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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<meta name="keywords" content="verifiable,verified,verified computation,verifiable compuation,outsourced computation,third-party computing,PCP,probabilistically-checkable proofs,arguments,interactive proofs,IPs" />
<link href="https://fonts.googleapis.com/css?family=Roboto" rel="stylesheet">
<link rel="stylesheet" type="text/css" href="bootstrap/css/bootstrap.css" />
<link rel="stylesheet" type="text/css" href="index.css" />
<title>Pepper: toward practical verifiable computation</title>
</head>
<body>
<div id="wrap">
<div class="container">
<!--fixed navbar on top of the page-->
<div class="navbar navbar-inverse navbar-fixed-top">
<div class="container">
<div class="navbar-header">
<a class="navbar-brand" href="index.htm">
<span>Pepper: toward practical verifiable computation</span>
</a>
</div>
</div>
</div>
</div>
<div class="container">
<div class="row">
<div class="sidebar col-xs-3">
<div class="container">
<ul id="nav-tab" class="nav sidenav affix">
<li class="active">
<a class="tab-toggle" href="index.htm">Home</a>
</li>
<li>
<a class="collapse-toggle" href="what-is-pepper.htm">About <span class="down-caret"></span></a>
<ul id="about-collapse" class="collapse">
<li class=""><a class="tab-toggle" href="what-is-pepper.htm">What is Pepper?</a></li>
<li class=""><a class="tab-toggle" href="our-approach.htm">Approach and research</a></li>
<li class=""><a class="tab-toggle" href="summary-results.htm">Summary of results</a></li>
<li class=""><a class="tab-toggle" href="summary-systems.htm">Built systems</a></li>
<li class=""><a class="tab-toggle" href="summary-perf.htm">Performance</a></li>
</ul>
</li >
<li class=""><a class="tab-toggle" href="publications.htm">Publications</a></li>
<li class=""><a class="tab-toggle" href="talks.htm">Presentations</a></li>
<li class=""><a class="tab-toggle" href="tutorials.htm">Tutorials and exercises</a></li>
<li class=""><a class="tab-toggle" href="people.htm">People</a></li>
<li class=""><a class="tab-toggle" href="related.htm">Related projects</a></li>
<li class=""><a class="tab-toggle" href="source.htm">Source code</a></li>
<li class=""><a class="tab-toggle" href="funding.htm">Funding and support</a></li>
<li class=""><a class="tab-toggle" href="contact.htm">Contact</a></li>
</ul>
</div>
</div>
<!--content for each tab -->
<div class="tab-content col-xs-9">
<div class="my-tab-pane active" id="home">
<div class="content">
<div class = "jumbotron" >
<h2>Elevator pitch</h2>
<p>
The Pepper project at NYU and UT Austin is tackling the problem of
verifying outsourced computations. Our approach is to reduce to practice
powerful tools from complexity theory and
cryptography:
probabilistically checkable proofs (PCPs), efficient
arguments, etc.
</p>
<p>
Highlights of the project’s results include:
</p>
<ul>
<li>improving the performance of a PCP-based
<a href="http://www.cs.ucla.edu/~rafail/PUBLIC/79.pdf">efficient argument</a>
by a factor of 10<sup>20</sup></li>
<li>broadening the computational model used in
verifiable computation: from Boolean
circuits to a general-purpose model</li>
<li>extending verifiability to representative uses of
cloud computing: MapReduce jobs, simple database queries,
interactions with private state, etc.</li>
<li>a series of <a href="source.htm">built</a>
<a href="summary-systems.htm">systems</a> that implement the aforementioned
refinements, with the following features:
<ul>
<li>GPU acceleration</li>
<li>a compiler that allows the developer to
express a computation in a restricted subset of
C; the compiler produces executables that
implement the protocol entities</li>
</ul>
<li>Verifiable ASICs, a new approach to building trustworthy hardware using untrusted components</li>
</li>
</ul>
<p>
Though these systems <a href="summary-perf.htm">are not yet at true
practicality</a>, they are arguably practical in some
regimes. More importantly, these systems highlight
the potential applicability of the theory, and indeed, there
is now <a href="related.htm">a thriving research area</a> based on this
promise. Thus, we are hopeful that over the next few
years, the underlying theoretical tools will find
their way into real systems.
</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="what-is-pepper">
<div class="content">
<div class="descriptive">
<h3>Overview: what is Pepper?</h3>
<p>Pepper is an academic research project whose goal is to make
verified computation
practical. By verified computation (which is sometimes also called
“verifiable computation”), we mean a system that implements
the following picture:
</p>
<div class="image-container">
<img id="overview" class="image-center" src="overview.png" alt="Overview of Pepper" />
</div>
<p>One motivation is <i>cloud computing</i> (more
generally, <i>third-party computing</i>).
