1,231 research outputs found
Shortest vector from lattice sieving: A few dimensions for free
Asymptotically, the best known algorithms for solving the Shortest Vector Problem (SVP) in a lattice of dimension n are sieve algorithms, which have heuristic complexity estimates ranging from (4/3)n+o(n) down to (3/2)n/2+o(n) when Locality Sensitive Hashing techniques are used. Sieve algorithms are however outperformed by pruned enumeration algorithms in practice by several orders of magnitude, despite the larger super-exponential asymptotical complexity 2Î(n log n) of the latter. In this work, we show a concrete improvement of sieve-type algorithms. Precisely, we show that a few calls to the sieve algorithm in lattices of dimension less than n - d solves SVP in dimension n, where d = Î(n/ log n). Although our improvement is only sub-exponential, its practical effect in relevant dimensions is quite significant. We implemented it over a simple sieve algorithm with (4/3)n+o(n) complexity, and it outperforms the best sieve algorithms from the literature by a factor of 10 in dimensions 7080. It performs less than an order of magnitude slower than pruned enumeration in the same range. By design, this improvement can also be applied to most other variants of sieve algorithms, including LSH sieve algorithms and tuple-sieve algorithms. In this light, we may expect sieve-techniques to outperform pruned enumeration in practice in the near future
Understanding Nanopore Window Distortions in the Reversible Molecular Valve Zeolite RHO
Molecular valves are becoming popular for potential biomedical applications.
However, little is known concerning their performance in energy and
environmental areas. Zeolite RHO shows unique pore deformations upon changes in
hydration, cation siting, cation type, or temperature-pressure conditions. By
varying the level of distortion of double eight-rings, it is possible to
control the adsorption properties, which confer a molecular valve behavior to
this material. We have employed interatomic potentials-based simulations to
obtain a detailed atomistic view of the structural distortion mechanisms of
zeolite RHO, in contrast with the averaged and space group restricted
information provided by diffraction studies. We have modeled four
aluminosilicate structures, containing Li, Na, K, Ca, and
Sr cations. The distortions of the three different zeolite rings are
coupled, and the six- and eight-membered rings are largely flexible. A large
dependence on the polarizing power of the extra-framework cations and with the
loading of water has been found for the minimum aperture of the eight-membered
rings that control the nanovalve effect. The calculated energy barriers for
moving the cations across the eight-membered rings are very high, which
explains the experimentally observed slow kinetics of the phase transition as
well as the appearance of metastable phases
Improved Pump and Jump BKZ by Sharp Simulator
The General Sieve Kernel (G6K) implemented a variety of lattice reduction algorithms based on sieving algorithms. One of the representative of these lattice reduction algorithms is Pump and jump-BKZ (pnj-BKZ) algorithm which is currently considered as the fastest lattice reduction algorithm. The pnj-BKZ is a BKZ-type lattice reduction algorithm which includes the jump strategy, and uses Pump as the SVP Oracle. Here, Pump which was also proposed in G6K, is an SVP sloving algorithm that combines progressive sieve technology and dimforfree technology. However unlike classical BKZ, there is no simulator for predicting the behavior of the pnj-BKZ algorithm when jump greater than 1, which is helpful to find a better lattice reduction strategy. There are two main differences between pnj-BKZ and the classical BKZ algorithm: one is that after pnj-BKZ performs the SVP Oracle on a certain projected sublattice, it won\u27t calling SVP Oracle for the next nearest projected sublattice. Instead, pnj-BKZ jumps to the corresponding projected sublattice after J indexs to run the algorithm for solving the SVP. By using this jump technique, the number of times that the SVP algorithm needs to be called for each round of pnj-BKZ will be reduced to about 1/J times of original. The second is that pnj-BKZ uses Pump as the SVP Oracle on the projected sublattice. Based on the BKZ2.0 simulator, we proposes a pnj-BKZ simulator by using the properties of HKZ reduction basis. Experiments show that our proposed pnj-BKZ simulator can well predicate the behavior of pnj-BKZ with jump greater than 1. Besides, we use this pnj-BKZ simulator to give the optimization strategy for choosing jump which can improve the reducing efficiency of pnj-BKZ. Our optimized pnj-BKZ is 2.9 and 2.6 times faster in solving TU LWE challenge ( n=75,alpha=0.005 ) and TU LWE challenge ( n=60,alpha=0.010 ) than G6K\u27s default LWE sloving strategy
Several Improvements on BKZ Algorithm
Lattice problem such as NTRU problem and LWE problem is widely used as the security
base of post-quantum cryptosystems. And currently doing lattice reduction by BKZ algorithm
is the most efficient way to solve it. In this paper, we give several further improvements
on BKZ algorithm, which can be used for different SVP subroutines base on both enumeration
and sieving. These improvements in combination provide a speed up of in total.
It is significant in concrete attacks. Using these new techniques, we solved the 656 dimensional
ideal lattice challenge in only 380 thread hours (also with a enumeration based SVP subroutine),
much less than the previous records (which costs 4600 thread hours in total). With these
improvements enabled, we can still simulate the new BKZ algorithm easily. One can also use this
simulator to find the blocksize strategy (and the corresponding cost) to make
of the basis (defined in section 5.2) decrease as fast as possible, which means the length of
the first basis vector decrease the fastest if we accept the GSA assumption. It is useful for analyzing
concrete attacks on lattice-based cryptography
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