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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">David Chaum</span></span>
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</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">David Chaum</div></th></tr><tr><td colspan="2" class="infobox-image"><div class="infobox-caption">Chaum in 2018</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">1955 (age 69–70)</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="University_of_California%2C_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a></td></tr><tr><th scope="row" class="infobox-label">Occupations</th><td class="infobox-data role"><style data-mw-deduplicate="TemplateStyles:r1126788409">
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<ul><li><a href="Invention" title="Invention">Inventor</a></li>
<li><a href="Cryptography" title="Cryptography">Cryptographer</a></li></ul>
</div></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><div class="plainlist" style="margin-left:1em;text-indent:-1em;">
<ul><li><a href="DigiCash" title="DigiCash">DigiCash</a></li>
<li><a href="Ecash" title="Ecash">ecash</a></li>
<li><a href="International_Association_for_Cryptologic_Research" title="International Association for Cryptologic Research">IACR</a></li>
<li><a href="Mix-net" class="mw-redirect" title="Mix-net">mixes</a></li>
<li><a href="Voting_systems" class="mw-redirect" title="Voting systems">voting systems</a></li>
<li><a href="Dining_cryptographers_protocol" class="mw-redirect" title="Dining cryptographers protocol">Dining cryptographers protocol</a></li>
<li><a href="Privacy-enhancing_technologies" title="Privacy-enhancing technologies">Privacy Enhancing Technologies</a></li></ul>
</div></td></tr><tr><td colspan="2" class="infobox-full-data"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="Computer_science" title="Computer science">Computer science</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i> Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups </i> <span style="font-size:97%;">(1982)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data">Bernard Marcel Mont-Reynaud</td></tr><tr style="display:none"><td colspan="2">
</td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="http://www.chaum.com/">www<wbr>.chaum<wbr>.com</a></span></td></tr></tbody></table>
<p><b>David Lee Chaum</b> (born 1955) is an American <a href="Computer_scientist" title="Computer scientist">computer scientist</a>, <a href="List_of_cryptographers" title="List of cryptographers">cryptographer</a>, and inventor. He is known as a pioneer in cryptography and privacy-preserving technologies, and widely recognized as the inventor of <a href="Digital_currency" title="Digital currency">digital cash</a>. His 1982 dissertation "Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups" is the first known proposal for a <a href="Blockchain" title="Blockchain">blockchain</a> protocol.<sup id="cite_ref-Sherman_et_al._1-0" class="reference"><a href="#cite_note-Sherman_et_al.-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Complete with the code to implement the protocol, Chaum's dissertation proposed all but one element of the blockchain later detailed in the <a href="Bitcoin" title="Bitcoin">Bitcoin</a> <a href="White_paper" title="White paper">whitepaper</a>. He has been referred to as "the father of online anonymity",<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and "the godfather of cryptocurrency".<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>He is also known for developing <a href="Ecash" title="Ecash">ecash</a>, an electronic cash application that aims to preserve a user's anonymity, and inventing many <a href="Cryptography" title="Cryptography">cryptographic</a> protocols like the <a href="Blind_signature" title="Blind signature">blind signature</a>, <a href="Mix_networks" class="mw-redirect" title="Mix networks">mix networks</a> and the <a href="Dining_cryptographers_protocol" class="mw-redirect" title="Dining cryptographers protocol">Dining cryptographers protocol</a>. In 1995 his company <a href="DigiCash" title="DigiCash">DigiCash</a> created the first digital currency with eCash.<sup id="cite_ref-Greenberg_4-0" class="reference"><a href="#cite_note-Greenberg-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 65–70">: 65–70 </span></sup> His 1981 paper, "Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms", laid the groundwork for the field of anonymous communications research.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>
