{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T04:27:30Z","timestamp":1778128050909,"version":"3.51.4"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan\u2013Vercauteren scheme by replacing the integral plaintext modulus\n                    <jats:italic>t<\/jats:italic>\n                    by a linear polynomial\n                    <jats:italic>X<\/jats:italic>\n                    \u2212\n                    <jats:italic>b<\/jats:italic>\n                    . Our generalization studies plaintext moduli of the form\n                    <jats:italic>\n                      X\n                      <jats:sup>m<\/jats:sup>\n                    <\/jats:italic>\n                    +\n                    <jats:italic>b<\/jats:italic>\n                    . Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2015-0051","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T13:48:20Z","timestamp":1592228900000},"page":"55-65","source":"Crossref","is-referenced-by-count":11,"title":["Efficiently Processing Complex-Valued Data in Homomorphic Encryption"],"prefix":"10.1515","volume":"14","author":[{"given":"Carl","family":"Bootland","sequence":"first","affiliation":[{"name":"KU Leuven imec-COSIC , Kasteelpark Arenberg 10\/2452, 3001 , Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wouter","family":"Castryck","sequence":"additional","affiliation":[{"name":"KU Leuven Department of Mathematics , Celestijnenlaan 200B, 3001 , Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilia","family":"Iliashenko","sequence":"additional","affiliation":[{"name":"KU Leuven imec-COSIC , Kasteelpark Arenberg 10\/2452, 3001 , Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frederik","family":"Vercauteren","sequence":"additional","affiliation":[{"name":"KU Leuven imec-COSIC , Kasteelpark Arenberg 10\/2452, 3001 , Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,6,14]]},"reference":[{"key":"2025120600161801991_j_jmc-2015-0051_ref_001_w2aab3b7c41b1b6b1ab2b1b1Aa","unstructured":"Anthony Barnett, Jay Santokhi, Michael Simpson, Nigel P. 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