| Download | - View final version: Efficient methods for simultaneous homomorphic inversion (PDF, 1.4 MiB)
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| DOI | Resolve DOI: https://doi.org/10.62056/abe0iv7sf |
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| Author | Search for: Klamti, Jean1ORCID identifier: https://orcid.org/0000-0001-9231-1129; Search for: Hasan, M.ORCID identifier: https://orcid.org/0000-0003-4103-7945; Search for: Karabina, Koray1ORCID identifier: https://orcid.org/0000-0001-9538-8877 |
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| Affiliation | - National Research Council of Canada. Digital Technologies
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| Format | Text, Article |
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| Subject | fully homomorphic encryption; homomorphic inversion; Goldschmidt inversion; Montgomery’s trick |
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| Abstract | Efficient implementation of some privacy-preserving algorithms and applications rely on efficient implementation of homomorphic inversion. For example, a recently proposed homomorphic image filtering algorithm and the privacy-preserving body mass index (BMI) calculations repetitively use homomorphic inversion. In this paper, inspired by Montgomery's trick to perform simultaneous plaintext inversion, we tackle the simultaneous homomorphic inversion problem to compute s inverses simultaneously over ciphertexts. The advantage of Montgomery's trick for plaintext arithmetic is well-known. We first observe that the advantage can quickly vanish when homomorphic encryption is employed because of the increased depth of the circuits. Therefore, we propose three algorithms (Montgomery's trick and two other variants) that reduce the number of homomorphic inversions from s to 1 and that offer different levels of trade-offs between the number of multiplications and the circuit depth. We provide a theoretical complexity analysis of our algorithms and implement them using the CKKS scheme in the OpenFHE library. Our experiments show that, for some cases, the run time of homomorphic s-inversion can be improved up to 35 percent while in some other cases, regular inversion seems to outperform Montgomery-based inversion algorithms. |
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| Publication date | 2025-04-08 |
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| Publisher | International Association for Cryptologic Research |
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| Licence | |
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| In | |
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| Language | English |
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| Peer reviewed | Yes |
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| Export citation | Export as RIS |
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| Report a correction | Report a correction (opens in a new tab) |
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| Record identifier | 7218f082-37b4-4ed7-a5fa-0fabbc7e480e |
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| Record created | 2025-07-10 |
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| Record modified | 2025-07-11 |
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