Non-linear operations and verifiable decryption in BGV

Fully Homomorphic Encryption (FHE) schemes are cryptosystems that allow to compute over encrypted messages. Due to the inherent difficulty of training models using private data, this special property is closely watched. One of the most celebrated FHE schemes is BGV, which allows to compute arithmeti...

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Detalles Bibliográficos
Autor: Bernabé Rodríguez, Julen
Tipo de recurso: tesis de maestría
Fecha de publicación:2023
País:España
Institución:Universitat Oberta de Catalunya (UOC)
Repositorio:O2, repositorio institucional de la UOC
OAI Identifier:oai:openaccess.uoc.edu:10609/148192
Acceso en línea:http://hdl.handle.net/10609/148192
Access Level:acceso abierto
Palabra clave:fully homomorphic encryption
BGV
non-linear operations
verifiable decryption
Data encryption (Computer science) -- TFM
Xifratge (Informàtica) -- TFM
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spelling Non-linear operations and verifiable decryption in BGVBernabé Rodríguez, Julenfully homomorphic encryptionBGVnon-linear operationsverifiable decryptionData encryption (Computer science) -- TFMXifratge (Informàtica) -- TFMFully Homomorphic Encryption (FHE) schemes are cryptosystems that allow to compute over encrypted messages. Due to the inherent difficulty of training models using private data, this special property is closely watched. One of the most celebrated FHE schemes is BGV, which allows to compute arithmetic operations over encrypted integers. Non-linear operations, though, need more work to be computed. In this work, several techniques to perform non-linear operations such as comparisons on BGV are introduced. An implementation of these techniques in the OpenFHE open-source library is given too. Finally, an introduction to the verifiable decryption problem is introduced. Due to the very nature of FHE, the scientist only gets the encrypted results, and therefore has to ask the data owner to decrypt it. Verifiable decryption protocols are born precisely to ensure that this data decryption is done correctly. In this work, the verifiable decryption protocols for the BGV scheme in [4] and [50] are analyzed and the latter is implemented for OpenFHE.Universitat Oberta de Catalunya (UOC)Kowalska, KatarzynaIsern-Deya, Andreu Pere202320232023info:eu-repo/semantics/masterThesisapplication/pdfapplication/pdfhttp://hdl.handle.net/10609/148192reponame:O2, repositorio institucional de la UOCinstname:Universitat Oberta de Catalunya (UOC)InglésCC BY-NC-NDhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:openaccess.uoc.edu:10609/1481922026-05-28T12:42:01Z
dc.title.none.fl_str_mv Non-linear operations and verifiable decryption in BGV
title Non-linear operations and verifiable decryption in BGV
spellingShingle Non-linear operations and verifiable decryption in BGV
Bernabé Rodríguez, Julen
fully homomorphic encryption
BGV
non-linear operations
verifiable decryption
Data encryption (Computer science) -- TFM
Xifratge (Informàtica) -- TFM
title_short Non-linear operations and verifiable decryption in BGV
title_full Non-linear operations and verifiable decryption in BGV
title_fullStr Non-linear operations and verifiable decryption in BGV
title_full_unstemmed Non-linear operations and verifiable decryption in BGV
title_sort Non-linear operations and verifiable decryption in BGV
dc.creator.none.fl_str_mv Bernabé Rodríguez, Julen
author Bernabé Rodríguez, Julen
author_facet Bernabé Rodríguez, Julen
author_role author
dc.contributor.none.fl_str_mv Kowalska, Katarzyna
Isern-Deya, Andreu Pere
dc.subject.none.fl_str_mv fully homomorphic encryption
BGV
non-linear operations
verifiable decryption
Data encryption (Computer science) -- TFM
Xifratge (Informàtica) -- TFM
topic fully homomorphic encryption
BGV
non-linear operations
verifiable decryption
Data encryption (Computer science) -- TFM
Xifratge (Informàtica) -- TFM
description Fully Homomorphic Encryption (FHE) schemes are cryptosystems that allow to compute over encrypted messages. Due to the inherent difficulty of training models using private data, this special property is closely watched. One of the most celebrated FHE schemes is BGV, which allows to compute arithmetic operations over encrypted integers. Non-linear operations, though, need more work to be computed. In this work, several techniques to perform non-linear operations such as comparisons on BGV are introduced. An implementation of these techniques in the OpenFHE open-source library is given too. Finally, an introduction to the verifiable decryption problem is introduced. Due to the very nature of FHE, the scientist only gets the encrypted results, and therefore has to ask the data owner to decrypt it. Verifiable decryption protocols are born precisely to ensure that this data decryption is done correctly. In this work, the verifiable decryption protocols for the BGV scheme in [4] and [50] are analyzed and the latter is implemented for OpenFHE.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv http://hdl.handle.net/10609/148192
url http://hdl.handle.net/10609/148192
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv CC BY-NC-ND
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv CC BY-NC-ND
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universitat Oberta de Catalunya (UOC)
publisher.none.fl_str_mv Universitat Oberta de Catalunya (UOC)
dc.source.none.fl_str_mv reponame:O2, repositorio institucional de la UOC
instname:Universitat Oberta de Catalunya (UOC)
instname_str Universitat Oberta de Catalunya (UOC)
reponame_str O2, repositorio institucional de la UOC
collection O2, repositorio institucional de la UOC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301629

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