{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:26:47Z","timestamp":1750220807174,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":21,"publisher":"ACM","license":[{"start":{"date-parts":[[2019,11,11]],"date-time":"2019-11-11T00:00:00Z","timestamp":1573430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100002790","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2019-04821"],"award-info":[{"award-number":["RGPIN-2019-04821"]}],"id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1718595,1565375"],"award-info":[{"award-number":["1718595,1565375"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,11,11]]},"DOI":"10.1145\/3338498.3358640","type":"proceedings-article","created":{"date-parts":[[2019,11,11]],"date-time":"2019-11-11T18:15:00Z","timestamp":1573496100000},"page":"37-49","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["There Are 10 Types of Vectors (and Polynomials)"],"prefix":"10.1145","author":[{"given":"William","family":"Black","sequence":"first","affiliation":[{"name":"University of Calgary, Calgary, AB, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryan","family":"Henry","sequence":"additional","affiliation":[{"name":"University of Calgary, Calgary, AB, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,11,11]]},"reference":[{"key":"e_1_3_2_1_1_1","volume-title":"RELIC is an Efficient LIbrary for Cryptography. https:\/\/github.com\/relic-toolkit\/relic [commit hrefhttps:\/\/github.com\/relic-toolkit\/relic\/tree\/e656004f67c3090465f641b19466442664f54d74e56004] (June","author":"Aranha Diego","year":"2019","unstructured":"Diego F.@ Aranha and Conrado Porto Lopes Gouv\u00eaa . RELIC is an Efficient LIbrary for Cryptography. https:\/\/github.com\/relic-toolkit\/relic [commit hrefhttps:\/\/github.com\/relic-toolkit\/relic\/tree\/e656004f67c3090465f641b19466442664f54d74e56004] (June 2019 ). Diego F.@ Aranha and Conrado Porto Lopes Gouv\u00eaa. RELIC is an Efficient LIbrary for Cryptography. https:\/\/github.com\/relic-toolkit\/relic [commit hrefhttps:\/\/github.com\/relic-toolkit\/relic\/tree\/e656004f67c3090465f641b19466442664f54d74e56004] (June 2019)."},{"key":"e_1_3_2_1_3_1","series-title":"LNCS","first-page":"236","volume-title":"Proceedings of EUROCRYPT,1998","author":"Bellare Mihir","year":"1998","unstructured":"Mihir Bellare , Juan A.@ Garay , and Tal Rabin . hrefhttp:\/\/dx.doi.org\/10.1007\/BFb0054130Fast batch verification for modular exponentiation and digital signatures . In Proceedings of EUROCRYPT,1998 , volume 1403 of LNCS , pages 236 -- 250 , Espoo , Finland ( June 1998 ). 10.1007\/BFb0054130Fast Mihir Bellare, Juan A.@ Garay, and Tal Rabin. hrefhttp:\/\/dx.doi.org\/10.1007\/BFb0054130Fast batch verification for modular exponentiation and digital signatures. In Proceedings of EUROCRYPT,1998, volume 1403 of LNCS, pages 236--250, Espoo, Finland (June 1998)."},{"key":"e_1_3_2_1_4_1","series-title":"LNCS","first-page":"31","volume-title":"Proceedings of TCC,2016-B (Part II)","author":"Ben-Sasson Eli","year":"2016","unstructured":"Eli Ben-Sasson , Alessandro Chiesa , and Nicholas Spooner . hrefhttps:\/\/doi.org\/10.1007\/978-3-662-53644-5_2Interactive oracle proofs . In Proceedings of TCC,2016-B (Part II) , volume 9986 of LNCS , pages 31 -- 60 , Beijing, China (October--November 2016 ). 10.1007\/978-3-662-53644-5_2Interactive Eli Ben-Sasson, Alessandro Chiesa, and Nicholas Spooner. hrefhttps:\/\/doi.org\/10.1007\/978-3-662-53644-5_2Interactive oracle proofs. In Proceedings of TCC,2016-B (Part II), volume 9986 of LNCS, pages 31--60, Beijing, China (October--November 2016)."},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2090236.2090263"},{"key":"e_1_3_2_1_6_1","volume-title":"https:\/\/github.com\/WillBlack403\/ZKP-onehot (August","author":"Black William","year":"2019","unstructured":"William Black and Ryan Henry . ZKP-onehot. https:\/\/github.com\/WillBlack403\/ZKP-onehot (August 2019 ). William Black and Ryan Henry. ZKP-onehot. https:\/\/github.com\/WillBlack403\/ZKP-onehot (August 2019)."