1,650 research outputs found
Cryptography with Auxiliary Input and Trapdoor from Constant-Noise LPN
Dodis, Kalai and Lovett (STOC 2009) initiated the study of the Learning Parity with Noise (LPN) problem with (static) exponentially hard-to-invert auxiliary input. In particular, they showed that under a new assumption (called Learning Subspace with Noise) the above is quasi-polynomially hard in the high (polynomially close to uniform) noise regime.
Inspired by the ``sampling from subspace\u27\u27 technique by Yu (eprint 2009 / 467) and Goldwasser et al. (ITCS 2010), we show that standard LPN can work in a mode (reducible to itself) where the constant-noise LPN (by sampling its matrix from a random subspace) is robust against sub-exponentially hard-to-invert auxiliary input with comparable security to the underlying LPN. Plugging this into the framework of [DKL09], we obtain the same applications as considered in [DKL09] (i.e., CPA/CCA secure symmetric encryption schemes, average-case obfuscators, reusable and robust extractors) with resilience to a more general class of leakages, improved efficiency and better security under standard assumptions.
As a main contribution, under constant-noise LPN with certain sub-exponential hardness (i.e., for secret size ) we obtain a variant of the LPN with security on poly-logarithmic entropy sources, which in turn implies CPA/CCA secure public-key encryption (PKE) schemes and oblivious transfer (OT) protocols. Prior to this, basing PKE and OT on constant-noise LPN had been an open problem since Alekhnovich\u27s work (FOCS 2003)
Regularized Optimal Transport and the Rot Mover's Distance
This paper presents a unified framework for smooth convex regularization of
discrete optimal transport problems. In this context, the regularized optimal
transport turns out to be equivalent to a matrix nearness problem with respect
to Bregman divergences. Our framework thus naturally generalizes a previously
proposed regularization based on the Boltzmann-Shannon entropy related to the
Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We
call the regularized optimal transport distance the rot mover's distance in
reference to the classical earth mover's distance. We develop two generic
schemes that we respectively call the alternate scaling algorithm and the
non-negative alternate scaling algorithm, to compute efficiently the
regularized optimal plans depending on whether the domain of the regularizer
lies within the non-negative orthant or not. These schemes are based on
Dykstra's algorithm with alternate Bregman projections, and further exploit the
Newton-Raphson method when applied to separable divergences. We enhance the
separable case with a sparse extension to deal with high data dimensions. We
also instantiate our proposed framework and discuss the inherent specificities
for well-known regularizers and statistical divergences in the machine learning
and information geometry communities. Finally, we demonstrate the merits of our
methods with experiments using synthetic data to illustrate the effect of
different regularizers and penalties on the solutions, as well as real-world
data for a pattern recognition application to audio scene classification
Toward Synthesis of Network Updates
Updates to network configurations are notoriously difficult to implement
correctly. Even if the old and new configurations are correct, the update
process can introduce transient errors such as forwarding loops, dropped
packets, and access control violations. The key factor that makes updates
difficult to implement is that networks are distributed systems with hundreds
or even thousands of nodes, but updates must be rolled out one node at a time.
In networks today, the task of determining a correct sequence of updates is
usually done manually -- a tedious and error-prone process for network
operators. This paper presents a new tool for synthesizing network updates
automatically. The tool generates efficient updates that are guaranteed to
respect invariants specified by the operator. It works by navigating through
the (restricted) space of possible solutions, learning from counterexamples to
improve scalability and optimize performance. We have implemented our tool in
OCaml, and conducted experiments showing that it scales to networks with a
thousand switches and tens of switches updating.Comment: In Proceedings SYNT 2013, arXiv:1403.726
Extremal problems in logic programming and stable model computation
We study the following problem: given a class of logic programs C, determine
the maximum number of stable models of a program from C. We establish the
maximum for the class of all logic programs with at most n clauses, and for the
class of all logic programs of size at most n. We also characterize the
programs for which the maxima are attained. We obtain similar results for the
class of all disjunctive logic programs with at most n clauses, each of length
at most m, and for the class of all disjunctive logic programs of size at most
n. Our results on logic programs have direct implication for the design of
algorithms to compute stable models. Several such algorithms, similar in spirit
to the Davis-Putnam procedure, are described in the paper. Our results imply
that there is an algorithm that finds all stable models of a program with n
clauses after considering the search space of size O(3^{n/3}) in the worst
case. Our results also provide some insights into the question of
representability of families of sets as families of stable models of logic
programs
A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM
Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a
number of applications, in particular, as an essential building block for
two-party and multi-party computation. We construct a round-optimal (2 rounds)
universally composable (UC) protocol for oblivious transfer secure against
active adaptive adversaries from any OW-CPA secure public-key encryption scheme
with certain properties in the random oracle model (ROM). In terms of
computation, our protocol only requires the generation of a public/secret-key
pair, two encryption operations and one decryption operation, apart from a few
calls to the random oracle. In~terms of communication, our protocol only
requires the transfer of one public-key, two ciphertexts, and three binary
strings of roughly the same size as the message. Next, we show how to
instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE,
and CDH assumptions. Our instantiations based on the low noise LPN, McEliece,
and QC-MDPC assumptions are the first UC-secure OT protocols based on coding
assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3)
low communication and computational complexities. Previous results in this
setting only achieved static security and used costly cut-and-choose
techniques.Our instantiation based on CDH achieves adaptive security at the
small cost of communicating only two more group elements as compared to the
gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which
only achieves static security in the ROM
Learning with Errors is easy with quantum samples
Learning with Errors is one of the fundamental problems in computational
learning theory and has in the last years become the cornerstone of
post-quantum cryptography. In this work, we study the quantum sample complexity
of Learning with Errors and show that there exists an efficient quantum
learning algorithm (with polynomial sample and time complexity) for the
Learning with Errors problem where the error distribution is the one used in
cryptography. While our quantum learning algorithm does not break the LWE-based
encryption schemes proposed in the cryptography literature, it does have some
interesting implications for cryptography: first, when building an LWE-based
scheme, one needs to be careful about the access to the public-key generation
algorithm that is given to the adversary; second, our algorithm shows a
possible way for attacking LWE-based encryption by using classical samples to
approximate the quantum sample state, since then using our quantum learning
algorithm would solve LWE
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