On Constructing One-Way Permutations from Indistinguishability Obfuscation

On Constructing One-Way Permutations from Indistinguishability Obfuscation We prove that there is no black-box construction of a one-way permutation family from a one-way function and an indistinguishability obfuscator for the class of all oracle-aided circuits, where the construction is “domain invariant” (i.e., where each permutation may have its own domain, but these domains are independent of the underlying building blocks). Following the framework of Asharov and Segev (FOCS ’15), by considering indistinguishability obfuscation for oracle-aided circuits we capture the common techniques that have been used so far in constructions based on indistinguishability obfuscation. These include, in particular, non-black-box techniques such as the punctured programming approach of Sahai and Waters (STOC ’14) and its variants, as well as sub-exponential security assumptions. For example, we fully capture the construction of a trapdoor permutation family from a one-way function and an indistinguishability obfuscator due to Bitansky, Paneth, and Wichs (TCC ’16). Their construction is not domain invariant, and our result shows that this, somewhat undesirable property, is unavoidable using the common techniques. In fact, we observe that constructions which are not domain invariant circumvent all known negative results for constructing one-way permutations based on one-way functions, starting with Rudich’s seminal work (PhD thesis ’88). We revisit this classic and fundamental problem and resolve this somewhat surprising gap by ruling out all such black-box constructions—even those that are not domain invariant. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Cryptology Springer Journals

On Constructing One-Way Permutations from Indistinguishability Obfuscation

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Publisher
Springer US
Copyright
Copyright © 2017 by International Association for Cryptologic Research
Subject
Computer Science; Coding and Information Theory; Computational Mathematics and Numerical Analysis; Combinatorics; Probability Theory and Stochastic Processes; Communications Engineering, Networks
ISSN
0933-2790
eISSN
1432-1378
D.O.I.
10.1007/s00145-017-9268-6
Publisher site
See Article on Publisher Site

Abstract

We prove that there is no black-box construction of a one-way permutation family from a one-way function and an indistinguishability obfuscator for the class of all oracle-aided circuits, where the construction is “domain invariant” (i.e., where each permutation may have its own domain, but these domains are independent of the underlying building blocks). Following the framework of Asharov and Segev (FOCS ’15), by considering indistinguishability obfuscation for oracle-aided circuits we capture the common techniques that have been used so far in constructions based on indistinguishability obfuscation. These include, in particular, non-black-box techniques such as the punctured programming approach of Sahai and Waters (STOC ’14) and its variants, as well as sub-exponential security assumptions. For example, we fully capture the construction of a trapdoor permutation family from a one-way function and an indistinguishability obfuscator due to Bitansky, Paneth, and Wichs (TCC ’16). Their construction is not domain invariant, and our result shows that this, somewhat undesirable property, is unavoidable using the common techniques. In fact, we observe that constructions which are not domain invariant circumvent all known negative results for constructing one-way permutations based on one-way functions, starting with Rudich’s seminal work (PhD thesis ’88). We revisit this classic and fundamental problem and resolve this somewhat surprising gap by ruling out all such black-box constructions—even those that are not domain invariant.

Journal

Journal of CryptologySpringer Journals

Published: Sep 15, 2017

References

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