License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.86
URN: urn:nbn:de:0030-drops-117714
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Ball, Marshall ; Holmgren, Justin ; Ishai, Yuval ; Liu, Tianren ; Malkin, Tal

On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?

LIPIcs-ITCS-2020-86.pdf (0.6 MB)


Garbling schemes, also known as decomposable randomized encodings (DRE), have found many applications in cryptography. However, despite a large body of work on constructing such schemes, very little is known about their limitations.
We initiate a systematic study of the DRE complexity of Boolean functions, obtaining the following main results:
- Near-quadratic lower bounds. We use a classical lower bound technique of Nečiporuk [Dokl. Akad. Nauk SSSR '66] to show an Ω(n²/log n) lower bound on the size of any DRE for many explicit Boolean functions. For some natural functions, we obtain a corresponding upper bound, thus settling their DRE complexity up to polylogarithmic factors. Prior to our work, no superlinear lower bounds were known, even for non-explicit functions.
- Garbling-friendly PRFs. We show that any exponentially secure PRF has Ω(n²/log n) DRE size, and present a plausible candidate for a "garbling-optimal" PRF that nearly meets this bound. This candidate establishes a barrier for super-quadratic DRE lower bounds via natural proof techniques. In contrast, we show a candidate for a weak PRF with near-exponential security and linear DRE size.
Our results establish several qualitative separations, including near-quadratic separations between computational and information-theoretic DRE size of Boolean functions, and between DRE size of weak vs. strong PRFs.

BibTeX - Entry

  author =	{Marshall Ball and Justin Holmgren and Yuval Ishai and Tianren Liu and Tal Malkin},
  title =	{{On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{86:1--86:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-117714},
  doi =		{10.4230/LIPIcs.ITCS.2020.86},
  annote =	{Keywords: Randomized Encoding, Private Simultaneous Messages}

Keywords: Randomized Encoding, Private Simultaneous Messages
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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