Cryptology ePrint Archive: Report 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.

Category / Keywords: complexity of cryptography, homomorphic encryption

Original Publication (with minor differences): IACR-TCC-2016

Date: received 27 Oct 2015, last revised 13 Apr 2016

Contact author: chlee at ccs neu edu

Available format(s): PDF | BibTeX Citation

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.

Version: 20160413:173428 (All versions of this report)

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