These environments bring:
</p>
<ul>
<li>Issues of <i>scale</i>: with hundreds of
thousands or millions of machines, correct and
unfailing execution in all cases seems
unlikely.</li>
<li>Issues of <i>trust</i>: the computation “provider” and the “consumer” are
different entities.</li>
</ul>
<!--<p>Thus, we don't want to make any assumptions
about the performing computer, but we still want to
give a guarantee to the delegating computer that the
computation was done correctly.</p>-->
<p>Goal: A system that is</p>
<ol>
<li><b>Comprehensive</b> -- the
system makes no assumptions about the behavior and capabilities of the performing computer other than cryptographic hardness.</li>
<li><b>General-purpose</b> -- not
specialized to a particular family of functions.</li>
<li><b>Practical</b> -- can be used for real problems.</li>
</ol>
<p>Prior work does not meet all three of these properties.</p>
<p>We approach this problem using deep results in cryptography and
complexity theory. <a href="our-approach.htm">Here</a> is a high-level
description of the foundations of our approach.</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="our-approach">
<div class="content">
<div class="descriptive">
<h3>Our approach: PCPs, argument systems, and interactive proofs</h3>
<p>Our approach is to apply the fascinating theory of
Probabilistically Checkable Proofs (PCPs) and two closely related
constructs: argument systems and interactive proofs.</p>
<p>The theory
surrounding PCPs demonstrates, astonishingly, that it is possible
(in principle) to check a mathematical proof by investigating only a
few bits of that proof. In our context, this implies that the
<a href="what-is-pepper.htm">picture we wanted</a>
has a solution, one that is unconditional and
general-purpose.</p>
<h3>The research: make the theory practical</h3>
<p>Unfortunately, PCPs, as described in the
theoretical literature, are not remotely practical: in
the most asymptotically “efficient” schemes, the server would take
<i>trillions of years</i> to produce a proof.</p>
<p><i>Can we incorporate PCPs into a built system?</i> So far, we have been able to come close. <a
href="summary-results.htm">Here</a> is a top-level summary of
Pepper’s results to date.</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="summary-results">
<div class="content">
<div class="descriptive">
<h3>Summary of Pepper’s results so far</h3>
<p>Our line of work on
<a href="pepper-ndss12.pdf">Pepper</a>, <a href="ginger-usec12-v2.pdf">Ginger</a>, and <a href="zaatar-eurosys13.pdf">Zaatar</a> has instantiated an
<i>argument system</i> (an interactive protocol that assumes a
computationally bounded prover) due to Ishai, Kushilevitz, and Ostrovsky (CCC 2007),
in <a
href="http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4262770">this
paper</a> (also available <a
href="http://www.cs.ucla.edu/~rafail/PUBLIC/79.pdf">here</a>).
Through theoretical and practical refinements, we have reduced the
cost of this argument system by a factor of roughly 10<sup>20</sup> (seriously).</p>
<p>In another line of work, <a href="allspice-oakland13.pdf">Allspice</a>, we have built on an <a
href="http://dl.acm.org/citation.cfm?id=1374396">interactive proof
system</a> due to Goldwasser, Kalai, and Rothblum (STOC 2008), and
<a href="http://arxiv.org/abs/1105.2003">refined and implemented</a> by Cormode, Mitzenmacher, and
Thaler (ITCS 2012). One of the chief advantages of this
line of work is that it avoids expensive cryptographic operations.</p>
<p>One might wonder: which protocol is “best”? Our experience has
been that it depends on the computation. Accordingly, Allspice
includes a compiler that takes as input a high-level programming language and
performs static analysis to compile to the best available
protocol for that computation.</p>
<p>In the above works, the computational model does not support
<i>stateful</i> computations, namely those that work over RAM, or
computations for which the verifier does not have the full input.
In <a href="pantry-sosp13.pdf">Pantry</a>, we overcome this
limitation, and apply the verification machinery to MapReduce jobs,
queries against remote databases, and applications for which the
prover’s state is private.</p>
<p><a href="summary-systems.htm">Here</a> is a system-by-system
description.</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="summary-systems">
<div class="content">
<div class="descriptive">
<h3>Built systems under the Pepper project</h3>
<p>In the descriptions below, the <i>prover</i> is the
entity that performs a computation. The
<i>verifier</i> checks a proof (produced by the
prover) that the computation was performed
correctly.</p>
<div class="panel panel-default" id="pepper">
<div class="panel-heading">
<b>Pepper</b>
</div>
<div class="panel-body">
<a href="pepper-ndss12.pdf">Pepper</a> is the first system to challenge the folklore that
PCP-derived machinery is impractical. Pepper implements an <span
class="text-emphasis">efficient argument system</span> based on a
protocol of <a href="http://www.cs.ucla.edu/~rafail/PUBLIC/79.pdf">Ishai et al., CCC 2007</a>, and incorporates new
theoretical work to improve performance by 20 orders of magnitude.
Pepper is implemented and experimentally evaluated, and is arguably
practical for some computations and in some regimes.
<!-- More generally,
Pepper illustrates that, as a tool for building secure systems, PCPs
are not a lost cause. -->
<br/>
<div class="cite"> S. Setty, R. McPherson, A. J.
Blumberg, and M. Walfish, “Making argument
systems for outsourced computation practical
(sometimes)”, Network & Distributed
System Security Symposium (NDSS), February 2012.
[<a href="pepper-ndss12.pdf">pdf</a>]
</div>
</div>
</div>
<div class="panel panel-default" id="ginger">
<div class="panel-heading">
<b>Ginger</b>
</div>
<div class="panel-body">
<a href="ginger-usec12-v2.pdf">Ginger</a> is based on Pepper. It slashes query costs via
further refinements. In addition, Ginger broadens the
computational model to include (primitive) floating-point
fractions, inequality comparisons, logical operations, and
conditional control flow. Ginger also includes a parallel
GPU-based implementation, and a compiler that transforms
computations expressed in a high-level language to
executables that implement the protocol entities.
<br/>
<div class="cite"> S. Setty, V. Vu, N. Panpalia,
B. Braun, A. J. Blumberg, and M. Walfish,
“Taking proof-based verified computation a
few steps closer to practicality”, USENIX
Security Symposium, August 2012. [<a
href="ginger-usec12-v2.pdf">pdf</a> (corrected)]
</div>
</div>
</div>
<div class="panel panel-default" id="zaatar">
<div class="panel-heading">
<b>Zaatar</b>
</div>
<div class="panel-body">
<a href="zaatar-eurosys13.pdf">Zaatar</a> addresses a limitation in Ginger, namely that
avoiding immense work for the prover requires
computation-specific tailoring of the protocols. Zaatar is
built on our observation that the <a
href="http://eprint.iacr.org/2012/215">QAPs of Gennaro et al., EUROCRYPT 2013</a>
yield a linear PCP that works with the
Ginger/Pepper/IKO framework and is (relatively) efficient for the prover.
