>

<li><a href="Cryptojacking_malware" class="mw-redirect" title="Cryptojacking malware">Cryptojacking malware</a></li>

<li><a href="Ransomware" title="Ransomware">Ransomware</a></li>

<li><a href="Random_number_generation" title="Random number generation">Random number generation</a>

<ul><li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Cryptographically secure pseudorandom number generator</a> (CSPRNG)</li></ul></li>

<li><a href="Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a> (PRN)</li>

<li><a href="Secure_channel" title="Secure channel">Secure channel</a></li>

<li><a href="Insecure_channel" class="mw-redirect" title="Insecure channel">Insecure channel</a></li>

<li><a href="Subliminal_channel" title="Subliminal channel">Subliminal channel</a></li>

<li><a href="Encryption" title="Encryption">Encryption</a></li>

<li><a href="Decryption" class="mw-redirect" title="Decryption">Decryption</a></li>

<li><a href="End-to-end_encryption" title="End-to-end encryption">End-to-end encryption</a></li>

<li><a href="Harvest_now%2C_decrypt_later" title="Harvest now, decrypt later">Harvest now, decrypt later</a></li>

<li><a href="Information-theoretic_security" title="Information-theoretic security">Information-theoretic security</a></li>

<li><a href="Plaintext" title="Plaintext">Plaintext</a></li>

<li><a href="Codetext" class="mw-redirect" title="Codetext">Codetext</a></li>

<li><a href="Ciphertext" title="Ciphertext">Ciphertext</a></li>

<li><a href="Shared_secret" title="Shared secret">Shared secret</a></li>

<li><a href="Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li>

<li><a href="Trusted_timestamping" title="Trusted timestamping">Trusted timestamping</a></li>

<li><a href="Key-based_routing" title="Key-based routing">Key-based routing</a></li>

<li><a href="Onion_routing" title="Onion routing">Onion routing</a></li>

<li><a href="Garlic_routing" title="Garlic routing">Garlic routing</a></li>

<li><a href="Kademlia" title="Kademlia">Kademlia</a></li>

<li><a href="Mix_network" title="Mix network">Mix network</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Block_cipher" title="Block cipher">Block cipher</a></li>

<li><a href="Stream_cipher" title="Stream cipher">Stream cipher</a></li>

<li><a href="Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li>

<li><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li>

<li><a href="Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li>

<li><a href="Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li>

<li><a href="Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li>

<li><a href="Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li>

<li><a href="Message_authentication_code" title="Message authentication code">Message authentication code</a></li>

<li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a></li>

<li><a href="Steganography" title="Steganography">Steganography</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>

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