</p><p>More recently in 2020, Chaum founded xx network, a privacy-focused blockchain platform, and in 2021 launched xx coin (abbreviation XX), a cryptocurrency designed to enhance user privacy and provide quantum resistance.<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><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="Life_and_career">Life and career</h2></div>
<p>Chaum was born to a <a href="Jews" title="Jews">Jewish</a> family in <a href="Los_Angeles%2C_California" class="mw-redirect" title="Los Angeles, California">Los Angeles, California</a>.<sup id="cite_ref-Levy_8-0" class="reference"><a href="#cite_note-Levy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> He gained a doctorate in computer science from the <a href="University_of_California%2C_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a>, in 1982.<sup id="cite_ref-:0_9-0" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pitta_10-0" class="reference"><a href="#cite_note-Pitta-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Also that year, he founded the <a href="International_Association_for_Cryptologic_Research" title="International Association for Cryptologic Research">International Association for Cryptologic Research</a> (IACR), which currently organizes academic conferences in cryptography research.<sup id="cite_ref-Blanchette_11-0" class="reference"><a href="#cite_note-Blanchette-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 47">: 47 </span></sup> Subsequently, he taught at the <a href="New_York_University" title="New York University">New York University</a> Graduate School of Business Administration and at the <a href="University_of_California%2C_Santa_Barbara" title="University of California, Santa Barbara">University of California, Santa Barbara</a> (UCSB). He also formed a cryptography research group at <a href="Centrum_Wiskunde_%26_Informatica" title="Centrum Wiskunde & Informatica">CWI</a>, the Dutch National Research Institute for Mathematics and Computer Science in <a href="Amsterdam" title="Amsterdam">Amsterdam</a>.<sup id="cite_ref-idtrail1_12-0" class="reference"><a href="#cite_note-idtrail1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> He founded <a href="DigiCash" title="DigiCash">DigiCash</a>, an electronic cash company, in 1990.<sup id="cite_ref-Greenberg_4-1" class="reference"><a href="#cite_note-Greenberg-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 119">: 119 </span></sup>
</p><p>Chaum received the Information Technology European Award for 1995.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In 2004, he was named an IACR Fellow.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In 2010, at the <a href="RSA_Conference" title="RSA Conference">RSA Conference</a>, he was honored with the <a href="RSA_Award_for_Excellence_in_Mathematics" title="RSA Award for Excellence in Mathematics">RSA Award for Excellence in Mathematics</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In 2019, he was awarded the honorary title of Dijkstra Fellow by CWI.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> He received an honorary doctorate from the <a href="Universit%C3%A0_della_Svizzera_Italiana" class="mw-redirect" title="Università della Svizzera Italiana">University of Lugano</a> in 2021.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>
</p><p>Chaum resides in <a href="Sherman_Oaks%2C_Los_Angeles" title="Sherman Oaks, Los Angeles">Sherman Oaks, Los Angeles</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Notable_research_contributions">Notable research contributions</h2></div>
<div class="mw-heading mw-heading3"><h3 id="Vault_systems">Vault systems</h3></div>
<p>Recently credited by <a href="Alan_Sherman" title="Alan Sherman">Alan Sherman</a>'s "On the Origins and Variations of Blockchain Technologies",<sup id="cite_ref-Sherman_et_al._1-1" class="reference"><a href="#cite_note-Sherman_et_al.-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Chaum's 1982 Berkeley dissertation proposed every element of the <a href="Blockchain" title="Blockchain">blockchain</a> found in <a href="Bitcoin" title="Bitcoin">Bitcoin</a> except <a href="Proof_of_work" title="Proof of work">proof of work</a>. The proposed vault system lays out a plan for achieving consensus state between nodes, chaining the history of consensus in blocks, and immutably time-stamping the chained data. The paper also lays out the specific code to implement such a protocol.