The consequence is a prover whose total work is not much
more than linear in the running time of the computation (and
does not require special-purpose tailoring).
<br/>
<div class="cite"> S. Setty, B. Braun, V. Vu, A.
J. Blumberg, B. Parno, and M. Walfish,
“Resolving the conflict between generality
and plausibility in verified computation”,
ACM European Conference on Computer Systems
(EuroSys), April 2013. [<a
href="zaatar-eurosys13.pdf">pdf</a>] </div>
</div>
</div>
<div class="panel panel-default" id="allspice">
<div class="panel-heading">
<b>Allspice</b>
</div>
<div class="panel-body">
<a href="allspice-oakland13.pdf">Allspice</a> addresses a key
limitation of prior work for verifying computations: either it
relies on cryptography, which carries an expense (as with Zaatar,
Ginger, Pepper, and IKO), or else it applies to a restricted class
of computations (as with work by <a href="http://dl.acm.org/citation.cfm?id=2090245">Cormode et al., ITCS 2012</a>, which
builds on an interactive proof system of <a href="http://dl.acm.org/citation.cfm?id=1374396">Goldwasser et al., STOC
2008</a>). Allspice optimizes the non-cryptographic
protocols and extends them to a much larger class of computations.
Allspice also uses static analysis to compile an input program to
the best verification machinery for that program.
<br/>
<div class="cite">
V. Vu, S. Setty, A. J. Blumberg, and M. Walfish,
“A hybrid architecture for interactive
verifiable computation”, IEEE Symposium on
Security and Privacy (Oakland), May 2013. [<a
href="allspice-oakland13.pdf">pdf</a>]
</div>
</div>
</div>
<div class="panel panel-default" id="pantry">
<div class="panel-heading">
<b>Pantry</b>
</div>
<div class="panel-body">
<a href="http://eprint.iacr.org/2013/356">Pantry</a> extends
verifiable computation to handle <i>stateful</i> computations: those
that work over RAM, or computations for which the verifier does not
have the full input. Pantry composes techniques from untrusted
storage with existing verifiable computation machinery: the
verifier’s explicit input includes a <i>digest</i> of the full input
or state, and the prover is obliged to compute over state that
matches the digest. The result is to extend verifiability to real
applications of cloud computing (MapReduce jobs, queries against
remote databases, applications for which the prover’s state is
hidden, etc.). Besides the gain in expressiveness, Pantry improves
performance: by not handling inputs, the verifier saves CPU and
network costs.
<br/>
<div class="cite">
B. Braun, A. J. Feldman, Z. Ren, S. Setty, A. J.
Blumberg, and M. Walfish, “Verifying
computations with state”, ACM Symposium on
Operating Systems Principles (SOSP), November
2013. [<a href="pantry-sosp13.pdf">pdf</a>]
</div>
</div>
</div>
<div class="panel panel-default" id="buffet">
<div class="panel-heading">
<b>Buffet</b>
</div>
<div class="panel-body">
<a href="http://eprint.iacr.org/2014/674">Buffet</a> eliminates what was
a problematic cost-programmability tradeoff in this research area. Prior
to Buffet, there were two approaches to program representation. One
approach, due to <a
href="https://eprint.iacr.org/2013/879.pdf">Ben-Sasson et al., Usenix
Security 2014</a>, offered excellent programmability (the full C
programming language) but substantial overhead. Another approach
(embodied by Pantry, <a
href="http://research.microsoft.com/en-us/projects/verifcomp/">Pinocchio</a>,
and Zaatar) offered much lower overhead but could not handle
data-dependent control flow. Buffet takes Pantry as a base and applies
static program analysis (including loop flattening) together with an
adaptation of BCTV's <a href="https://eprint.iacr.org/2013/507">elegant
representation of RAM</a>. Buffet can handle essentially any example in
the verifiable computation literature (it supports an expansive subset
of C, disallowing only goto and function pointers) and achieves the
best performance in the area by multiple orders of magnitude.
<div class="cite">
R. S. Wahby, S. Setty, Z. Ren, A. J. Blumberg, and M. Walfish, "Efficient RAM and control
flow in verifiable outsourced computation."
Network & Distributed System Security Symposium,
<a href="http://www.internetsociety.org/events/ndss-symposium-2015">NDSS
2015</a>, February 2015. [<a href="buffet-ndss15.pdf">pdf</a>]<br/>
A slightly longer version is available as <a href="https://eprint.iacr.org">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2014/674">2014/674</a>.
</div>
</div>
</div>
<div class="panel panel-default" id="zebra">
<div class="panel-heading"><b>Zebra</b></div>
<div class="panel-body">
<a href="https://eprint.iacr.org/2015/1243">Zebra</a> instantiates a new model
for building trustworthy chips, called Verifiable ASICs.
This model uses a high-performance chip from an untrusted (and possibly malicious)
hardware vendor to accelerate the computation of a low-performance
chip supplied by a trusted vendor, while retaining the latter's trustworthiness.
To instantiate the model, Zebra builds on the interactive proofs of
<a href="http://dl.acm.org/citation.cfm?id=1374396">GKR</a>,
<a href="http://people.seas.harvard.edu/~jthaler/PracticalVerifiedComputation.html">CMT</a>,
and <a href="#allspice">Allspice</a>.
