22,365 research outputs found
Multi-Party Protocols, Information Complexity and Privacy
We introduce the new measure of Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of information-theoretic private computations. We are able to use this measure directly in the natural asynchronous message-passing peer-to-peer model and show a number of interesting properties and applications of our new notion:
the Public Information Complexity is a lower bound on the Communication Complexity and an upper bound on the Information Complexity; the difference between the Public Information Complexity and the Information Complexity provides a lower bound on the amount of randomness used in a protocol; any communication protocol can be compressed to its Public Information Cost; an explicit calculation of the zero-error Public Information Complexity of the k-party, n-bit Parity function, where a player outputs the bit-wise parity of the inputs. The latter result establishes that the amount of randomness needed for a private protocol that computes this function is Omega(n)
On the Communication Complexity of Secure Computation
Information theoretically secure multi-party computation (MPC) is a central
primitive of modern cryptography. However, relatively little is known about the
communication complexity of this primitive.
In this work, we develop powerful information theoretic tools to prove lower
bounds on the communication complexity of MPC. We restrict ourselves to a
3-party setting in order to bring out the power of these tools without
introducing too many complications. Our techniques include the use of a data
processing inequality for residual information - i.e., the gap between mutual
information and G\'acs-K\"orner common information, a new information
inequality for 3-party protocols, and the idea of distribution switching by
which lower bounds computed under certain worst-case scenarios can be shown to
apply for the general case.
Using these techniques we obtain tight bounds on communication complexity by
MPC protocols for various interesting functions. In particular, we show
concrete functions that have "communication-ideal" protocols, which achieve the
minimum communication simultaneously on all links in the network. Also, we
obtain the first explicit example of a function that incurs a higher
communication cost than the input length in the secure computation model of
Feige, Kilian and Naor (1994), who had shown that such functions exist. We also
show that our communication bounds imply tight lower bounds on the amount of
randomness required by MPC protocols for many interesting functions.Comment: 37 page
How to Securely Compute the Modulo-Two Sum of Binary Sources
In secure multiparty computation, mutually distrusting users in a network
want to collaborate to compute functions of data which is distributed among the
users. The users should not learn any additional information about the data of
others than what they may infer from their own data and the functions they are
computing. Previous works have mostly considered the worst case context (i.e.,
without assuming any distribution for the data); Lee and Abbe (2014) is a
notable exception. Here, we study the average case (i.e., we work with a
distribution on the data) where correctness and privacy is only desired
asymptotically.
For concreteness and simplicity, we consider a secure version of the function
computation problem of K\"orner and Marton (1979) where two users observe a
doubly symmetric binary source with parameter p and the third user wants to
compute the XOR. We show that the amount of communication and randomness
resources required depends on the level of correctness desired. When zero-error
and perfect privacy are required, the results of Data et al. (2014) show that
it can be achieved if and only if a total rate of 1 bit is communicated between
every pair of users and private randomness at the rate of 1 is used up. In
contrast, we show here that, if we only want the probability of error to vanish
asymptotically in block length, it can be achieved by a lower rate (binary
entropy of p) for all the links and for private randomness; this also
guarantees perfect privacy. We also show that no smaller rates are possible
even if privacy is only required asymptotically.Comment: 6 pages, 1 figure, extended version of submission to IEEE Information
Theory Workshop, 201
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Finite state verifiers with constant randomness
We give a new characterization of as the class of languages
whose members have certificates that can be verified with small error in
polynomial time by finite state machines that use a constant number of random
bits, as opposed to its conventional description in terms of deterministic
logarithmic-space verifiers. It turns out that allowing two-way interaction
with the prover does not change the class of verifiable languages, and that no
polynomially bounded amount of randomness is useful for constant-memory
computers when used as language recognizers, or public-coin verifiers. A
corollary of our main result is that the class of outcome problems
corresponding to O(log n)-space bounded games of incomplete information where
the universal player is allowed a constant number of moves equals NL.Comment: 17 pages. An improved versio
A Shannon Approach to Secure Multi-party Computations
In secure multi-party computations (SMC), parties wish to compute a function
on their private data without revealing more information about their data than
what the function reveals. In this paper, we investigate two Shannon-type
questions on this problem. We first consider the traditional one-shot model for
SMC which does not assume a probabilistic prior on the data. In this model,
private communication and randomness are the key enablers to secure computing,
and we investigate a notion of randomness cost and capacity. We then move to a
probabilistic model for the data, and propose a Shannon model for discrete
memoryless SMC. In this model, correlations among data are the key enablers for
secure computing, and we investigate a notion of dependency which permits the
secure computation of a function. While the models and questions are general,
this paper focuses on summation functions, and relies on polar code
constructions
Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy
We consider a scenario involving computations over a massive dataset stored
distributedly across multiple workers, which is at the core of distributed
learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework
to simultaneously provide (1) resiliency against stragglers that may prolong
computations; (2) security against Byzantine (or malicious) workers that
deliberately modify the computation for their benefit; and (3)
(information-theoretic) privacy of the dataset amidst possible collusion of
workers. LCC, which leverages the well-known Lagrange polynomial to create
computation redundancy in a novel coded form across workers, can be applied to
any computation scenario in which the function of interest is an arbitrary
multivariate polynomial of the input dataset, hence covering many computations
of interest in machine learning. LCC significantly generalizes prior works to
go beyond linear computations. It also enables secure and private computing in
distributed settings, improving the computation and communication efficiency of
the state-of-the-art. Furthermore, we prove the optimality of LCC by showing
that it achieves the optimal tradeoff between resiliency, security, and
privacy, i.e., in terms of tolerating the maximum number of stragglers and
adversaries, and providing data privacy against the maximum number of colluding
workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the
conventional uncoded implementation of distributed least-squares linear
regression by up to , and also achieves a
- speedup over the state-of-the-art straggler
mitigation strategies
- …