{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T11:42:23Z","timestamp":1770464543164,"version":"3.49.0"},"reference-count":0,"publisher":"Universitatsbibliothek der Ruhr-Universitat Bochum","license":[{"start":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T00:00:00Z","timestamp":1661904000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["TCHES"],"abstract":"<jats:p>First posed as a challenge in 1978 by Rivest et al., fully homomorphic encryption\u2014the ability to evaluate any function over encrypted data\u2014was only solved in 2009 in a breakthrough result by Gentry (Commun. ACM, 2010). After a decade of intense research, practical solutions have emerged and are being pushed for standardization.This paper explains the inner-workings of TFHE, a torus-based fully homomorphic encryption scheme. More exactly, it describes its implementation on a discretized version of the torus. It also explains in detail the technique of the programmable bootstrapping. Numerous examples are provided to illustrate the various concepts and definitions.<\/jats:p>","DOI":"10.46586\/tches.v2022.i4.661-692","type":"journal-article","created":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T05:54:02Z","timestamp":1662011642000},"page":"661-692","source":"Crossref","is-referenced-by-count":20,"title":["SoK: Fully Homomorphic Encryption over the [Discretized] Torus"],"prefix":"10.46586","author":[{"given":"Marc","family":"Joye","sequence":"first","affiliation":[]}],"member":"25480","published-online":{"date-parts":[[2022,8,31]]},"container-title":["IACR Transactions on Cryptographic Hardware and Embedded Systems"],"original-title":[],"link":[{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/download\/9836\/9339","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/download\/9836\/9339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T05:54:05Z","timestamp":1662011645000},"score":1,"resource":{"primary":{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/9836"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46586\/tches.v2022.i4.661-692","relation":{},"ISSN":["2569-2925"],"issn-type":[{"value":"2569-2925","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,31]]}}}