</p>
<div class="mw-heading mw-heading3"><h3 id="Digital_cash">Digital cash</h3></div>
<p>Chaum is credited as the inventor of secure digital cash for his 1983 paper, which also introduced the cryptographic primitive of a <a href="Blind_signature" title="Blind signature">blind signature</a>.<sup id="cite_ref-Cha82_19-0" class="reference"><a href="#cite_note-Cha82-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> These ideas have been described as the technical roots of the vision of the <a href="Cypherpunk" title="Cypherpunk">Cypherpunk</a> movement that began in the late 1980s.<sup id="cite_ref-narayanan_20-0" class="reference"><a href="#cite_note-narayanan-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Chaum's proposal allowed users to obtain digital currency from a bank and spend it in a manner that is untraceable by the bank or any other party.<sup id="cite_ref-Cha85_21-0" class="reference"><a href="#cite_note-Cha85-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>
In 1988, he extended this idea (with <a href="Amos_Fiat" title="Amos Fiat">Amos Fiat</a> and <a href="Moni_Naor" title="Moni Naor">Moni Naor</a>) to allow offline transactions that enable detection of double-spending.<sup id="cite_ref-CFN88_22-0" class="reference"><a href="#cite_note-CFN88-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>
</p><p>In 1990, he founded <a href="DigiCash" title="DigiCash">DigiCash</a>, an electronic cash company, in Amsterdam to commercialize the ideas in his research.<sup id="cite_ref-Greenberg_4-2" class="reference"><a href="#cite_note-Greenberg-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 119">: 119 </span></sup> The first electronic payment was sent in 1994.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> In 1998, DigiCash filed for bankruptcy, and in 1999 Chaum sold off DigiCash and ended his involvement with the company.<sup id="cite_ref-idtrail1_12-1" class="reference"><a href="#cite_note-idtrail1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="New_types_of_digital_signatures">New types of digital signatures</h3></div>
<p>In the same 1982 paper that proposed digital cash, Chaum introduced <a href="Blind_signature" title="Blind signature">blind signatures</a>.<sup id="cite_ref-Cha82_19-1" class="reference"><a href="#cite_note-Cha82-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> This form of <a href="Digital_signature" title="Digital signature">digital signature</a> blinds the content of a message before it is signed, so that the signer cannot determine the content. The resulting blind signature can be publicly verified against the original, unblinded message in the manner of a regular digital signature.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup>
</p><p>In 1989, he (with Hans van Antwerpen) introduced <a href="Undeniable_signature" title="Undeniable signature">undeniable signatures</a>.<sup id="cite_ref-CV89_26-0" class="reference"><a href="#cite_note-CV89-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> This form of digital signature uses a verification process that is interactive, so that the signatory can limit who can verify the signature. Since signers may refuse to participate in the verification process, signatures are considered valid unless a signer specifically uses a disavowal protocol to prove that a given signature was not authentic.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>
</p><p>In 1991, he (with Eugene van Heyst) introduced <a href="Group_signature" title="Group signature">group signatures</a>, which allow a member of a group to anonymously sign a message on behalf of the entire group.<sup id="cite_ref-CH91_28-0" class="reference"><a href="#cite_note-CH91-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> However an appointed group manager holds the power to revoke the anonymity of any signer in the case of disputes.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Anonymous_communication">Anonymous communication</h3></div>
<p>In 1981, Chaum proposed the idea of an anonymous communication network in a paper.<sup id="cite_ref-Cha81_30-0" class="reference"><a href="#cite_note-Cha81-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup>
His proposal, called <a href="Mix_network" title="Mix network">mix networks</a>, allows a group of senders to submit an encryption of a message and its recipient to a server. Once the server has a batch of messages, it will reorder and obfuscate the messages so that only this server knows which message came from which sender. The batch is then forwarded to another server who does the same process. Eventually, the messages reach the final server where they are fully decrypted and delivered to the recipient. A mechanism to allow return messages is also proposed. Mix networks are the basis of some <a href="Anonymous_remailer" title="Anonymous remailer">remailers</a> and are the conceptual ancestor to modern anonymous web browsing tools like <a href="Tor_(anonymity_network)" class="mw-redirect" title="Tor (anonymity network)">Tor</a> (based on <a href="Onion_routing" title="Onion routing">onion routing</a>). Chaum has advocated that every router be made, effectively, a Tor node.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup>
</p><p>In 1988, Chaum introduced a different type of anonymous communication system called a DC-Net, which is a solution to his proposed <a href="Dining_cryptographers_problem" title="Dining cryptographers problem">Dining Cryptographers Problem</a>.<sup id="cite_ref-Cha88_32-0" class="reference"><a href="#cite_note-Cha88-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> DC-Nets is the basis of the software tool Dissent.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup>
