{"id":{"repo_id":"catalunya","oai_identifier":"oai:openaccess.uoc.edu:10609/148192"},"canonical_url":"https://search.dev.ndltd.org/etd/catalunya/oai:openaccess.uoc.edu:10609/148192","repository":{"repo_id":"catalunya","name":"Universitat Oberta de Catalunya","base_url":"https://openaccess.uoc.edu/server/oai/request"},"display":{"title":"Non-linear operations and verifiable decryption in BGV","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Bernabé Rodríguez, Julen"],"institution":"Universitat Oberta de Catalunya (UOC)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-06-26","date_published":"2023-06-26","updated_at":"2026-07-27T19:06:46Z","subjects":["fully homomorphic encryption","BGV","non-linear operations","verifiable decryption"],"languages":["eng"],"rights":["CC BY-NC-ND"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10609/148192","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Kowalska, Katarzyna"]},{"key":"dc:creator","label":"Author","values":["Bernabé Rodríguez, Julen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-07-11T10:25:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-07-11T10:25:14Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-06-26"]},{"key":"dc:publisher","label":"Institution","values":["Universitat Oberta de Catalunya (UOC)"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/masterThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["fully homomorphic encryption","BGV","non-linear operations","verifiable decryption"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["CC BY-NC-ND"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10609/148192"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Non-linear operations and verifiable decryption in BGV"]}]}],"canonical_facts":{"dc:contributor.other":["Kowalska, Katarzyna"],"dc:creator":["Bernabé Rodríguez, Julen"],"dc:date.accessioned":["2023-07-11T10:25:14Z"],"dc:date.available":["2023-07-11T10:25:14Z"],"dc:date.issued":["2023-06-26"],"dc:description.abstract":["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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10609/148192"],"dc:language.iso":["eng"],"dc:publisher":["Universitat Oberta de Catalunya (UOC)"],"dc:rights":["CC BY-NC-ND"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"],"dc:subject":["fully homomorphic encryption","BGV","non-linear operations","verifiable decryption"],"dc:title":["Non-linear operations and verifiable decryption in BGV"],"dc:type":["info:eu-repo/semantics/masterThesis"]},"updated_at":"2026-07-27T19:06:46Z"}