},{"key":"e_1_3_2_1_7_1","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/978-3-540-74143-5_4","volume-title":"Proceedings of CRYPTO,2007","author":"Boneh Dan","year":"2007","unstructured":"Dan Boneh , Eyal Kushilevitz , Rafail Ostrovsky , and William E . @ Skeith III. hrefhttp:\/\/dx.doi.org\/10.1007\/978--3--540--74143--5_4Public key encryption that allows PIR queries . In Proceedings of CRYPTO,2007 , volume 4622 of LNCS , pages 50 -- 67 , Santa Barbara, CA , USA (August 2007 ). 10.1007\/978--3--540--74143--5_4Public Dan Boneh, Eyal Kushilevitz, Rafail Ostrovsky, and William E.@ Skeith III. hrefhttp:\/\/dx.doi.org\/10.1007\/978--3--540--74143--5_4Public key encryption that allows PIR queries. In Proceedings of CRYPTO,2007, volume 4622 of LNCS, pages 50--67, Santa Barbara, CA, USA (August 2007)."},{"key":"e_1_3_2_1_8_1","series-title":"LNCS","first-page":"243","volume-title":"Proceedings of ESORICS,2015, (Part I)","author":"Bootle Jonathan","year":"2015","unstructured":"Jonathan Bootle , Andrea Cerulli , Pyrros Chaidos , Essam Ghadafi , Jens Groth , and Christophe Petit . hrefhttps:\/\/doi.org\/10.1007\/978-3-319-24174-6_13Short accountable ring signatures based on DDH . In Proceedings of ESORICS,2015, (Part I) , volume 9326 of LNCS , pages 243 -- 265 , Vienna , Austria ( September 2015 ). 10.1007\/978-3-319-24174-6_13Short Jonathan Bootle, Andrea Cerulli, Pyrros Chaidos, Essam Ghadafi, Jens Groth, and Christophe Petit. hrefhttps:\/\/doi.org\/10.1007\/978-3-319-24174-6_13Short accountable ring signatures based on DDH . In Proceedings of ESORICS,2015, (Part I), volume 9326 of LNCS, pages 243--265, Vienna, Austria (September 2015)."},{"key":"e_1_3_2_1_9_1","series-title":"LNCS","first-page":"400","volume-title":"Proceedings of ACISP","author":"Brands Stefan","year":"2007","unstructured":"Stefan Brands , Liesje Demuynck , and Bart De Decker . hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-540-73458-1_29A practical system for globally revoking the unlinkable pseudonyms of unknown users . In Proceedings of ACISP , 2007 , volume 4586 of LNCS , pages 400 -- 415 , Townsville , Australia (July 2007). 10.1007\/978-3-540-73458-1_29A Stefan Brands, Liesje Demuynck, and Bart De Decker. hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-540-73458-1_29A practical system for globally revoking the unlinkable pseudonyms of unknown users. In Proceedings of ACISP, 2007, volume 4586 of LNCS, pages 400--415, Townsville, Australia (July 2007)."},{"key":"e_1_3_2_1_10_1","series-title":"LNCS","first-page":"410","volume-title":"Proceedings of CRYPTO,1997","author":"Camenisch Jan","year":"1997","unstructured":"Jan Camenisch and Markus Stadler . hrefhttp:\/\/dx.doi.org\/10.1007\/BFb0052252 Efficient group signature schemes for large groups (Extended abstract) . In Proceedings of CRYPTO,1997 , volume 1294 of LNCS , pages 410 -- 424 , Santa Barbara, CA , USA (August 1997 ). 10.1007\/BFb0052252 Jan Camenisch and Markus Stadler. hrefhttp:\/\/dx.doi.org\/10.1007\/BFb0052252 Efficient group signature schemes for large groups (Extended abstract). In Proceedings of CRYPTO,1997, volume 1294 of LNCS, pages 410--424, Santa Barbara, CA, USA (August 1997)."},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/SP.2015.27"},{"key":"e_1_3_2_1_12_1","series-title":"LNCS","first-page":"174","volume-title":"Proceedings of CRYPTO,1994","author":"Cramer Ronald","year":"1994","unstructured":"Ronald Cramer , Ivan Damg\u00e5rd , and Berry Schoenmakers . hrefhttp:\/\/dx.doi.org\/10.1007\/3-540-48658-5_19Proofs of partial knowledge and simplified design of witness hiding protocols . In Proceedings of CRYPTO,1994 , volume 839 of LNCS , pages 174 -- 187 , Santa Barbara, CA , USA (August 1994 ). 10.1007\/3-540-48658-5_19Proofs Ronald Cramer, Ivan Damg\u00e5rd, and Berry Schoenmakers. hrefhttp:\/\/dx.doi.org\/10.1007\/3-540-48658-5_19Proofs of partial knowledge and simplified design of witness hiding protocols. In Proceedings of CRYPTO,1994, volume 839 of LNCS, pages 174--187, Santa Barbara, CA, USA (August 1994)."