</p><p>In 2017, Chaum published a description of a new variety of mix network.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> A real-world implementation of this network, called cMix and running on the xx network, later became the <a href="Data_transmission_protocol" class="mw-redirect" title="Data transmission protocol">data transmission layer</a> for the <a href="Instant_messaging" title="Instant messaging">instant messaging</a> platform <a href="Xx_messenger" title="Xx messenger">xx messenger</a>.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Trustworthy_voting_systems">Trustworthy voting systems</h3></div>
<p>Chaum has made numerous contributions to secure voting systems, including the first proposal of a system that is <a href="End-to-end_auditable_voting_systems" class="mw-redirect" title="End-to-end auditable voting systems">end-to-end verifiable</a>. This proposal, made in 1981,<sup id="cite_ref-Cha81_30-1" class="reference"><a href="#cite_note-Cha81-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> was given as an application of mix networks. In this system, the individual ballots of voters were kept private which anyone could verify that the tally was counted correctly. This, and other early cryptographic voting systems, assumed that voters could reliably compute values with their personal computers. In 1991, Chaum introduced SureVote which allowed voters to cast a ballot from an untrustworthy voting system,<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> proposing a process now called "code voting" and used in remote voting systems like Remotegrity and DEMOS.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup>
</p><p>In 1994, Chaum introduced the first in-person voting system in which voters cast ballots electronically at a polling station and cryptographically verify that the DRE did not modify their vote (or even learn what it was).<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> In the following years, Chaum proposed (often with others) a series a cryptographically verifiable voting systems that use conventional paper ballots: <a href="Pr%C3%AAt_%C3%A0_Voter" title="Prêt à Voter">Prêt à Voter</a>,<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> <a href="Punchscan" title="Punchscan">Punchscan</a>,<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> and <a href="Scantegrity" title="Scantegrity">Scantegrity</a>.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> The city of <a href="Takoma_Park%2C_Maryland" title="Takoma Park, Maryland">Takoma Park, Maryland</a> used Scantegrity for its November, 2009 election.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> This was the first time a public sector election was run using any cryptographically verifiable voting system.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup>
</p><p>In 2011, Chaum proposed Random Sample Elections.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> This electoral system allows a verifiably random selection of voters, who can maintain their anonymity, to cast votes on behalf the entire electorate.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Other_contributions">Other contributions</h3></div>
<p>In a 1979 report published as Memorandum No. UCB/ERL M79/10<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> by the Electronics Research Laboratory at the <a href="University_of_California%2C_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a>, Chaum proposed a mechanism for splitting a cryptographic key into partial keys that could be distributed among mutually suspicious groups. This concept was a significant predecessor to what is now known as <a href="Secret_sharing" title="Secret sharing">secret sharing</a>.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup>
</p><p>In 1985, Chaum proposed the original <a href="Digital_credential" title="Digital credential">anonymous credential</a> system,<sup id="cite_ref-Cha85_21-1" class="reference"><a href="#cite_note-Cha85-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> which is sometimes also referred to as a pseudonym system.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> This stems from the fact that the credentials of such a system are obtained from and shown to organizations using different pseudonyms which cannot be linked.
</p><p>In 1988, Chaum with <a href="Gilles_Brassard" title="Gilles Brassard">Gilles Brassard</a> and <a href="Claude_Cr%C3%A9peau" title="Claude Crépeau">Claude Crépeau</a> published a paper<sup id="cite_ref-BCC88_50-0" class="reference"><a href="#cite_note-BCC88-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> that introduced <a href="Zero-knowledge_proofs" class="mw-redirect" title="Zero-knowledge proofs">zero-knowledge arguments</a>, as well as a security model using information-theoretic private-channels, and also first formalized the concept of a <a href="Commitment_scheme" title="Commitment scheme">commitment scheme</a>.
</p><p>1991, with Torben Pedersen, he demonstrated a well-cited <a href="Zero-knowledge_proof" title="Zero-knowledge proof">zero-knowledge proof</a> of a <a href="Decisional_Diffie%E2%80%93Hellman_assumption" title="Decisional Diffie–Hellman assumption">DDH tuple</a>.<sup id="cite_ref-CP92_51-0" class="reference"><a href="#cite_note-CP92-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> This proof is particularly useful as it can prove proper reencryption of an <a href="ElGamal_encryption" title="ElGamal encryption">ElGamal</a> ciphertext.
