Equivalent Keys in HFE, C*, and Variations

ℳultivariate uadratic public key schemes have been suggested as early as 1985 by Matsumoto and Imai as an alternative for the RSA scheme. Since then, several schemes have been proposed, for example hidden field equations, unbalanced oil and vinegar schemes, and stepwise triangular schemes. All these schemes have a rather large key space for a secure choice of parameters. Surprisingly, the question of equivalent keys has not been discussed in the open literature until recently. In this article, we show that for all basic classes mentioned above, it is possible to reduce the private – and hence the public – key space by several orders of magnitude, i.e. the size of the set of possible private and hence public keys can be reduced. For the Matsumoto–Imai scheme, we are even able to show that the reductions we found are the only ones possible, i.e. that these reductions are tight. While the theorems developed in this article are of independent interest themselves as they broaden our understanding of ℳultivariate uadratic public key systems, we see applications of our results both in cryptanalysis and in memory efficient implementations of -schemes.

Multivariate Quadratic public key schemes have been suggested back in 1985 by Matsumoto and Imai as an alternative for the RSA scheme. Since then, several other schemes have been proposed, for example Hidden Field Equations, Unbalanced Oil and Vinegar schemes, and Stepwise Triangular Schemes. All these schemes have a rather large key space for a secure choice of parameters. Surprisingly, the question of equivalent keys has not been discussed in the open literature until recently. In this article, we show that for all basic classes mentioned above, it is possible to reduce the private | and hence the public | key space by several orders of magnitude. For the Matsumoto-Imai scheme, we are even able to show that the reductions we found are the only ones possible, i.e., that these reductions are tight. While the theorems developed in this article are of independent interest themselves as they broaden our understanding of Multivariate Quadratic public key systems, we see applications of our results both in cryptanalysis and in memory e‐cient implementations of MQ-schemes.

This thesis treats different aspects of the class of Mixed-Integer Optimal Control Problems (MIOCPs). These are optimization problems that combine the difficulties of underlying dynamic processes with combinatorial decisions. Typically, these combinatorial decisions are realized as switching decisions between the system’s different operations modes. During the last decades, direct methods emerged as the state-of-the-art solvers for MIOCPs. The formulation of a valid, tight and dependable integral relaxation, i.e., the formulation of a model for fractional values, plays an important role for these direct solution methods. We give detailed insight into several relaxation approaches for MIOCPs and compare them with regard to their respective structures. In particular, these are the typical solution’s structures and properties as convexity, problem size and numerical behavior. From these structural properties, we deduce some required specifications of a solver. Additionally, the modeling and subsequent limitation of the switching process directly tackle the class-specific typical issue of chattering solutions. One of the relaxation methods for MIOCPs is the outer convexification, where the binary variables only enter affinely. For the approximation of this relaxation’s solution, we took up on the control approximation problem in integral sense derived by Sager as part of a decomposition approach for MIOCPs with affine binary controls. This problem describes the optimal approximation of fractional controls with binary controls such that the corresponding dynamic process is changed as little as possible. For the multi-dimensional problem, we developed a new heuristic, which for the first time gives a bound that only depends on the control grid and not anymore on the number of the system’s controls. For the generalization of the control approximation problem with additional constraints, we derived a tailored branch-and-bound algorithm, which is based on the properties of the Lagrangian relaxation of the one-dimensional problem. This algorithm beats state-of-the-art commercial solvers for Mixed-Integer Linear Programs (MILPs) for this special approximation problem by several orders of magnitude. Overall, we present several, partially new modeling approaches for MIOCPs together with the accompanying structural properties. On this basis, we develop new theories for the approximation of certain relaxed solutions. We discuss the efficient implementation of the resulting structure exploiting algorithms. This leads to a deeper and better understanding of MIOCPs. We show the practicability of the theoretical observations with the help of four prototypical problems. The presented methods and algorithms allow on their basis the direct development of decision support and analysis tools in practice.