Zebra demonstrates that, for a class of real computations, the Verifiable ASICs approach
reduces costs and improves performance compared to chips built solely by a trusted
manufacturer.
<div class="cite">
R. S. Wahby, M. Howald, S. Garg, a. shelat, and M. Walfish, "Verifiable ASICs."
IEEE Symposium on Security and Privacy (<a href="http://www.ieee-security.org/TC/SP2016/">Oakland</a>), May 2016.
[<a href="zebra-oakland16.pdf">pdf</a>] <em>(Distinguished student paper award.)</em><br/>
An extended version is available as <a href="https://eprint.iacr.org">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2015/1243">2015/1243</a>.
</div>
</div>
</div>
<div class="panel panel-default" id="giraffe">
<div class="panel-heading"><b>Giraffe</b></div>
<div class="panel-body">
<a href="https://eprint.iacr.org/2017/242">Giraffe</a> builds on the
Verifiable ASICs model introduced by Zebra.
Giraffe removes Zebra's requirement that a trusted entity supply the verifier with
an endless stream of precomputations.
In doing so, it charges for <em>all</em> protocol costs and makes outsourcing with
probabilistic proofs worthwhile for the first time.
<p> Giraffe includes a new probabilistic proof for data-parallel computations that
refines the protocol of <a href="https://arxiv.org/abs/1304.3812">Thaler13</a>
to give asymptotically optimal prover cost; this is of independent interest.
Giraffe also develops a <em>design template</em> that automatically produces optimized
hardware designs for a wide range of computations and circuit technologies.
It combines this template with program analysis and compiler techniques that extend
the Verifiable ASICs model to a wider range of computations.
Compared to Zebra, Giraffe handles computations that are 500× larger, and it can
automatically outsource <em>parts</em> of programs that are not worthwhile to
outsource in full.
</p>
<div class="cite">
R. S. Wahby, Y. Ji, A. J. Blumberg, a. shelat, J. Thaler, M. Walfish, and T. Wies, "Full accounting for verifiable outsourcing."
ACM Conference on Computer and Communications Security (<a
href="https://www.sigsac.org/ccs/CCS2017/">CCS</a>), October 2017.
[<a href="giraffe-ccs17.pdf">pdf</a>]<br/>
An extended version is available as <a href="https://eprint.iacr.org">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2017/242">2017/242</a>.
</div>
</div>
</div>
<a href="summary-perf.htm">Here</a> is a summary of the
performance of the above systems.
</div>
</div>
</div>
<div class="my-tab-pane" id="summary-perf">
<div class="content">
<div class="descriptive">
<h3>Summary of performance</h3>
<p>Here is a high-level summary. (Our <a
href="publications.htm">publications</a>
provide detail. See especially <a href="http://dl.acm.org/citation.cfm?id=2728770.2641562">this
CACM article</a> and
<a class="cross-tab-toggle"
href="summary-systems.htm#buffet">Buffet</a>.) </p>
<p>None of our systems (or the <a
href="related.htm">others in this area</a>)
have achieved true practicality yet.</p>
<p>There are two principal issues, for all
of these projects:</p>
<p>
<b>(1) Costs to the verifier.</b> To check that a
remote computation was performed correctly, the
verifier must incur a <i>per-computation setup
cost</i>: this cost (which consists of CPU
and network costs) amortizes over multiple
instances of the same computation (potentially
over <a href="related.htm">all future
instances</a>), on different inputs.
However, the cross-over point, in terms of when
the setup cost is paid for, is quite high:
tens or hundreds of thousands of
instances of the same computation.
</p>
<ul>
<li>This setup cost can be slashed
(as in
<a class="cross-tab-toggle" href="summary-systems.htm#allspice">Allspice</a>)
or eliminated (as
in <a href="related.htm">CMT</a>).
Unfortunately, these solutions apply
only to restricted classes of
computations.</li>
<li>Using the techniques of <a
href="related.htm">BCTV</a>, the setup cost can be reused over all
computations of the same size.
However, the cost of these techniques is very high,
and in practice, one would need to incur the setup
cost thousands of times anyway (as explained in <a
class="cross-tab-toggle"
href="summary-systems.htm#buffet">Buffet</a>).</li>
<li>Using <a
href="http://eprint.iacr.org/2014/595">other
techniques</a> of BCTV,
the setup cost can be made independent of the computation.
However, these techniques are primarily theory at this
point; for example, the prover's computational costs are many orders of
magnitude higher than the other works in the
area.</li>
</ul>
<p>
<b>(2) Costs to the prover.</b> The CPU costs to the
prover are currently immense: orders of
magnitude (factors between a thousand and a
million) more than simply executing the
computation. An additional bottleneck is memory:
the prover must materialize a transcript
of a computation's execution.
</p>
<p>
As a consequence of the above costs, all
projects in this area are currently limited to
small-scale computations: programs that take several million
steps, but not more.
</p>
</div>
</div>
</div>
<div class="my-tab-pane" id="publications">
<div class="content">
<h2>Publications</h2>
<ul class="list-group">
<li class="list-group-item">
<b>Doubly-efficient zkSNARKs without trusted setup</b> [<a href="hyrax-oakland18.pdf">pdf</a>]<br/>
Riad S. Wahby, Ioanna Tzialla, abhi shelat, Justin Thaler, and Michael Walfish<br/>
IEEE Symposium on Security and Privacy, <a href="https://www.ieee-security.org/TC/SP2018/">Oakland 2018</a>, San Francisco, CA, May 2018.<br/>
An extended version is available as <a href="https://eprint.iacr.org/">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2017/1132/">2017/1132</a>.
