272,923 research outputs found
An Improved BKW Algorithm for LWE with Applications to Cryptography and Lattices
In this paper, we study the Learning With Errors problem and its binary
variant, where secrets and errors are binary or taken in a small interval. We
introduce a new variant of the Blum, Kalai and Wasserman algorithm, relying on
a quantization step that generalizes and fine-tunes modulus switching. In
general this new technique yields a significant gain in the constant in front
of the exponent in the overall complexity. We illustrate this by solving p
within half a day a LWE instance with dimension n = 128, modulus ,
Gaussian noise and binary secret, using
samples, while the previous best result based on BKW claims a time
complexity of with samples for the same parameters. We then
introduce variants of BDD, GapSVP and UniqueSVP, where the target point is
required to lie in the fundamental parallelepiped, and show how the previous
algorithm is able to solve these variants in subexponential time. Moreover, we
also show how the previous algorithm can be used to solve the BinaryLWE problem
with n samples in subexponential time . This
analysis does not require any heuristic assumption, contrary to other algebraic
approaches; instead, it uses a variant of an idea by Lyubashevsky to generate
many samples from a small number of samples. This makes it possible to
asymptotically and heuristically break the NTRU cryptosystem in subexponential
time (without contradicting its security assumption). We are also able to solve
subset sum problems in subexponential time for density , which is of
independent interest: for such density, the previous best algorithm requires
exponential time. As a direct application, we can solve in subexponential time
the parameters of a cryptosystem based on this problem proposed at TCC 2010.Comment: CRYPTO 201
Deterministic Construction of Binary, Bipolar and Ternary Compressed Sensing Matrices
In this paper we establish the connection between the Orthogonal Optical
Codes (OOC) and binary compressed sensing matrices. We also introduce
deterministic bipolar RIP fulfilling matrices of order
such that . The columns of these matrices are binary BCH code vectors where the
zeros are replaced by -1. Since the RIP is established by means of coherence,
the simple greedy algorithms such as Matching Pursuit are able to recover the
sparse solution from the noiseless samples. Due to the cyclic property of the
BCH codes, we show that the FFT algorithm can be employed in the reconstruction
methods to considerably reduce the computational complexity. In addition, we
combine the binary and bipolar matrices to form ternary sensing matrices
( elements) that satisfy the RIP condition.Comment: The paper is accepted for publication in IEEE Transaction on
Information Theor
Noisy population recovery in polynomial time
In the noisy population recovery problem of Dvir et al., the goal is to learn
an unknown distribution on binary strings of length from noisy samples.
For some parameter , a noisy sample is generated by flipping
each coordinate of a sample from independently with probability
. We assume an upper bound on the size of the support of the
distribution, and the goal is to estimate the probability of any string to
within some given error . It is known that the algorithmic
complexity and sample complexity of this problem are polynomially related to
each other.
We show that for , the sample complexity (and hence the algorithmic
complexity) is bounded by a polynomial in , and
improving upon the previous best result of due to Lovett and Zhang.
Our proof combines ideas from Lovett and Zhang with a \emph{noise attenuated}
version of M\"{o}bius inversion. In turn, the latter crucially uses the
construction of \emph{robust local inverse} due to Moitra and Saks
Complexity-Aware Assignment of Latent Values in Discriminative Models for Accurate Gesture Recognition
Many of the state-of-the-art algorithms for gesture recognition are based on
Conditional Random Fields (CRFs). Successful approaches, such as the
Latent-Dynamic CRFs, extend the CRF by incorporating latent variables, whose
values are mapped to the values of the labels. In this paper we propose a novel
methodology to set the latent values according to the gesture complexity. We
use an heuristic that iterates through the samples associated with each label
value, stimating their complexity. We then use it to assign the latent values
to the label values. We evaluate our method on the task of recognizing human
gestures from video streams. The experiments were performed in binary datasets,
generated by grouping different labels. Our results demonstrate that our
approach outperforms the arbitrary one in many cases, increasing the accuracy
by up to 10%.Comment: Conference paper published at 2016 29th SIBGRAPI, Conference on
Graphics, Patterns and Images (SIBGRAPI). 8 pages, 7 figure
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