The numerical evaluation of surface integrals is the most time-consuming part of the extended boundary condition method (EBCM) for calculating the T matrix. An efficient implementation of the method is presented for homogeneous particles with discrete geometric symmetries and is applied to regular polyhedral prisms of finite length. For such prisms, an efficient quadrature scheme for computing the surface integrals is developed. Exploitation of these symmetries in conjunction with the new quadrature scheme leads to a reduction in CPU time by 3 orders of magnitude from that of a general EBCM implementation with no geometry-specific adaptations. The improved quadrature scheme and the exploitation of symmetries account for, respectively, 1 and 2 orders of magnitude in the total reduction of the CPU time. Test results for scattering by rectangular parallelepipeds and hexagonal plates are shown to agree well with corresponding results obtained by use of the discrete-dipole approximation. A model application for various polyhedral prisms is presented.

The RDM-QIM algorithm has been proposed as a solution to the gain attack in QIM-based data hiding schemes. Several data hiding applications, such as broadcasting monitoring and live performance watermarking, requires a real-time multi-channel behavior. While Digital Signal Processors (DSP) have been used for implementing these schemes achieving real-time performance for audio signal processing, FPGAs offer the posibility of fully exploiting the inherent parallelism of this type of algorithms for more demanding applications. This letter presents an efficient FPGA implementation of RDM-QIM algorithm that overcomes a DSP-based implementation for more than two orders of magnitude and allows real-time multi-channel behavior.

Scientific approaches to formation and classification of the space technologies and services markets are considered in this article. The topic is highly essential during transition of the national economy of Ukraine to the innovative way of development which facilitates efficient implementation of the potential accumulated by the rocket-space industry and promotion of the space products to the world market. The rocket-space industry takes considerable place in the government policy of Ukraine determining its status as a country of high technologies in the world market. World space industry of the leading countries such as the USA, Russia, France, Germany, Japan and Canada becomes more profitable and in 2012 its income amounted to $100 bln USD. However, participants of the space technologies market are facing competition, protectionism and other specific peculiarities of the science-intensive product markets. In connection with the aforesaid, the world space technologies (ST) market represents significant scientific-technological and commercial interests for the rocket-space industry of Ukraine. Criterion of accessibility of the world space technologies markets is index of competitiveness of 13 world leading (key) space countries. Criteria of the space technologies regional markets formation are proximity of scientific, technical-technological levels of countries development of a separate region. Regional division of the world market allows developers and users of space technologies to determine most optimal location of the subsidiaries, branches, representative offices with the purpose of maximum coverage of a certain segment of the regional market. Special attention is paid to development of markets of concentrated space technologies exchange (CSTEM). Criteria were formed that compose the basis of strategic partnership in the field of scientific-research and technological projects development. The article identifies criteria of space products world markets classification, establishes their interconnection, provides characteristics of each market type and identifies degree of the Ukrainian rocket-space industry integration into the system of the world trade

Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence

Monte Carlo Light Transport algorithms such as Path Tracing (PT), Bi-Directional Path Tracing (BDPT) and Metropolis Light Transport (MLT) make use of random walks to sample light transport paths. When parallelizing these algorithms on the GPU the stochastic termination of random walks results in an uneven workload between samples, which reduces SIMD efficiency. In this paper we propose to combine stream compaction and sample regeneration to keep SIMD efficiency high during random walk construction, in spite of stochastic termination. Furthermore, for BDPT and MLT, we propose to evaluate all bidirectional connections of a sample in parallel in order to balance the workload between GPU threads and improve SIMD efficiency during sample evaluation. We present efficient parallel GPU-only implementations for PT, BDPT, and MLT in CUDA. We show that our GPU implementations outperform similar CPU implementations by an order of magnitude.