</li>
<li class="list-group-item">
<b>Full accounting for verifiable outsourcing</b> [<a href="giraffe-ccs17.pdf">pdf</a>]<br/>
Riad S. Wahby, Ye Ji, Andrew J. Blumberg, abhi shelat, Justin Thaler, Michael Walfish, and Thomas Wies<br/>
ACM Conference on Computer and Communications Security, <a href="https://www.sigsac.org/ccs/CCS2017/">CCS 2017</a>, Dallas, TX, October 2017.<br/>
An extended version is available as <a href="https://eprint.iacr.org/">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2017/242/">2017/242</a>.
</li>
<li class="list-group-item">
<b>Verifiable ASICs</b> [<a href="zebra-oakland16.pdf">pdf</a>] <em>(Distinguished student paper award.)</em><br/>
Riad S. Wahby, Max Howald, Siddharth Garg, abhi shelat, and Michael Walfish<br/>
IEEE Symposium on Security and Privacy, <a href="http://www.ieee-security.org/TC/SP2016/">Oakland 2016</a>, San Jose, CA, May 2016.<br/>
An extended version is available as <a href="https://eprint.iacr.org/">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2015/1243/">2015/1243</a>.
</li>
<li class="list-group-item">
<b>Efficient RAM and control flow in verifiable
outsourced computation</b> [<a href="buffet-ndss15.pdf">pdf</a>]<br/>
Riad S. Wahby, Srinath Setty, Zuocheng Ren, Andrew J. Blumberg,
and Michael Walfish <br/>
Network & Distributed System Security
Symposium, <a href="http://www.internetsociety.org/events/ndss-symposium-2015">NDSS
2015</a>, San Diego, CA, February 2015.<br/>
A slightly longer version is available as <a href="https://eprint.iacr.org">Cryptology ePrint</a> <a href="https://eprint.iacr.org/2014/674">2014/674</a>.
</li>
<li class="list-group-item">
<b>Verifying computations without reexecuting them: from theoretical possibility to near practicality</b>
[<a href="http://dl.acm.org/citation.cfm?id=2641562">link</a>]<br/>
Michael Walfish and Andrew J. Blumberg<br/>
(<span class="text-emphasis">This survey is written for a
general CS audience and is probably a good first paper to
read for those curious about the area.</span>)<br/>
Communications of the ACM (<a href="http://cacm.acm.org/">CACM</a>),
Volume 58, Number 2, pages 74–84, February 2015.<br/>
Prior versions: November 2013, July 2014.
(<a href="http://eccc.hpi-web.de/">ECCC</a> <a href="http://eccc.hpi-web.de/report/2013/165/">TR13-165</a>).<br/>
</li>
<li class="list-group-item">
<b>Verifying computations with state</b>
[<a href="pantry-sosp13.pdf">pdf</a>,
<a href="http://eprint.iacr.org/2013/356">extended version</a>]<br/>
Benjamin Braun, Ariel J. Feldman, Zuocheng Ren, Srinath Setty, Andrew J. Blumberg, and Michael Walfish <br/>
ACM Symposium on Operating Systems Principles,
<a href="http://sigops.org/sosp/sosp13/">SOSP 2013</a>, Farmington, PA, November 2013
</li>
<li class="list-group-item">
<b>A hybrid architecture for interactive verifiable computation</b>
[<a href="allspice-oakland13.pdf">pdf</a>]<br/>
Victor Vu, Srinath Setty, Andrew J. Blumberg, and Michael Walfish<br/>
IEEE Symposium on Security and Privacy, <a href="http://www.ieee-security.org/TC/SP2013/">Oakland 2013</a>,
San Francisco, CA, May 2013
</li>
<li class="list-group-item">
<b>Resolving the conflict between generality and plausibility in verified computation</b>
[<a href="zaatar-eurosys13.pdf">pdf</a>, <a href="http://eprint.iacr.org/2012/622">extended version</a>] <br/>
Srinath Setty, Benjamin Braun, Victor Vu,
Andrew J. Blumberg, Bryan Parno, and Michael Walfish<br/>
ACM European Conference on Computer Systems, <a href="http://eurosys2013.tudos.org/">EuroSys 2013</a>,
Prague, Czech Republic, April 2013
</li>
<li class="list-group-item">
<b>Taking proof-based verified computation a few steps closer
to practicality</b> [<a href="ginger-usec12-v2.pdf">pdf</a> (corrected),
<a href="http://eprint.iacr.org/2012/598">extended version</a>] <br/>
Srinath Setty, Victor Vu, Nikhil Panpalia, Benjamin Braun, Andrew J. Blumberg, and Michael Walfish <br/>
USENIX Security Symposium, <a href="https://www.usenix.org/conference/usenixsecurity12">Security 2012</a>, Bellevue, WA, August 2012
</li>
<li class="list-group-item">
<b>Making argument systems for outsourced computation practical (sometimes)</b> [<a href="pepper-ndss12.pdf">pdf</a>]<br/>
Srinath Setty, Richard McPherson, Andrew J. Blumberg, and Michael Walfish <br/>
Network & Distributed System Security Symposium, <a href="http://www.isoc.org/isoc/conferences/ndss/12/">NDSS 2012</a>,
San Diego, CA, February 2012
</li>
<li class="list-group-item">
<b>Toward practical and unconditional verification of remote computations</b> [<a href="vercomp-hotos11.pdf">pdf</a>]<br/>
Srinath Setty, Andrew J. Blumberg, and Michael Walfish <br/>
Workshop on Hot Topics in Operating Systems, <a href="http://www.usenix.org/events/hotos11/">HotOS 2011</a>, Napa Valley, CA, May 2011
</li>
</ul>
</div>
</div>
<div class="my-tab-pane" id="talks">
<div class="content">
<h2>Presentations</h2>
<ul class="list-group">
<li class="list-group-item">
<b>Practical proof systems: implementations, applications, and next steps</b> [<a href="simons-vc-survey.pdf">pdf</a> (4.2 MB), <a href="https://www.youtube.com/watch?v=roRPgh4bQMI">video</a>]
<br/>
Presented at the <a href="https://simons.berkeley.edu/workshops/proofs2019-1">Workshop on Probabilistically Checkable and Interactive Proof Systems</a>, part of the <a href="https://simons.berkeley.edu/programs/proofs2019">Simons Institute Program on Proofs, Consensus, and Decentralizing Society</a>, September, 2019.
