### Impossibility of Strong KDM Security with Auxiliary Input

Cody Freitag, Ilan Komargodski, and Rafael Pass

##### Abstract

In this note, we show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function $f$, it is computationally hard to distinguish between an encryption of 0s and an encryption of f(pk, z), where pk is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than pk under the additional assumption that (non-leveled) fully homomorphic encryption exists.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
KDM SecurityImpossibility
Contact author(s)
cfreitag @ cs cornell edu
komargodski @ cornell edu
rafael @ cs cornell edu
History
Short URL
https://ia.cr/2019/293

CC BY

BibTeX

@misc{cryptoeprint:2019/293,
author = {Cody Freitag and Ilan Komargodski and Rafael Pass},
title = {Impossibility of Strong KDM Security with Auxiliary Input},
howpublished = {Cryptology ePrint Archive, Paper 2019/293},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/293}},
url = {https://eprint.iacr.org/2019/293}
}

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