Efficient Circuits for Permuting and Mapping Packed Values Across Leveled Homomorphic Ciphertexts

Jelle Vos*, Daniël Vos, Zekeriya Erkin

*Corresponding author for this work

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

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Cloud services are an essential part of our digital infrastructure as organizations outsource large amounts of data storage and computations. While organizations typically keep sensitive data in encrypted form at rest, they decrypt it when performing computations, leaving the cloud provider free to observe the data. Unfortunately, access to raw data creates privacy risks. To alleviate these risks, researchers have developed secure outsourced data processing techniques. Such techniques enable cloud services that keep sensitive data encrypted, even during computations. For this purpose, fully homomorphic encryption is particularly promising, but operations on ciphertexts are computationally demanding. Therefore, modern fully homomorphic cryptosystems use packing techniques to store and process multiple values within a single ciphertext. However, a problem arises when packed data in one ciphertext does not align with another. For this reason, we propose a method to construct circuits that perform arbitrary permutations and mappings of such packed values. Unlike existing work, our method supports moving values across multiple ciphertexts, considering that the values in real-world scenarios cannot all be packed within a single ciphertext. We compare our open-source implementation against the state-of-the-art method implemented in HElib, which we adjusted to work with multiple ciphertexts. When data is spread among five or more ciphertexts, our method outperforms the existing method by more than an order of magnitude. Even when we only consider a permutation within a single ciphertext, our method still outperforms the state-of-the-art works implemented by HElib for circuits of similar depth.

Original languageEnglish
Title of host publicationComputer Security – ESORICS 2022 - 27th European Symposium on Research in Computer Security, Proceedings
EditorsVijayalakshmi Atluri, Roberto Di Pietro, Christian D. Jensen, Weizhi Meng
Number of pages16
ISBN (Print)9783031171390
Publication statusPublished - 2022
Event27th European Symposium on Research in Computer Security, ESORICS 2022 - Virtual, Online
Duration: 26 Sep 202230 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13554 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th European Symposium on Research in Computer Security, ESORICS 2022
CityVirtual, Online

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Applied cryptography
  • Data packing
  • Fully homomorphic encryption
  • Secure outsourced data processing

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