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Exploration of Polynomial Multiplication Algorithms for Homomorphic Encryption Schemes

Vincent Migliore 1 Maria Méndez Real 1 Vianney Lapotre 1 Arnaud Tisserand 2 Caroline Fontaine 3, 4 Guy Gogniat 1
1 Lab-STICC_UBS_CACS_MOCS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
2 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
4 Lab-STICC_TB_CID_SFIIS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : Homomorphic encryption schemes allow performing computations in the ciphertext domain, without the need of the secret key. In most promising schemes based on the ringlearning with errors (R-LWE) problem, polynomial multiplication operation is considered as an important bottleneck. In this study, a comparison between the Karatsuba and the fast Fourier transform (FFT) multiplication algorithms in the context of homomorphic encryption is proposed in terms of complexity, flexibility and possible optimizations. A complete hardware architecture to speeding up polynomial multiplication is provided and impacts of such an architecture on the Karatsuba and the FFT algorithms is thoroughly studied. The study demonstrates that in a realistic architecture, Karatsuba can be a better alternative to the FFT one.
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https://hal.archives-ouvertes.fr/hal-01273192
Contributor : Vianney Lapôtre <>
Submitted on : Thursday, February 25, 2021 - 7:23:37 PM
Last modification on : Monday, May 17, 2021 - 11:24:01 AM

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Vincent Migliore, Maria Méndez Real, Vianney Lapotre, Arnaud Tisserand, Caroline Fontaine, et al.. Exploration of Polynomial Multiplication Algorithms for Homomorphic Encryption Schemes. International Conference on Reconfigurable Computing and FPGAs (ReConFig), Dec 2015, Cancun, Mexico. ⟨10.1109/ReConFig.2015.7393307⟩. ⟨hal-01273192⟩

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