</li>
<li class="list-group-item">
<b>Doubly-efficient zkSNARKs Without Trusted Setup</b>
<br/>
Security & Privacy (Oakland), May 2018 [<a href="hyrax-oakland18-talk.pdf">pdf (1.2 MB)</a>, <a href="https://www.youtube.com/watch?v=yq2AfLlMww0">video</a>]
</li>
<li class="list-group-item">
<b>Full accounting for verifiable outsourcing</b>
<br/>
ACM CCS, October 2017 [<a href="giraffe-ccs17-talk.pdf">pdf (2.7 MB)</a>, <a href="https://www.youtube.com/watch?v=uU9noMY3OR0">video</a>]
<br/>
Also presented at <a href="http://dimacs.rutgers.edu/Workshops/Outsourcing/">DIMACS Workshop on Outsourcing Computation Securely</a>, July 2017 [<a href="giraffe-dimacs_outsourcing17-talk.pdf">pdf (2.6 MB)</a>, <a href="https://www.youtube.com/watch?v=RCzcF0niZGI">video</a>]
</li>
<li class="list-group-item">
<b>Verifiable ASICs</b>
<br/>
Security & Privacy (Oakland), May 2016 [<a href="zebra-oakland16-talk.pdf">pdf (2.2 MB)</a>, <a href="https://www.youtube.com/watch?v=Wr0QiNatBdE">video</a>]
<br/>
A slightly longer version of this talk appeared at the <a href="http://dimacs.rutgers.edu/Workshops/RAM/">DIMACS/MACS Workshop on Cryptography in the RAM Model of Computation</a>, June 2016 [<a href="zebra-dimacs_ram_model16-talk.pdf">pdf (3.2 MB)</a>]
</li>
<li class="list-group-item">
<b>(Implementations of) verifiable computation and succinct arguments: survey and wishlist</b>
<br/>
(<span class="text-emphasis">This talk surveys
the last few years of progress on (implementations of) protocols for verifiable
computation and closely related
problems, such as succinct non-interactive (zero knowledge)
arguments. Watching the talk is likely to be an efficient way to
begin a literature search and to get pointers to research
questions for the area.</span>)
<br/>
Simons Institute: Securing Computation, June 2015 [<a href="surveywishlist.pptx">pptx (1.1 MB)</a>,
<a href="http://simons.berkeley.edu/talks/mike-walfish-2015-06-10">video</a>]
</li>
<li class="list-group-item">
<b>Efficient RAM and control flow in verifiable outsourced computation</b>
<br/>
NDSS, February 2015 [<a href="buffet-ndss15-talk.pdf">pdf (351 kB)</a>]
</li>
<li class="list-group-item">
<b>Verifying computations with state</b>
<br/>
SOSP, November 2013 [<a href="pantry-sosp13-talk.pdf">pdf (243 kB)</a>,
<a href="pantry-sosp13-talk.key">key (773 kB)</a>]
</li>
<li class="list-group-item">
<b>Verifying remote executions: from wild implausibility to near practicality</b>
<br/>
Keynote at HotDep, November 2013 [<a href="hotdep13-keynote.pptx">pptx (5 MB)</a>]
</li>
<li class="list-group-item">
<b>Making verifiable computation a systems problem</b>
<br/>
Microsoft Research Faculty Summit, July 2013 [<a href="msrfs.pptx">pptx (2.7 MB)</a>,
<a href="http://research.microsoft.com/apps/video/dl.aspx?id=199523">video</a>]
</li>
<li class="list-group-item">
<b>A hybrid architecture for interactive verifiable computation</b>
<br/>
Security & Privacy (Oakland), May 2013 [<a href="allspice-oakland13.pptx">pptx (906 kB)</a>]
</li>
<li class="list-group-item">
<b>Resolving the conflict between generality and plausibility in verified computation</b>
<br/>
EuroSys, April 2013 [<a href="zaatar-eurosys13-talk.pdf">pdf (182 kB)</a>,
<a href="zaatar-eurosys13-talk.key">key (590 kB)</a>]
</li>
<li class="list-group-item">
<b>Taking proof-based verified computation a few steps closer to practicality</b>
<br/>
Security, August 2012 [<a href="ginger-usec12-talk-v2.pdf">pdf (corrected, 126 kB)</a>]
</li>
<li class="list-group-item">
<b>Making argument systems for outsourced computation practical (sometimes)</b>
<br/>
NDSS, February 2012 [<a href="pepper-ndss12-talk.pdf">pdf (12 MB)</a>,
<a href="pepper-ndss12-talk.pptx">pptx (673 kB)</a>]
</li>
</ul>
</div>
</div>
<div class="my-tab-pane" id="tutorials">
<div class="content">
<div class="panel panel-default">
<div class="panel-heading"><b>Tutorials with exercises</b></div>
<div class="panel-body">
<ul class="list-group">
<li class="list-group-item">
<b>Overview of "practical" probabilistic proofs</b>
<br/>
This surveys the landscape of "practical" probabilistic proofs.
