NDLI: On the Complexity of Constructing Pseudorandom Functions (Especially when They Don’t Exist)

Content Provider	Springer Nature Link
Author	Miles, Eric Viola, Emanuele
Copyright Year	2013
Abstract	We study the complexity of black-box constructions of pseudorandom functions (PRFs) from one-way functions (OWFs) that are secure against non-uniform adversaries. We show that if OWFs do not exist, then given as an oracle any (inefficient) hard-to-invert function, one can compute a PRF in polynomial time with only k(n) oracle queries, for any k(n)=ω(1) (e.g., k(n)=log∗ n). Combining this with the fact that OWFs imply PRFs, we show that unconditionally there exists a (pathological) construction of a PRF from OWF making at most k(n) queries. This result shows a limitation of a certain class of techniques for proving efficiency lower bounds on the construction of PRFs from OWFs. Our result builds on the work of Reingold, Trevisan, and Vadhan (TCC’04), who show that when OWFs do not exist there is a pseudorandom generator (PRG) construction that makes only one oracle query to the hard-to-invert function. Our proof combines theirs with the Nisan–Wigderson generator (JCSS’94), and with a recent technique by Berman and Haitner (TCC’12).Working in the same context (i.e., when OWFs do not exist), we also construct a poly-time PRG with arbitrary polynomial stretch that makes non-adaptive queries to an (inefficient) one-bit-stretch oracle PRG. This contrasts with the well-known adaptive stretch-increasing construction due to Goldreich and Micali.Both above constructions simply apply an affine function (parity or its complement) to the query answers. We complement this by showing that if the post-processing is restricted to only taking projections then non-adaptive constructions of PRFs, or even linear-stretch PRGs, can be ruled out.
Starting Page	509
Ending Page	532
Page Count	24
File Format	PDF
ISSN	09332790
Journal	Journal of Cryptology
Volume Number	28
Issue Number	3
e-ISSN	14321378
Language	English
Publisher	Springer US
Publisher Date	2013-11-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Black-box reductions Pseudorandom functions adaptivity Coding and Information Theory Computational Mathematics and Numerical Analysis Combinatorics Probability Theory and Stochastic Processes Communications Engineering, Networks
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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