2,223 research outputs found
Parallelization of the Wolff Single-Cluster Algorithm
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have reached the speedup about 1.79 times on two processors and about 2.67 times on four processors, as compared to the serial code. According to our estimation, the speedup about three times on four processors is reachable for the O(n) models with n ≥ 2. Furthermore, the application of the developed OpenMP code allows us to simulate larger lattices due to greater operative (shared) memory available
Pseudorandom States, Non-Cloning Theorems and Quantum Money
We propose the concept of pseudorandom states and study their constructions,
properties, and applications. Under the assumption that quantum-secure one-way
functions exist, we present concrete and efficient constructions of
pseudorandom states. The non-cloning theorem plays a central role in our
study---it motivates the proper definition and characterizes one of the
important properties of pseudorandom quantum states. Namely, there is no
efficient quantum algorithm that can create more copies of the state from a
given number of pseudorandom states. As the main application, we prove that any
family of pseudorandom states naturally gives rise to a private-key quantum
money scheme.Comment: 20 page
Random Oracles in a Quantum World
The interest in post-quantum cryptography - classical systems that remain
secure in the presence of a quantum adversary - has generated elegant proposals
for new cryptosystems. Some of these systems are set in the random oracle model
and are proven secure relative to adversaries that have classical access to the
random oracle. We argue that to prove post-quantum security one needs to prove
security in the quantum-accessible random oracle model where the adversary can
query the random oracle with quantum states.
We begin by separating the classical and quantum-accessible random oracle
models by presenting a scheme that is secure when the adversary is given
classical access to the random oracle, but is insecure when the adversary can
make quantum oracle queries. We then set out to develop generic conditions
under which a classical random oracle proof implies security in the
quantum-accessible random oracle model. We introduce the concept of a
history-free reduction which is a category of classical random oracle
reductions that basically determine oracle answers independently of the history
of previous queries, and we prove that such reductions imply security in the
quantum model. We then show that certain post-quantum proposals, including ones
based on lattices, can be proven secure using history-free reductions and are
therefore post-quantum secure. We conclude with a rich set of open problems in
this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a
related paper by Boneh and Zhandr
Pseudorandom Number Generators and the Square Site Percolation Threshold
A select collection of pseudorandom number generators is applied to a Monte
Carlo study of the two dimensional square site percolation model. A generator
suitable for high precision calculations is identified from an application
specific test of randomness. After extended computation and analysis, an
ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation
threshold.Comment: 11 pages, 6 figure
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory
The present survey reports on the state of the art of the different
cryptographic functionalities built upon the ring learning with errors problem
and its interplay with several classical problems in algebraic number theory.
The survey is based to a certain extent on an invited course given by the
author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other
authors/ comment of the author: quotation has been added to Theorem 5.
Distribution of periodic trajectories of Anosov C-system
The hyperbolic Anosov C-systems have a countable set of everywhere dense
periodic trajectories which have been recently used to generate pseudorandom
numbers. The asymptotic distribution of periodic trajectories of C-systems with
periods less than a given number is well known, but a deviation of this
distribution from its asymptotic behaviour is less known. Using fast
algorithms, we are studying the exact distribution of periodic trajectories and
their deviation from asymptotic behaviour for hyperbolic C-systems which are
defined on high dimensional tori and are used for Monte-Carlo simulations. A
particular C-system which we consider in this article is the one which was
implemented in the MIXMAX generator of pseudorandom numbers. The generator has
the best combination of speed, reasonable size of the state, and availability
for implementing the parallelization and is currently available generator in
the ROOT and CLHEP software packages at CERN.Comment: 22 pages, 14 figure
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