},{"key":"e_1_3_2_1_13_1","series-title":"LNCS","first-page":"530","volume-title":"Proceedings of PKC,2018, (Part II)","author":"Damg\u00e5rd Ivan","year":"2018","unstructured":"Ivan Damg\u00e5rd , Ji Luo , Sabine Oechsner , Peter Scholl , and Mark Simkin . hrefhttps:\/\/doi.org\/10.1007\/978-3-319-76581-5_18Compact zero-knowledge proofs of small hamming weight . In Proceedings of PKC,2018, (Part II) , volume 10770 of LNCS , pages 530 -- 560 , Rio de Janeiro , Brazil ( March 2018 ). 10.1007\/978-3-319-76581-5_18Compact Ivan Damg\u00e5rd, Ji Luo, Sabine Oechsner, Peter Scholl, and Mark Simkin. hrefhttps:\/\/doi.org\/10.1007\/978-3-319-76581-5_18Compact zero-knowledge proofs of small hamming weight. In Proceedings of PKC,2018, (Part II), volume 10770 of LNCS, pages 530--560, Rio de Janeiro, Brazil (March 2018)."},{"key":"e_1_3_2_1_14_1","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1007\/978-3-540-30539-2_20","volume-title":"Proceedins of ASIACRYPT,2004","author":"Gennaro Rosario","year":"2004","unstructured":"Rosario Gennaro , Darren Leigh , Ravi Sundaram , and William S . @ Yerazunis. hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-540-30539-2_20Batching Schnorr identification scheme with applications to privacy-preserving authorization and low-bandwidth communication devices . In Proceedins of ASIACRYPT,2004 , volume 3329 of LNCS , pages 276 -- 292 , Jeju Island , South Korea ( December 2004 ). 10.1007\/978-3-540-30539-2_20Batching Rosario Gennaro, Darren Leigh, Ravi Sundaram, and William S.@ Yerazunis. hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-540-30539-2_20Batching Schnorr identification scheme with applications to privacy-preserving authorization and low-bandwidth communication devices. In Proceedins of ASIACRYPT,2004, volume 3329 of LNCS, pages 276--292, Jeju Island, South Korea (December 2004)."},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2976749.2978407"},{"key":"e_1_3_2_1_16_1","series-title":"LNCS","first-page":"253","volume-title":"Proceedings of EUROCRYPT,2015 (Part II)","author":"Groth Jens","year":"2015","unstructured":"Jens Groth and Markulf Kohlweiss . hrefhttps:\/\/doi.org\/10.1007\/978-3-662-46803-6_9One-out-of-many proofs: Or how to leak a secret and spend a coin . In Proceedings of EUROCRYPT,2015 (Part II) , volume 9057 of LNCS , pages 253 -- 280 , Sofia , Bulgaria ( April 2015 ). 10.1007\/978-3-662-46803-6_9One-out-of-many Jens Groth and Markulf Kohlweiss. hrefhttps:\/\/doi.org\/10.1007\/978-3-662-46803-6_9One-out-of-many proofs: Or how to leak a secret and spend a coin. In Proceedings of EUROCRYPT,2015 (Part II), volume 9057 of LNCS, pages 253--280, Sofia, Bulgaria (April 2015)."},{"key":"e_1_3_2_1_17_1","series-title":"LNCS","first-page":"502","volume-title":"Proceedings of ACNS","author":"Henry Ryan","year":"2013","unstructured":"Ryan Henry and Ian Goldberg . hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-642-38980-1_32 Batch proofs of partial knowledge . In Proceedings of ACNS , 2013 , volume 7954 of LNCS , pages 502 -- 517 , Banff, AB , Canada (June 2013). 10.1007\/978-3-642-38980-1_32 Ryan Henry and Ian Goldberg. hrefhttp:\/\/dx.doi.org\/10.1007\/978-3-642-38980-1_32 Batch proofs of partial knowledge. In Proceedings of ACNS, 2013, volume 7954 of LNCS, pages 502--517, Banff, AB, Canada (June 2013)."},{"key":"e_1_3_2_1_18_1","volume-title":"Proceedings of NDSS,2013","author":"Henry Ryan","year":"2013","unstructured":"Ryan Henry , Yizhou Huang , and Ian Goldberg . hrefhttp:\/\/internetsociety.org\/doc\/one-block-size-fits-all-pir-and-spir-variable-length-records-multi-block-queries One (block) size fits all: PIR and SPIR with variable-length records via multi-block queries . In Proceedings of NDSS,2013 , San Diego, CA, USA ( February 2013 ). Ryan Henry, Yizhou Huang, and Ian Goldberg. hrefhttp:\/\/internetsociety.org\/doc\/one-block-size-fits-all-pir-and-spir-variable-length-records-multi-block-queriesOne (block) size fits all: PIR and SPIR with variable-length records via multi-block queries. In Proceedings of NDSS,2013, San Diego, CA, USA (February 2013)."