<br/>
<a href="tutorials/t1-biu-mw.pdf">slides</a> (610 kB), <a href="https://www.youtube.com/watch?v=ar7LYfF-TxU">video</a>
</li>
<li class="list-group-item">
<b>Linear PCPs and the role of Quadratic Arithmetic Programs (QAPs)</b>
<br/>
This tutorial reviews <em>linear</em> PCPs, which are at the heart of many "practical" probabilistic proofs.
<br/>
<a href="tutorials/t2-biu-mw.pdf">slides and exercises</a> (732 kB), <a href="https://www.youtube.com/watch?v=upoVu1swaxo">video</a>
</li>
<li class="list-group-item">
<b>Folklore arithmetization of programs</b>
<br/>
This tutorial explains how various program constructs (conditionals, equality tests, inequalities, etc.) are represented as systems of equations over a finite field.
<br/>
<a href="tutorials/t3-biu-mw.pdf">slides and exercises</a> (2 MB), <a href="https://www.youtube.com/watch?v=dVuC6ILojUM&t=18s">video</a>
<br/>
(Owing to a production error, the slide video is out of sync with the rest of the presentation.)
</li>
</ul>
<p>In these slides, grey boxes are explicit exercises.
<p>The slides also contain "blanks" that the presentation fills in, by writing on the slides. You can either try to fill these in as further exercises, or watch the videos.</p>
<p>These presentations are all excerpts from the <a href="http://cyber.biu.ac.il/event/the-6th-biu-winter-school/">2016 Bar-Ilan Winter School on Verifiable Computation</a>.</p>
</div>
</div>
<div class="panel panel-default">
<div class="panel-heading"><b>Comprehensive survey of proofs, arguments, and zero knowledge</b></div>
<div class="panel-body">
This <a href="http://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.html">comprehensive survey</a> by <a href="http://people.cs.georgetown.edu/jthaler/">Justin Thaler</a> covers probabilistic proofs, with emphasis on "practical" protocols.
</div>
</div>
</div>
</div>
<div class="my-tab-pane active" id="people">
<div class="content">
<div class="descriptive">
<h2>People</h2>
<p>Project members:</p>
<ul>
<li><a href="http://www.math.utexas.edu/users/blumberg/">Andrew J. Blumberg</a> (faculty)</li>
<li>Max Howald (undergraduate student)</li>
<li><a href="http://www.cs.utexas.edu/~srinath">Srinath Setty</a> (graduate student alum; researcher)</li>
<li><a href="http://cs.nyu.edu/~rsw">Riad S. Wahby</a> (graduate student)</li>
<li><a href="http://cs.nyu.edu/~mwalfish">Michael Walfish</a> (faculty; PI)</li>
</ul>
<p>Current and former collaborators:</p>
<ul>
<li>Muqeet Ali</li>
<li><a href="http://www.stanford.edu/~bbraun/">Ben Braun</a></li>
<li><a href="https://www.cis.upenn.edu/~arielfel/">Ariel Feldman</a></li>
<li><a href="http://engineering.nyu.edu/people/siddharth-garg">Siddharth Garg</a></li>
<li>Ye Ji</li>
<li>Richard McPherson</li>
<li>Nikhil Panpalia</li>
<li><a href="http://research.microsoft.com/en-us/people/parno/">Bryan Parno</a></li>
<li><a href="https://www.cs.utexas.edu/~ren/">Zuocheng Ren</a></li>
<li><a href="https://www.cs.virginia.edu/~shelat/">abhi shelat</a></li>
<li><a href="https://people.cs.georgetown.edu/jthaler/">Justin Thaler</a></li>
<li>Victor Vu</li>
<li><a href="http://cs.nyu.edu/wies/">Thomas Wies</a></li>
</ul>
</div>
</div>
</div>
<div class="my-tab-pane" id="related">
<div class="content">
<div class="descriptive">
<p>For an overview of the research space, see:</p>
<ul>
<li>this <a
href="http://dl.acm.org/citation.cfm?id=2728770.2641562">survey
article</a></li>
<li>this <a href="http://mybiasedcoin.blogspot.com/2013/09/guest-post-by-justin-thaler-mini-survey.html">blog post</a></li>
<li>this <a href="http://research.microsoft.com/apps/video/dl.aspx?id=199523">video</a> (this is a session on verifiable
computation at the 2013 Microsoft Research Faculty Summit, hosted by Bryan Parno)</li>
</ul>
<p>We know of three projects that are related to ours:</p>
<ul>
<li>
<div class="bullet">
<div class="bullet-heading">
<b>CMT</b> [see <a
href="http://dl.acm.org/citation.cfm?id=2090245">here</a> and
<a href="http://people.seas.harvard.edu/~jthaler/">here</a>]<br/>
</div>
<div class="bullet-body">
Refines a non-cryptographic interactive proof protocol. Can achieve
<a href="http://people.seas.harvard.edu/~jthaler/TimeOptimalIPs.html">much lower overhead</a> than the other approaches
but requires that computations be naturally
parallelizable.
</div>
</div>
</li>
<li>
<div class="bullet">
<div class="bullet-heading">
<b>GGPR and Pinocchio</b> [<a href="http://research.microsoft.com/en-us/projects/verifcomp/">project page</a>]
<br/>
</div>
<div class="bullet-body">
Introduces the remarkable QAP/QSP encoding, which is borrowed by many of the projects in the area.
