54 research outputs found
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
Efficient One-Way Secret-Key Agreement and Private Channel Coding via Polarization
We introduce explicit schemes based on the polarization phenomenon for the
tasks of one-way secret key agreement from common randomness and private
channel coding. For the former task, we show how to use common randomness and
insecure one-way communication to obtain a strongly secure key such that the
key construction has a complexity essentially linear in the blocklength and the
rate at which the key is produced is optimal, i.e., equal to the one-way
secret-key rate. For the latter task, we present a private channel coding
scheme that achieves the secrecy capacity using the condition of strong secrecy
and whose encoding and decoding complexity are again essentially linear in the
blocklength.Comment: 18.1 pages, 2 figures, 2 table
Quantum state merging and negative information
We consider a quantum state shared between many distant locations, and define
a quantum information processing primitive, state merging, that optimally
merges the state into one location. As announced in [Horodecki, Oppenheim,
Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is
the conditional entropy if classical communication is free. Since this quantity
can be negative, and the state merging rate measures partial quantum
information, we find that quantum information can be negative. The classical
communication rate also has a minimum rate: a certain quantum mutual
information. State merging enabled one to solve a number of open problems:
distributed quantum data compression, quantum coding with side information at
the decoder and sender, multi-party entanglement of assistance, and the
capacity of the quantum multiple access channel. It also provides an
operational proof of strong subadditivity. Here, we give precise definitions
and prove these results rigorously.Comment: 23 pages, 3 figure
Precise evaluation of leaked information with universal2 privacy amplification in the presence of quantum attacker
We treat secret key extraction when the eavesdropper has correlated quantum
states. We propose quantum privacy amplification theorems different from
Renner's, which are based on quantum conditional R\'{e}nyi entropy of order
1+s. Using those theorems, we derive an exponential decreasing rate for leaked
information and the asymptotic equivocation rate, which have not been derived
hitherto in the quantum setting
Optimization of System Performance for DVC Applications with Energy Constraints over Ad Hoc Networks
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