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 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.

Grantor dc:publisher

Universitat Oberta de Catalunya (UOC)

Year dc:date.issued

2023

Author dc:creator

• Bernabé Rodríguez, Julen

• fully homomorphic encryption
• BGV
• non-linear operations
• verifiable decryption

Statement dc:rights

• CC BY-NC-ND

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-nd/3.0/es/

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10609/148192

OAI identifier oai:identifier

oai:openaccess.uoc.edu:10609/148192