Structure Versus Hardness Through the Obfuscation Lens
Name
17m1136559.pdf
Description
Published version
Size
720.13 KB
Format
Adobe PDF
Checksum (MD5)
524ce26fe2839f6ff540dfdf5ceb50ed
Author(s)
Bitansky, Nir
Degwekar, Akshay
Vaikuntanathan, Vinod
Date Issued
2021
Journal
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Bitansky, Nir, Degwekar, Akshay and Vaikuntanathan, Vinod. 2021. "Structure Versus Hardness Through the Obfuscation Lens." SIAM Journal on Computing, 50 (1).
Version
Final published version
Abstract
Much of modern cryptography, starting from public-key encryption and going beyond, is based on the hardness of structured (mostly algebraic) problems like factoring, discrete log, or finding short lattice vectors. While structure is perhaps what enables advanced applications, it also puts the hardness of these problems in question. In particular, this structure often puts them in low (and so-called structured) complexity classes such as NP ∩ coNP or statistical zero-knowledge (SZK). Is this structure really necessary? For some cryptographic primitives, such as one-way permutations and homomorphic encryption, we know that the answer is yes-they imply hard problems in NP∩coNP and SZK, respectively. In contrast, one-way functions do not imply such hard problems, at least not by black-box reductions. Yet, for many basic primitives such as public-key encryption, oblivious transfer, and functional encryption, we do not have any answer. We show that the above primitives, and many others, do not imply hard problems in NP∩coNP or SZK via black-box reductions. In fact, we first show that even the very powerful notion of indistinguishability obfuscation (IO) does not imply such hard problems, and then deduce the same for a large class of primitives that can be constructed from IO.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/17M1136559