</p><p>Chaum contributed to an important <a href="Commitment_scheme" title="Commitment scheme">commitment scheme</a> which is often attributed to Pedersen. In fact, Pedersen, in his 1991 paper,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> cites a rump session talk on an unpublished paper by Jurjen Bos and Chaum for the scheme. It appeared even earlier in a paper by Chaum, Damgard, and Jeroen van de Graaf.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup>
</p><p>In 1993 with <a href="Stefan_Brands" title="Stefan Brands">Stefan Brands</a>, Chaum introduced the concept of a <a href="Distance-bounding_protocol" title="Distance-bounding protocol">distance-bounding protocol</a>.<sup id="cite_ref-BC93_54-0" class="reference"><a href="#cite_note-BC93-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup>
</p><p>In 2019, he was one of the speakers at the fifth <a href="Ethereum" title="Ethereum">Ethereum</a> developer conference, which was held in <a href="Japan" title="Japan">Japan</a>.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup>
</p><p>In July 2024, Chaum sat down with <a href="Vitalik_Buterin" title="Vitalik Buterin">Vitalik Buterin</a>, co-founder of <a href="Ethereum" title="Ethereum">Ethereum</a> for a panel on the future of privacy at Plasmacon conference at the <a href="United_Nations_University" title="United Nations University">United Nations University</a> in Tokyo, Japan.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2></div>
<ul><li><i>Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms</i>, 1981</li>
<li><i>Advances in Cryptology – Proceedings of Crypto 82,</i> 1983<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup></li>
<li><i>Advances in Cryptology – Proceedings of Crypto 83</i>, 1984<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup></li>
<li>David Chaum, Amos Fiat and Moni Naor, <i>Untraceable Electronic Cash</i><sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></li>
<li>David Lee Chaum, <a rel="nofollow" class="external text" href="https://chaum.com/publications/techrep.pdf"><i>Computer Systems Established, Maintained and Trusted by Mutually Suspicious Groups</i></a>, University of California, Berkeley, 1982<sup id="cite_ref-:0_9-1" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li>
<li>David Chaum, <i>Towards Trustworthy Elections</i>, Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2010</li>
<li>How to issue a central bank digital currency (working paper), 2021<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text">Joshua Davis. "<a rel="nofollow" class="external text" href="https://www.wired.com/2012/05/st-essay-voting/">How Selecting Voters Randomly Can Lead to Better Elections</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230106191157/https://www.wired.com/2012/05/st-essay-voting/">Archived</a> 2023-01-06 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a>." Wired, 16.05.2012.</span>
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<li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><cite id="CITEREFChaum1979" class="citation report cs1">Chaum, David L. (February 22, 1979). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220615040203/https://www2.eecs.berkeley.edu/Pubs/TechRpts/1979/ERL-m-79-10.pdf">Computer Systems Established, Maintained, and Trusted by Mutually Suspicious Groups</a> <span class="cs1-format">(PDF)</span> (Report). Memorandum. University of California, Berkeley, Electronics Research Laboratory. Archived from <a rel="nofollow" class="external text" href="https://www2.eecs.berkeley.edu/Pubs/TechRpts/1979/ERL-m-79-10.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2022-06-15<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-21</span></span>.</cite></span>
</li>
<li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><cite id="CITEREFChaum1985" class="citation book cs1">Chaum, D. (1985). <a rel="nofollow" class="external text" href="https://chaum.com/wp-content/uploads/2022/01/Chaum1985-Chapter-How-To-Keep-a-Secret-Alive.pdf">"How to Keep a Secret Alive"</a> <span class="cs1-format">(PDF)</span>. <i>Advances in Cryptology</i>. Lecture Notes in Computer Science. Vol. 196. Berlin, Heidelberg: Springer. pp. <span class="nowrap">481–</span>485. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-39568-7_40">10.1007/3-540-39568-7_40</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-15658-1</bdi>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230316080459/https://chaum.com/wp-content/uploads/2022/01/Chaum1985-Chapter-How-To-Keep-a-Secret-Alive.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2023-03-16<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-21</span></span>.</cite></span>
</li>
