Water vapor (WV) is a vital basis of water and energy cycles varies with space time. When researching the variations moisture in atmosphere, it intuitive to think about total WV atmosphere column, precipitable (PW). It an element that needs high-altitude observations. A surface quantity, pressure (SVP), has close relationship PW because internal physical linkage between them. The stability thei...

The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of latticebased cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and ...

Abstract. The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since ov...

In this paper we introduce a new lattice problem, the subspace avoiding problem (Sap). We describe a probabilistic single exponential time algorithm for Sap for arbitrary `p norms. We also describe polynomial time reductions for four classical problems from the geometry of numbers, the shortest vector problem (Svp), the closest vector problem (Cvp), the successive minima problem (Smp), and the ...

Using density functional and Monte Carlo methods, we have studied the properties of Ne adsorbed on a Cs surface, focusing on the region at and near saturated vapor pressure (SVP). In the case of Ne/Rb, the experimental data of Hess, Sabatini, and Chan are consistent with the calculations based on an ab initio fluid-substrate potential, while in the Ne/Cs case there is indication that the potent...

Lattice-based cryptography is one of the candidates in the area of post-quantum cryptography. Cryptographic schemes with security reductions to hard lattice problems (like the Shortest Vector Problem SVP) offer an alternative to recent number theory-based schemes. In order to guarantee asymptotic efficiency, most lattice-based schemes are instantiated using polynomial rings over integers. These...

We write A ≤T B to denote that A is Turing-reducible to B; A is Turing-reducible to a problem B if given an oracle for B, one can compute answers to A. In this case we will show taht if we can compute correct answers for CV Pγ , we can use this to compute the γ-shortest vector of some fixed lattice. Note that the decision formulation of CV P is NP-hard while (the natural decision version of) SV...

We prove the following quantitative hardness results for the Shortest Vector Problem in the `p norm (SVPp), where n is the rank of the input lattice. 1. For “almost all” p > p0 ≈ 2.1397, there no 2p -time algorithm for SVPp for some explicit constant Cp > 0 unless the (randomized) Strong Exponential Time Hypothesis (SETH) is false. 2. For any p > 2, there is no 2-time algorithm for SVPp unless ...