Homomorphic evaluation requires depth

Paper 2015/1044

Homomorphic evaluation requires depth

Andrej Bogdanov and Chin Ho Lee

Abstract

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.

Note: The previous version made an unconditional claim about AC^0. We do not know that the claim is false. But this version does not make it.

Metadata

Available format(s): PDF
Publication info: A minor revision of an IACR publication in TCC 2016
Keywords: complexity of cryptography homomorphic encryption
Contact author(s): chlee @ ccs neu edu
History: 2016-04-13: revised; 2015-10-28: received; See all versions
Short URL: https://ia.cr/2015/1044
License: CC BY

BibTeX

@misc{cryptoeprint:2015/1044,
      author = {Andrej Bogdanov and Chin Ho Lee},
      title = {Homomorphic evaluation requires depth},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/1044},
      year = {2015},
      url = {https://eprint.iacr.org/2015/1044}
}