<li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><cite id="CITEREFLysyanskayaRivestSahaiWolf2000" class="citation book cs1"><a href="Anna_Lysyanskaya" title="Anna Lysyanskaya">Lysyanskaya, Anna</a>; <a href="Ron_Rivest" title="Ron Rivest">Rivest, Ronald L.</a>; Sahai, Amit; Wolf, Stefan (2000). "Pseudonym systems". In <a href="Howard_Heys" title="Howard Heys">Heys, Howard M.</a>; <a href="Carlisle_Adams" title="Carlisle Adams">Adams, Carlisle M.</a> (eds.). <a href="Selected_Areas_in_Cryptography" title="Selected Areas in Cryptography"><i>Selected Areas in Cryptography</i></a>. <a href="Lecture_Notes_in_Computer_Science" title="Lecture Notes in Computer Science">Lecture Notes in Computer Science</a>. Vol. 1758. Springer. pp. <span class="nowrap">184–</span>199. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-46513-8_14">10.1007/3-540-46513-8_14</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-67185-5</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:77189">77189</a>.</cite></span>
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<li id="cite_note-BCC88-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-BCC88_50-0">^</a></b></span> <span class="reference-text">Gilles Brassard, David Chaum, and Claude Crepeau, <i><a rel="nofollow" class="external text" href="http://crypto.cs.mcgill.ca/~crepeau/PDF/BCC88-jcss.pdf">Minimum Disclosure Proofs of Knowledge</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110927181436/http://crypto.cs.mcgill.ca/~crepeau/PDF/BCC88-jcss.pdf">Archived</a> 2011-09-27 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i>, Journal of Computer and System Sciences, vol. 37, pp. 156–189, 1988.</span>
</li>
<li id="cite_note-CP92-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-CP92_51-0">^</a></b></span> <span class="reference-text">David Chaum and Torben P. Pedersen. 1992. Wallet Databases with Observers. In Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '92), Ernest F. Brickell (Ed.). Springer-Verlag, London, UK, UK, 89-105.</span>
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<li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><cite id="CITEREFPedersen1992" class="citation book cs1">Pedersen, T. P. (1992). "Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing". <i>Advances in Cryptology – CRYPTO '91</i>. Lecture Notes in Computer Science. Vol. 576. Berlin, Heidelberg: Springer. pp. <span class="nowrap">129–</span>140. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-46766-1_9">10.1007/3-540-46766-1_9</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-55188-1</bdi>.</cite></span>
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<li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><cite id="CITEREFChaumDamgårdGraaf1988" class="citation book cs1">Chaum, D.; Damgård, I. B.; Graaf, J. (1988). "Multiparty Computations Ensuring Privacy of Each Party's Input and Correctness of the Result". <i>Advances in Cryptology – CRYPTO '87</i>. Lecture Notes in Computer Science. Vol. 293. p. 87. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-48184-2_7">10.1007/3-540-48184-2_7</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-18796-7</bdi>.</cite></span>
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<li id="cite_note-BC93-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-BC93_54-0">^</a></b></span> <span class="reference-text">Stefan Brands, David Chaum: Distance-bounding protocols (extended abstract). Proceedings Eurocrypt '93.</span>
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<li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=hvdxT_uO0dc"><span class="">David Chaum (Devcon5)</span></a> on <a href="YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></span>
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<li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=hLpGXchvaMM"><span class="">David Chaum & Vitalik Buterin - Plasmacon - Future of Privacy</span></a> on <a href="YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></span>
</li>
<li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><cite class="citation book cs1"><i>Advances in Cryptology – Proceedings of CRYPTO 82</i>. Chaum, David., Rivest, Ronald L., Sherman, Alan T. New York: Plenum Press. 1983. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0306413663</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/9488557">9488557</a>.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite book}}</code>: CS1 maint: others (link)</span></span>
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<li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><cite class="citation book cs1"><i>Advances in Cryptology – Proceedings of Crypto 83</i>. Chaum, David. New York: Plenum Press. 1984. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781468447309</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/681096555">681096555</a>.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite book}}</code>: CS1 maint: others (link)</span></span>
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<li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><cite id="CITEREFChaumFiatNaor1990" class="citation book cs1">Chaum, David; Fiat, Amos; Naor, Moni (1990). "Untraceable Electronic Cash". In Goldwasser, Shafi (ed.). <i>Advances in Cryptology — CRYPTO' 88</i>. Lecture Notes in Computer Science. Vol. 403. Springer New York. pp. <span class="nowrap">319–</span>327. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F0-387-34799-2_25">10.1007/0-387-34799-2_25</a></span>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780387971964</bdi>.</cite></span>
