2,266 research outputs found
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of
machine learning using quantum computers. We describe the main results known
for three models of learning: exact learning from membership queries, and
Probably Approximately Correct (PAC) and agnostic learning from classical or
quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation.
This version will appear as Complexity Theory Column in SIGACT News in June
2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a
referenc
On the Usability of Probably Approximately Correct Implication Bases
We revisit the notion of probably approximately correct implication bases
from the literature and present a first formulation in the language of formal
concept analysis, with the goal to investigate whether such bases represent a
suitable substitute for exact implication bases in practical use-cases. To this
end, we quantitatively examine the behavior of probably approximately correct
implication bases on artificial and real-world data sets and compare their
precision and recall with respect to their corresponding exact implication
bases. Using a small example, we also provide qualitative insight that
implications from probably approximately correct bases can still represent
meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph
Testing probability distributions underlying aggregated data
In this paper, we analyze and study a hybrid model for testing and learning
probability distributions. Here, in addition to samples, the testing algorithm
is provided with one of two different types of oracles to the unknown
distribution over . More precisely, we define both the dual and
cumulative dual access models, in which the algorithm can both sample from
and respectively, for any ,
- query the probability mass (query access); or
- get the total mass of , i.e. (cumulative
access)
These two models, by generalizing the previously studied sampling and query
oracle models, allow us to bypass the strong lower bounds established for a
number of problems in these settings, while capturing several interesting
aspects of these problems -- and providing new insight on the limitations of
the models. Finally, we show that while the testing algorithms can be in most
cases strictly more efficient, some tasks remain hard even with this additional
power
Quantum algorithms for highly non-linear Boolean functions
Attempts to separate the power of classical and quantum models of computation
have a long history. The ultimate goal is to find exponential separations for
computational problems. However, such separations do not come a dime a dozen:
while there were some early successes in the form of hidden subgroup problems
for abelian groups--which generalize Shor's factoring algorithm perhaps most
faithfully--only for a handful of non-abelian groups efficient quantum
algorithms were found. Recently, problems have gotten increased attention that
seek to identify hidden sub-structures of other combinatorial and algebraic
objects besides groups. In this paper we provide new examples for exponential
separations by considering hidden shift problems that are defined for several
classes of highly non-linear Boolean functions. These so-called bent functions
arise in cryptography, where their property of having perfectly flat Fourier
spectra on the Boolean hypercube gives them resilience against certain types of
attack. We present new quantum algorithms that solve the hidden shift problems
for several well-known classes of bent functions in polynomial time and with a
constant number of queries, while the classical query complexity is shown to be
exponential. Our approach uses a technique that exploits the duality between
bent functions and their Fourier transforms.Comment: 15 pages, 1 figure, to appear in Proceedings of the 21st Annual
ACM-SIAM Symposium on Discrete Algorithms (SODA'10). This updated version of
the paper contains a new exponential separation between classical and quantum
query complexit
Online Learning of Noisy Data with Kernels
We study online learning when individual instances are corrupted by
adversarially chosen random noise. We assume the noise distribution is unknown,
and may change over time with no restriction other than having zero mean and
bounded variance. Our technique relies on a family of unbiased estimators for
non-linear functions, which may be of independent interest. We show that a
variant of online gradient descent can learn functions in any dot-product
(e.g., polynomial) or Gaussian kernel space with any analytic convex loss
function. Our variant uses randomized estimates that need to query a random
number of noisy copies of each instance, where with high probability this
number is upper bounded by a constant. Allowing such multiple queries cannot be
avoided: Indeed, we show that online learning is in general impossible when
only one noisy copy of each instance can be accessed.Comment: This is a full version of the paper appearing in the 23rd
International Conference on Learning Theory (COLT 2010
Stacco: Differentially Analyzing Side-Channel Traces for Detecting SSL/TLS Vulnerabilities in Secure Enclaves
Intel Software Guard Extension (SGX) offers software applications enclave to
protect their confidentiality and integrity from malicious operating systems.
The SSL/TLS protocol, which is the de facto standard for protecting
transport-layer network communications, has been broadly deployed for a secure
communication channel. However, in this paper, we show that the marriage
between SGX and SSL may not be smooth sailing.
Particularly, we consider a category of side-channel attacks against SSL/TLS
implementations in secure enclaves, which we call the control-flow inference
attacks. In these attacks, the malicious operating system kernel may perform a
powerful man-in-the-kernel attack to collect execution traces of the enclave
programs at page, cacheline, or branch level, while positioning itself in the
middle of the two communicating parties. At the center of our work is a
differential analysis framework, dubbed Stacco, to dynamically analyze the
SSL/TLS implementations and detect vulnerabilities that can be exploited as
decryption oracles. Surprisingly, we found exploitable vulnerabilities in the
latest versions of all the SSL/TLS libraries we have examined.
To validate the detected vulnerabilities, we developed a man-in-the-kernel
adversary to demonstrate Bleichenbacher attacks against the latest OpenSSL
library running in the SGX enclave (with the help of Graphene) and completely
broke the PreMasterSecret encrypted by a 4096-bit RSA public key with only
57286 queries. We also conducted CBC padding oracle attacks against the latest
GnuTLS running in Graphene-SGX and an open-source SGX-implementation of mbedTLS
(i.e., mbedTLS-SGX) that runs directly inside the enclave, and showed that it
only needs 48388 and 25717 queries, respectively, to break one block of AES
ciphertext. Empirical evaluation suggests these man-in-the-kernel attacks can
be completed within 1 or 2 hours.Comment: CCS 17, October 30-November 3, 2017, Dallas, TX, US
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