We show that homomorphic evaluation of any non-trivial functionality of sufficiently many inputs with respect to any CPA secure homomorphic encryption scheme cannot be implemented by circuits of polynomial size and constant depth, i.e., in the class AC0. In contrast, we observe that there exist ordinary public-key encryption schemes of quasipolynomial security in AC0 assuming noisy parities are exponentially hard to learn. We view this as evidence that homomorphic evaluation is inherently more complex than basic operations in encryption schemes.
CITATION STYLE
Bogdanov, A., & Lee, C. H. (2016). Homomorphic evaluation requires depth. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9562, pp. 365–371). Springer Verlag. https://doi.org/10.1007/978-3-662-49096-9_15
Mendeley helps you to discover research relevant for your work.