5 research outputs found
A New Upperbound for the Oblivious Transfer Capacity of Discrete Memoryless Channels
We derive a new upper bound on the string oblivious transfer capacity of
discrete memoryless channels. The main tool we use is the tension region of a
pair of random variables introduced in Prabhakaran and Prabhakaran (2014) where
it was used to derive upper bounds on rates of secure sampling in the source
model. In this paper, we consider secure computation of string oblivious
transfer in the channel model. Our bound is based on a monotonicity property of
the tension region in the channel model. We show that our bound strictly
improves upon the upper bound of Ahlswede and Csisz\'ar (2013).Comment: 7 pages, 3 figures, extended version of submission to IEEE
Information Theory Workshop, 201
An Elementary Completeness Proof for Secure Two-Party Computation Primitives
In the secure two-party computation problem, two parties wish to compute a
(possibly randomized) function of their inputs via an interactive protocol,
while ensuring that neither party learns more than what can be inferred from
only their own input and output. For semi-honest parties and
information-theoretic security guarantees, it is well-known that, if only
noiseless communication is available, only a limited set of functions can be
securely computed; however, if interaction is also allowed over general
communication primitives (multi-input/output channels), there are "complete"
primitives that enable any function to be securely computed. The general set of
complete primitives was characterized recently by Maji, Prabhakaran, and
Rosulek leveraging an earlier specialized characterization by Kilian. Our
contribution in this paper is a simple, self-contained, alternative derivation
using elementary information-theoretic tools.Comment: 6 pages, extended version of ITW 2014 pape
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