We introduce fast algorithms for selecting a random sample of n records without replacement from a pool of N records, where the value of N is unknown beforehand. The main result of the paper is the design and analysis of Algorithm Z; it does the sampling in one pass using constant space and in O ( n (1 + log( N/n ))) expected time, which is optimum, up to a constant factor. Several optimizations are studied that collectively improve the speed of the naive version of the algorithm by an order of magnitude. We give an efficient Pascal-like implementation that incorporates these modifications and that is suitable for general use. Theoretical and empirical results indicate that Algorithm Z outperforms current methods by a significant margin.

In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

Orthogonal frequency-division multiplexing (OFDM) has been widely studied and adopted in visible-light communication (VLC) systems because of its high spectral efficiency and low-complexity implementation. However, OFDM-based VLC systems suffer from a high peak-to-average power ratio (PAPR), along with the nonlinear transfer characteristics of light-emitting diodes (LEDs). In this paper, a subcarrier grouping scheme for an OFDM-based VLC system is proposed. This scheme exploits the property that one LED lamp usually contains multiple independent LED chips. In the proposed scheme, all OFDM signal subcarriers are divided into groups, and each group is transmitted by an individual LED chip while the same receiver structure is maintained. The PAPR is reduced significantly because only some of the subcarriers are located on each LED chip. Hence, the achievable input power can be increased, leading to a higher signal-to-noise ratio (SNR) and a lower bit error rate (BER). Simulated and experimental results demonstrate that the BER performance can be improved by over two orders of magnitude. Moreover, an adaptive switching mechanism is also proposed in this paper, in which a subcarrier grouping scheme is employed adaptively when the required input power is high. Simulation results validate that the proposed mechanism can enhance system robustness significantly.

This paper presents the design and implementation of a high performance FPGA-based core for BLAST sequence alignment with the two-hit method. BLAST with two-hit is a very widely used heuristic biological sequence alignment algorithm, and this paper is the first reported FPGA implementation of it, to our knowledge. The architecture of our core is parameterized in terms of the sequence lengths, match scores, gap penalties, and cut-off and threshold values. It is composed of various blocks each of which performs one step of the algorithm in parallel with the others. This results in a high performance and efficient FPGA implementation, which outperforms equivalent software implementations by one order of magnitude or more. Real hardware implementations show that our core is 52 times faster than equivalent software implementations, on average. Furthermore, the core was captured in an FPGA-platform-independent language, namely the Handel-C language, to which no specific resource inference or placement constraints were applied. Hence, the same code can be easily ported to different FPGA families and architectures.

IMECO: A Reconfigurable FPGA-based Image Enhancement Co-Processor Framework

Probabilistic programming languages (PPLs) are at the interface between statistics and the theory of programming languages. PPLs formulate statistical models as stochastic programs that enable automatic inference algorithms and optimization. Pyro [1] and its sibling NumPyro [2] are PPLs built on top of the deep learning frameworks PyTorch [3] and Jax [4], respectively. Both PPLs provide simple, highly similar interfaces for inference using efficient implementations of Hamiltonian Monte Carlo (HMC), the No-U-Turn Sampler (NUTS), and Stochastic Variational Inference (SVI). They automatically generate variational distributions from a model, automatically enumerate discrete variables, and support formulating deep probabilistic models such as variational autoencoders and deep Markov models. The Sine von Mises distribution and its skewed variant are toroidal distributions relevant to protein bioinformatics. They provide a natural way to model the dihedral angles of protein structures, which is important in protein structure prediction, simulation and analysis. We present efficient implementations of the Sine von Mises distribution and its skewing in Pyro and NumPyro, and devise a simulation method that increases efficiency with several orders of magnitude when using parallel hardware (i.e., modern CPUs, GPUs, and TPUs). We demonstrate the use of the skewed Sine von Mises distribution by modeling dihedral angles of proteins using a Bayesian mixture model inferred using NUTS, exploiting NumPyro's facilities for automatic enumeration [5].

A fast hierarchical clustering algorithm for large-scale protein sequence data sets