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<li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.snb.ch/en/mmr/papers/id/working_paper_2021_03">"Swiss National Bank (SNB) - How to issue a central bank digital currency"</a>. <i>www.snb.ch</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210327194438/https://www.snb.ch/en/mmr/papers/id/working_paper_2021_03">Archived</a> from the original on 2021-03-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-29</span></span>.</cite></span>
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</ol></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li><cite id="CITEREFChaum1984" class="citation book cs1">Chaum, D. (1984). "A New Paradigm for Individuals in the Information Age". <a rel="nofollow" class="external text" href="https://chaum.com/wp-content/uploads/2022/01/Chaum-New-Paradigm-for-Individuals-in-Information-Age.pdf"><i>1984 IEEE Symposium on Security and Privacy</i></a> <span class="cs1-format">(PDF)</span>. IEEE. p. 99. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSP.1984.10025">10.1109/SP.1984.10025</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-8186-0532-1</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1717835">1717835</a>.</cite></li>
<li><cite id="CITEREFChaum1985" class="citation journal cs1">Chaum, D. (1985). <a rel="nofollow" class="external text" href="https://chaum.com/security-without-identification/">"Security without identification: Transaction systems to make big brother obsolete"</a>. <i>Communications of the ACM</i>. <b>28</b> (10): <span class="nowrap">1030–</span>1044. <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=10.1.1.319.3690">10.1.1.319.3690</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F4372.4373">10.1145/4372.4373</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:15340054">15340054</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230519141052/https://chaum.com/security-without-identification/">Archived</a> from the original on 2023-05-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-05-20</span></span>.</cite></li>
<li>Chaum, D. (1992). "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20030605181509/http://www.chaum.com/articles/Achieving_Electronic_Privacy.htm">Achieving Electronic Privacy</a>," <i>Scientific American</i>, August 1992, p. 96-101.</li>
<li><cite id="CITEREFChaum1997" class="citation journal cs1">Chaum, D. (1997). "David Chaum on Electronic Commerce How much do you trust Big Brother?". <i>IEEE Internet Computing</i>. <b>1</b> (6): <span class="nowrap">8–</span>16. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMIC.1997.643931">10.1109/MIC.1997.643931</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:8072432">8072432</a>.</cite></li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://www.chaum.com/">Home page</a></li>
<li><a rel="nofollow" class="external text" href="https://chaum.com/patents/">David Chaum patents</a></li>
<li><a rel="nofollow" class="external text" href="https://xx.network/">xx network Homepage</a></li>
<li><a rel="nofollow" class="external text" href="http://www.punchscan.org/">Punchscan Homepage</a></li>
<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20091221055739/http://www.electiontechnology.com/who.php?id=4">David Chaum research papers</a></li></ul>
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</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q1173973#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1877" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q1173973#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1877" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000066741136">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/94442415">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.worldcat.org/fast/105013">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJv4m4M6vjX4Rh7JRFFHYP">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n82220906">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p073320722">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90224635">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810569871505606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007435366105171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=118579">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dl.acm.org/profile/81100121641">Association for Computing Machinery</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:chaum.david">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/c/DavidChaum">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/47740">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/254985661">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/person/6b852b7a-6d40-4c87-b91c-8d4f8df914c8">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div></div><!--htdig_noindex--><div><div class="zim-footer">
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