Homomorphic Evaluation of Lattice-Based Symmetric Encryption Schemes

Optimizing performance of Fully Homomorphic Encryption (FHE) is nowadays an active trend of research in cryptography. One way of improvement is to use a hybrid construction with a classical symmetric encryption scheme to transfer encrypted data to the Cloud. This allows to reduce the bandwidth since the expansion factor of symmetric schemes (the ratio between the ciphertext and the plaintext length) is close to one, whereas for FHE schemes it is in the order of 1,000 to 1,000,000. However, such a construction requires the decryption circuit of the symmetric scheme to be easy to evaluate homomorphically. Several works have studied the cost of homomorphically evaluating classical block ciphers, and some recent works have suggested new homomorphic oriented constructions of block ciphers or stream ciphers. Since the multiplication gate of FHE schemes significantly increases the noise of the ciphertext, we cannot afford too many multiplication stages in the decryption circuit. Consequently, FHE-friendly symmetric encryption schemes have a decryption circuit with small multiplication depth. We aim at minimizing the cost of the homomorphic evaluation of the decryption of symmetric encryption schemes. To do so, we focus on schemes based on learning problems: Learning With Errors (LWE), Learning Parity with Noise (LPN) and Learning With Rounding (LWR). We show that they have lower multiplicative depth than usual block ciphers, and hence allow more FHE operations before a heavy bootstrapping becomes necessary. Moreover, some of them come with a security proof. Finally, we implement our schemes in HElib. Experimental evidence shows that they achieve lower amortized and total running time than previous performance from the literature: our schemes are from 10 to 10,000 more efficient for the time per bit and the total running time is also reduced by a factor between 20 to 10,000. Of independent interest, the security of our LWR-based scheme is related to LWE and we provide an efficient security proof that allows to take smaller parameters

Évaluation du crédit d’impôt innovation / An Evaluation of the Innovation Tax Credit

The Innovation tax credit (crédit d’impôt innovation, CII) is an extension of the Research tax credit (crédit d’impôt recherche, CIR) intended to boost the incentive effect of the latter on SMEs to encourage them to engage in the creation of new products via the development of prototypes or pilot installations. Introduced in 2013, it represented € 120 million of tax credit in 2014 for some 5,300 recipients. This article seeks to measure the impact of the introduction of this scheme on its beneficiaries over the period from 2013 to 2016. Using a difference-in-differences method following propensity score matching, we find a greater increase in employment in the short term for companies benefiting from the scheme, along with a more marked increase in their turnover in the medium term. A greater increase in the number of new products produced by the beneficiaries is also observed. Finally, the introduction of the CII was accompanied by a reduction in the research expenditure reported under the CIR.Le crédit d’impôt innovation (CII) est une extension du crédit d’impôt recherche (CIR) destinée à renforcer l’effet incitatif du CIR pour les PME, afin qu’elles s’engagent dans la création de nouveaux produits via le développement de prototypes ou d’installations pilotes. Instauré en 2013, il représentait 120 M€ de créance d’impôt en 2014, pour environ 5 300 bénéficiaires. Cet article propose de mesurer l’impact de l’introduction de ce dispositif sur ses bénéficiaires, sur la période 2013‑2016. À l’aide d’une méthode de doubles différences après appariement sur score de propension, il est mis en évidence une hausse de l’emploi plus importante à court terme chez les entreprises bénéficiaires du dispositif, ainsi qu’une hausse plus marquée à moyen terme de leur chiffre d’affaires. Il est également observé une augmentation plus importante du nombre de nouveaux produits fabriqués par les bénéficiaires. Enfin, l’introduction du CII s’est accompagnée d’une baisse des dépenses de recherche déclarées dans le cadre du CIR.Bunel Simon, Hadjibeyli Benjamin. Évaluation du crédit d’impôt innovation / An Evaluation of the Innovation Tax Credit. In: Economie et Statistique / Economics and Statistics, n°526-527, 2021. pp. 113-135