Exploration of Polynomial Multiplication Algorithms for Homomorphic Encryption Schemes

International audienceHomomorphic 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. Inthis 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