### Towards Non-Black-Box Separations of Public Key Encryption and One Way Function

Dana Dachman-Soled

##### Abstract

Separating public key encryption from one way functions is one of the fundamental goals of complexity-based cryptography. Beginning with the seminal work of Impagliazzo and Rudich (STOC, 1989), a sequence of works have ruled out certain classes of reductions from public key encryption (PKE)---or even key agreement---to one way function. Unfortunately, known results---so called black-box separations---do not apply to settings where the construction and/or reduction are allowed to directly access the code, or circuit, of the one way function. In this work, we present a meaningful, non-black-box separation between public key encryption (PKE) and one way function. Specifically, we introduce the notion of $\textsf{BBN}^-$ reductions (similar to the $\textsf{BBN}\text{p}$ reductions of Baecher et al. (ASIACRYPT, 2013)), in which the construction $E$ accesses the underlying primitive in a black-box way, but wherein the universal reduction $R$ receives the efficient code/circuit of the underlying primitive as input and is allowed oracle access to the adversary $\textsf{Adv}$. We additionally require that the number of oracle queries made to $\textsf{Adv}$, and the success probability of $R$ are independent of the run-time/circuit size of the underlying primitive. We prove that there is no non-adaptive, $\textsf{BBN}^-$ reduction from PKE to one way function, under the assumption that certain types of strong one way functions exist. Specifically, we assume that there exists a regular one way function $f$ such that there is no Arthur-Merlin protocol proving that $z \not\in \textsf{Range}(f)$'', where soundness holds with high probability over no instances,'' $y \sim f(U_n)$, and Arthur may receive polynomial-sized, non-uniform advice. This assumption is related to the average-case analogue of the widely believed assumption $\textbf{coNP} \not\subseteq \textbf{NP}/\textbf{poly}$.

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black-box separationpublic key encryptionone-way function
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https://ia.cr/2016/812

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BibTeX

@misc{cryptoeprint:2016/812,
author = {Dana Dachman-Soled},
title = {Towards Non-Black-Box Separations of Public Key Encryption and One Way Function},
howpublished = {Cryptology ePrint Archive, Paper 2016/812},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/812}},
url = {https://eprint.iacr.org/2016/812}
}

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