Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.Comment: submitted to Transaction on Information Theor

Thermophysical properties of liquid carbon dioxide under shock compressions: Quantum molecular dynamic simulations

Quantum molecular dynamic simulations are introduced to study the dynamical, electrical, and optical properties of carbon dioxide under dynamic compressions. The principal Hugoniot derived from the calculated equation of states is demonstrated to be well accordant with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions, and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are also theoretically predicted along the Hugoniot

On the Geometric Ergodicity of Metropolis-Hastings Algorithms for Lattice Gaussian Sampling

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods is adapted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the restriction suffered by the default Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, tries to establish a Markov chain through an independent proposal distribution. We show that the Markov chain arising from the independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, leading to a predictable mixing time. In order to further exploit the convergence potential, a symmetric Metropolis-Klein (SMK) algorithm is proposed. It is proven that the Markov chain induced by the SMK algorithm is geometrically ergodic, where a reasonable selection of the initial state is capable to enhance the convergence performance.Comment: Submitted to IEEE Transactions on Information Theor

High performance deep packet inspection on multi-core platform

Deep packet inspection (DPI) provides the ability to perform quality of service (QoS) and Intrusion Detection on network packets. But since the explosive growth of Internet, performance and scalability issues have been raised due to the gap between network and end-system speeds. This article describles how a desirable DPI system with multi-gigabits throughput and good scalability should be like by exploiting parallelism on network interface card, network stack and user applications. Connection-based parallelism, affinity-based scheduling and lock-free data structure are the main technologies introduced to alleviate the performance and scalability issues. A common DPI application L7-Filter is used as an example to illustrate the applicaiton level parallelism

The equation of state and nonmetal-metal transition of benzene under shock compression

We employ quantum molecular dynamic simulations to investigate the behavior of benzene under shock conditions. The principal Hugoniot derived from the equation of state is determined. We compare our firs-principles results with available experimental data and provide predictions of chemical reactions for shocked benzene. The decomposition of benzene is found under the pressure of 11 GPa. The nonmetal-metal transition, which is associated with the rapid C-H bond breaking and the formation of atomic and molecular hydrogen, occurs under the pressure around 50 GPa. Additionally, optical properties are also studied.Comment: 12 pages, 5 figure