},{"key":"e_1_3_2_1_19_1","first-page":"677","volume-title":"Proceedings of CCS, 2011","author":"Henry Ryan","year":"2011","unstructured":"Ryan Henry , Femi Olumofin , and Ian Goldberg . hrefhttp:\/\/doi.acm.org\/10.1145\/2046707.2046784Practical PIR for electronic commerce . In Proceedings of CCS, 2011 , pages 677 -- 690 , Chicago, IL, USA ( October 2011 ). Ryan Henry, Femi Olumofin, and Ian Goldberg. hrefhttp:\/\/doi.acm.org\/10.1145\/2046707.2046784Practical PIR for electronic commerce. In Proceedings of CCS, 2011, pages 677--690, Chicago, IL, USA (October 2011)."},{"key":"e_1_3_2_1_20_1","series-title":"LNCS","first-page":"129","volume-title":"Proceedings of CRYPTO,1991","author":"Pedersen Torben","year":"1991","unstructured":"Torben P.@ Pedersen . hrefhttp:\/\/dx.doi.org\/10.1007\/3-540-46766-1_9Non-interactive and information-theoretic secure verifiable secret sharing . In Proceedings of CRYPTO,1991 , volume 576 of LNCS , pages 129 -- 140 , Santa Barbara, CA , USA (August 1991 ). 10.1007\/3-540-46766-1_9Non-interactive Torben P.@ Pedersen. hrefhttp:\/\/dx.doi.org\/10.1007\/3-540-46766-1_9Non-interactive and information-theoretic secure verifiable secret sharing. In Proceedings of CRYPTO,1991, volume 576 of LNCS, pages 129--140, Santa Barbara, CA, USA (August 1991)."},{"key":"e_1_3_2_1_21_1","volume-title":"hrefhttp:\/\/doi.acm.org\/10.1145\/1237500.1237502Batch zero-knowledge proof and verification and its applications. ACM Transactions on Information and System Security (TISSEC), 10(2):Article No.,6 (May","author":"Peng Kun","year":"2007","unstructured":"Kun Peng , Colin Boyd , and Ed Dawson . hrefhttp:\/\/doi.acm.org\/10.1145\/1237500.1237502Batch zero-knowledge proof and verification and its applications. ACM Transactions on Information and System Security (TISSEC), 10(2):Article No.,6 (May 2007 ). Kun Peng, Colin Boyd, and Ed Dawson. hrefhttp:\/\/doi.acm.org\/10.1145\/1237500.1237502Batch zero-knowledge proof and verification and its applications. ACM Transactions on Information and System Security (TISSEC), 10(2):Article No.,6 (May 2007)."},{"key":"e_1_3_2_1_22_1","volume-title":"NTL: A Library for doing Number Theory [version 11.3.2]. https:\/\/www.shoup.net\/ntl\/ (November","author":"Shoup Victor","year":"2018","unstructured":"Victor Shoup . NTL: A Library for doing Number Theory [version 11.3.2]. https:\/\/www.shoup.net\/ntl\/ (November 2018 ). Victor Shoup. NTL: A Library for doing Number Theory [version 11.3.2]. https:\/\/www.shoup.net\/ntl\/ (November 2018)."}],"event":{"name":"CCS '19: 2019 ACM SIGSAC Conference on Computer and Communications Security","sponsor":["SIGSAC ACM Special Interest Group on Security, Audit, and Control"],"location":"London United Kingdom","acronym":"CCS '19"},"container-title":["Proceedings of the 18th ACM Workshop on Privacy in the Electronic Society"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338498.3358640","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3338498.3358640","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3338498.3358640","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:12:48Z","timestamp":1750201968000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338498.3358640"}},"subtitle":["Efficient Zero-Knowledge Proofs of \"One-Hotness\" via Polynomials with One Zero"],"short-title":[],"issued":{"date-parts":[[2019,11,11]]},"references-count":21,"alternative-id":["10.1145\/3338498.3358640","10.1145\/3338498"],"URL":"https:\/\/doi.org\/10.1145\/3338498.3358640","relation":{},"subject":[],"published":{"date-parts":[[2019,11,11]]},"assertion":[{"value":"2019-11-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}