140 research outputs found
Optimal Randomizer Efficiency in the Bounded-Storage Model
In the bounded-storage model for information-theoretically secure encryption and key-agreement one can prove the security of a cipher based on the sole assumption that the adversary's storage capacity is bounded, say by bits, even if her computational power is unlimited. Assume that a random -bit string is either publicly available (e.g., the signal of a deep-space radio source) or broadcast by one of the legitimate parties. If ), or the adversary was assumed to be able to store only actual bits of rather than arbitrary bits of information about , or the adversary received a non-negligible amount of information about . In this paper we prove the first non-restricted security result in the bounded-storage model: is short, is very long, and needs to be only moderately larger than . In fact, can be arbitrarily close to and hence the storage bound is essentially optimal. The security can be proved also if is not uniformly random, provided that the min-entropy of is sufficiently greater than $s
Fast and Efficient Compressive Sensing using Structurally Random Matrices
This paper introduces a new framework of fast and efficient sensing matrices
for practical compressive sensing, called Structurally Random Matrix (SRM). In
the proposed framework, we pre-randomize a sensing signal by scrambling its
samples or flipping its sample signs and then fast-transform the randomized
samples and finally, subsample the transform coefficients as the final sensing
measurements. SRM is highly relevant for large-scale, real-time compressive
sensing applications as it has fast computation and supports block-based
processing. In addition, we can show that SRM has theoretical sensing
performance comparable with that of completely random sensing matrices.
Numerical simulation results verify the validity of the theory as well as
illustrate the promising potentials of the proposed sensing framework
Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function
We give an exponential separation between one-way quantum and classical
communication complexity for a Boolean function. Earlier such a separation was
known only for a relation. A very similar result was obtained earlier but
independently by Kerenidis and Raz [KR06]. Our version of the result gives an
example in the bounded storage model of cryptography, where the key is secure
if the adversary has a certain amount of classical storage, but is completely
insecure if he has a similar amount of quantum storage.Comment: 8 pages, no figure
Sampling of min-entropy relative to quantum knowledge
Let X_1, ..., X_n be a sequence of n classical random variables and consider
a sample of r positions selected at random. Then, except with (exponentially in
r) small probability, the min-entropy of the sample is not smaller than,
roughly, a fraction r/n of the total min-entropy of all positions X_1, ...,
X_n, which is optimal. Here, we show that this statement, originally proven by
Vadhan [LNCS, vol. 2729, Springer, 2003] for the purely classical case, is
still true if the min-entropy is measured relative to a quantum system. Because
min-entropy quantifies the amount of randomness that can be extracted from a
given random variable, our result can be used to prove the soundness of locally
computable extractors in a context where side information might be
quantum-mechanical. In particular, it implies that key agreement in the
bounded-storage model (using a standard sample-and-hash protocol) is fully
secure against quantum adversaries, thus solving a long-standing open problem.Comment: 48 pages, late
On the Power of Multiple Anonymous Messages
An exciting new development in differential privacy is the shuffled model, in
which an anonymous channel enables non-interactive, differentially private
protocols with error much smaller than what is possible in the local model,
while relying on weaker trust assumptions than in the central model. In this
paper, we study basic counting problems in the shuffled model and establish
separations between the error that can be achieved in the single-message
shuffled model and in the shuffled model with multiple messages per user.
For the problem of frequency estimation for users and a domain of size
, we obtain:
- A nearly tight lower bound of on the error in the single-message shuffled model. This implies
that the protocols obtained from the amplification via shuffling work of
Erlingsson et al. (SODA 2019) and Balle et al. (Crypto 2019) are essentially
optimal for single-message protocols. A key ingredient in the proof is a lower
bound on the error of locally-private frequency estimation in the low-privacy
(aka high ) regime.
- Protocols in the multi-message shuffled model with
bits of communication per user and error, which provide an
exponential improvement on the error compared to what is possible with
single-message algorithms.
For the related selection problem on a domain of size , we prove:
- A nearly tight lower bound of on the number of users in the
single-message shuffled model. This significantly improves on the
lower bound obtained by Cheu et al. (Eurocrypt 2019), and
when combined with their -error multi-message protocol,
implies the first separation between single-message and multi-message protocols
for this problem.Comment: 70 pages, 2 figures, 3 table
Online Local Differential Private Quantile Inference via Self-normalization
Based on binary inquiries, we developed an algorithm to estimate population
quantiles under Local Differential Privacy (LDP). By self-normalizing, our
algorithm provides asymptotically normal estimation with valid inference,
resulting in tight confidence intervals without the need for nuisance
parameters to be estimated. Our proposed method can be conducted fully online,
leading to high computational efficiency and minimal storage requirements with
space. We also proved an optimality result by an elegant
application of one central limit theorem of Gaussian Differential Privacy (GDP)
when targeting the frequently encountered median estimation problem. With
mathematical proof and extensive numerical testing, we demonstrate the validity
of our algorithm both theoretically and experimentally
Simple extractors via constructions of cryptographic pseudo-random generators
Trevisan has shown that constructions of pseudo-random generators from hard
functions (the Nisan-Wigderson approach) also produce extractors. We show that
constructions of pseudo-random generators from one-way permutations (the
Blum-Micali-Yao approach) can be used for building extractors as well. Using
this new technique we build extractors that do not use designs and
polynomial-based error-correcting codes and that are very simple and efficient.
For example, one extractor produces each output bit separately in
time. These extractors work for weak sources with min entropy , for
arbitrary constant , have seed length , and their
output length is .Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small
corrections, some comments and references adde
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