Secure Fixed-point Division for Homomorphically Encrypted Operands

Chibuike Ugwuoke, Zekeriya Erkin, Inald Lagendijk

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

3 Citations (Scopus)


Due to privacy threats associated with computation of outsourced data, processing data on the encrypted domain has become a viable alternative. Secure computation of encrypted data is relevant for analysing datasets in areas (such as genome processing, private data aggregation, cloud computations) that require basic arithmetic operations. Performing division operation over-all encrypted inputs has not been achieved using homomorphic schemes in non-interactive modes. In interactive protocols, the cost of obtaining an encrypted quotient (from encrypted values) is computationally expensive. To the best of our knowledge, existing homomorphic solutions on encrypted division are often relaxed to consider public or private divisor. We acknowledge that there are other techniques such as secret sharing and garbled circuits adopted to compute secure division, but we are interested in homomorphic solutions. We propose an efficient and interactive two-party protocol that computes the fixed-point quotient of two encrypted inputs, using an efficient and secure comparison protocol as a sub-protocol. Our proposal provides a computational advantage, with a linear complexity in the digit precision of the quotient. We provide proof of security in the universally composable framework and complexity analyses. We present experimental results for two cryptosystem implementations in order to compare performance. An efficient prototype of our protocol is implemented using additive homomorphic scheme (Paillier), whereas a non-efficient fully-homomorphic scheme (BGV) version is equally presented as a proof of concept and analyses of our proposal.
Original languageEnglish
Title of host publicationARES 2018
Subtitle of host publicationProceedings of the 13th International Conference on Availability, Reliability and Security
Place of PublicationNew York
PublisherAssociation for Computer Machinery
Number of pages10
ISBN (Print)978-1-4503-6448-5
Publication statusPublished - 2018
EventARES 2018: 13th International Conference on Availability, Reliability and Security - Hamburg, Germany
Duration: 27 Aug 201830 Aug 2018
Conference number: 13


ConferenceARES 2018
Internet address


  • Encrypted Fixed-point Division
  • Privacy-Preserving
  • Homomorphic Encryption
  • Secure Comparison
  • Multi-party Computation


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