Structure vs. Hardness Through the Obfuscation Lens
Name
2016-574.pdf
Description
Accepted version
Size
726.19 KB
Format
Adobe PDF
Checksum (MD5)
96cbfc019b48b4a323f4768350f02a08
Author(s)
Bitansky, Nir
Degwekar, Akshay
Vaikuntanathan, Vinod
Date Issued
2017
Publisher
Springer Nature
Citation
Bitansky, Nir, Degwekar, Akshay and Vaikuntanathan, Vinod. 2017. "Structure vs. Hardness Through the Obfuscation Lens."
Version
Author's final manuscript
Abstract
© International Association for Cryptologic Research 2017. 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 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 fully 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 fully 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. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/978-3-319-63688-7_23