Pinocchio and <a class="cross-tab-toggle" href="summary-systems.htm#zaatar">Zaatar</a>
have similar performance
except that Pinocchio has much better amortization behavior.
<!-- (roughly, Pinocchio requires per-computation setup work
while Zaatar must pay that cost per-batch).-->
</div>
</div>
</li>
<li>
<div class="bullet">
<div class="bullet-heading">
<b>BCTV, BCGTV, and TinyRAM</b> [<a href="http://www.scipr-lab.org/">project page</a>]
<br/>
</div>
<div class="bullet-body">
Introduces an <a
href="http://dl.acm.org/citation.cfm?id=2422481">innovative
program representation</a> and combines it with an optimized
implementation of Pinocchio's verification engine.
This approach brings excellent programmability (enabling
support of the full C programming language) and
the best amortization behavior in the literature but
overhead is very high.
Compared to <a class="cross-tab-toggle"
href="summary-systems.htm#buffet">Buffet</a>, for
example,
programmability is slightly better
but performance is orders of magnitude worse.
</div>
</div>
</li>
</ul>
<p>For a quick performance comparison, based on <a href="source.htm">re-implementations</a>
of many of the systems, see <a
href="http://research.microsoft.com/en-us/UM/redmond/events/fs2013/presentations/Michael-Walfish_EfficientlyVerifying.pptx">this
presentation</a> (accompanies the Microsoft Faculty Summit video
above). Also, the <a class="cross-tab-toggle"
href="summary-systems.htm#buffet">Buffet</a>
paper contains a careful, apples-to-apples performance comparison
of BCTV and
<a class="cross-tab-toggle"
href="summary-systems.htm#pantry">Pantry</a>
(and by extension, Pinocchio and
<a class="cross-tab-toggle"
href="summary-systems.htm#zaatar">Zaatar</a>).
</div>
</div>
</div>
<div class="my-tab-pane" id="source">
<div class="content">
<div class="descriptive">
<p>Source code for all of our built <a
href="summary-systems.htm">systems</a> is available online, under a BSD-style license.
In addition, we provide full re-implementations of
most of the <a href="related.htm">related systems</a>;
this facilitates performance comparisons.</p>
<div class="panel panel-default">
<div class="panel-heading">
<b>Implemented systems</b>
</div>
<div class="panel-body">
<p>We maintain a <a href="https://github.com/pepper-project/pepper">github repository</a>
with our latest released code.
For experimenting or building on our work, we suggest using this release.
We also maintain a slightly simplified (but still feature-rich) codebase,
<a href="https://github.com/pepper-project/pequin/">Pequin</a>.
If you want to get started quickly, Pequin is a good choice.
<p>We also provide snapshots of our systems at the time of publication, useful
for reproducing our results:</p>
<ul>
<li>Hyrax (<a href="https://github.com/hyraxZK">link</a>)</li>
<li>Giraffe (<a href="https://github.com/pepper-project/giraffe">link</a>)</li>
<li>Zebra (<a href="https://github.com/pepper-project/zebra">link</a>)</li>
<li>Buffet (<a href="https://github.com/pepper-project/releases/blob/master/buffet.tar.gz?raw=true">link</a>)</li>
<li>Pantry (<a href="https://github.com/pepper-project/releases/blob/master/pantry.tar.gz?raw=true">link</a>)</li>
<li>Zaatar (<a href="https://github.com/pepper-project/releases/blob/master/zaatar.tar.gz?raw=true">link</a>)</li>
<li>Allspice and Ginger (<a href="https://github.com/pepper-project/releases/blob/master/ginger-allspice.tar.gz?raw=true">link</a>)</li>
<li>Pepper (<a href="https://github.com/pepper-project/releases/blob/master/pepper.tar.gz?raw=true">link</a>)</li>
</ul>
<p>Our systems rely on a number of third-party packages.
We provide an <a href="https://github.com/pepper-project/thirdparty">archive</a>
of versions of these packages that are known to work with our system.</p>
</div>
</div>
<div class="panel panel-default">
<div class="panel-heading">
<b>Re-implementations of related systems</b>
</div>
<div class="panel-body">
<ul>
<li>CMT (included with Allspice and in our latest development branch)</li>
<li>Pinocchio (included with Pantry, Pantry-enhanced, Buffet, and our latest development branch)</li>
<li>TinyRAM (<a href="https://github.com/pepper-project/tinyram">link</a>; also included with Buffet and as a git submodule in our latest development branch)</li>
</ul>
</div>
</div>
<p>HOWTOs are included with all of the source
code.</p>
<p>Please contact srinath at cs dot utexas dot edu for questions, updates, and bug
fixes.</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="funding">
<div class="content">
<div class="descriptive">
<h2>Funding and support</h2>
<p>We are grateful for the support of:</p>
<ul>
<li>DARPA (under award HR0011-20-2-0022)</li>
<li>the Air Force Office of Scientific Research (under
Young Investigator award FA9550-10-1-0073 and grant FA9550-15-1-0302)
</li>
<li>the National Science Foundation
(under CAREER award 1055057, FIA grant 1040083, CNS-1423249, and CNS-1514422)</li>
<li>the Office of Naval Research (under grants N00014-16-1-2154 and N00014-14-1-0469)</li>
<li>the Sloan Foundation (under a Sloan Fellowship)</li>
<li>Intel Corporation (under an Early Career Faculty Award)</li>
</ul>
<p>The opinions and findings are the
researchers’ alone.</p>
</div>
</div>
</div>
<div class="my-tab-pane active" id="contact">
<div class="content">
<div class="descriptive">
<p>Please get in touch with comments, questions,
etc.</p>
<p>Our email alias is pepper@pepper-project.org.</p>
</div>