Operator Research Articles

Dynamical nonlocality in quantum time via modular operators

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our formalization are provided through illustrative examples.

Unlimited dynamic range signal recovery for folded graph signals

Recovery of a graph signal from samples has many important applications in signal processing over networks and graph-structured data. To capture very high or even unlimited dynamic range signals, modulo sampling has been investigated. Folded signals are signals generated from a modulo operation. In this paper, we investigate the problem of recovering bandlimited graph signals from folded signal samples. We derive sufficient conditions to achieve successful recovery of the graph signal, which can be achieved via integer programming. To resolve the scalability issue of integer programming, we propose a sparse optimization recovery method for graph signals satisfying certain technical conditions. Such an approach requires a novel graph sampling scheme that selects vertices with small signal variation. The proposed algorithm exploits the inherent relationship among the graph vertices in both the vertex and time domains to recover the graph signal from folded samples. Simulations and experiments validate the feasibility of our proposed approach.

On the structure of hypergroups with respect to the induced topology

Let H be a hypergroup with left Haar measure and let L1(H) be the complex Lebesgue space associated with it. Let L∞(H) be the set of all locally measurable functions that are bounded except on a locally null set, modulo functions that are zero locally a.e. It is a standard device to embed L∞(H) into ℬ(L1(H),L∞(H)). We denote the strong operator topology and the weak operator topology on L∞(H) by τso and τwo. Unlike the uniform norm and weak topologies on L∞(H), they depend essentially on the hypergroup structure of H. We derive that the τso-topology is always different from the weak∗-topology whenever H is infinite. We can conclude that for a compact hypergroup H, L1(H) is the dual of (L∞(H),τso). The properties of τso and τwo are then studied further and we pay attention to the τwo-almost periodic elements of L∞(H). Finally we give some further results about bounded linear operators which are τso-τso-continuous.

PH and Design on n-Alkyl Alcohol Bulk Liquid Membranes for Improving Phenol Derivative Transport and Separation.

Regardless of the type of liquid membrane (LM) (Bulk Liquid Membranes (BLM), Supported Liquid Membranes (SLM) or Emulsion Liquid Membranes (ELM)), transport and separation of chemical species are conditioned by the operational (OP) and constructive design parameters (DP) of the permeation module. In the present study, the pH of the aqueous source phase (SP) and receiving phase (RP) of the proposed membrane system were selected as operational parameters. The mode of contacting the phases was chosen as the convective transport generator. The experiments used BLM-type membranes with spheres in free rotation as film contact elements of the aqueous phases with the membrane. The target chemical species were selected in the range of phenol derivatives (PD), 4–nitrophenol (NP), 2,4–dichlorophenol (DCP) and 2,4–dinitrophenol (DNP), all being substances of technical-economic and environmental interest. Due to their acid character, they allow the evaluation of the influence of pH as a determining operational parameter of transport and separation through a membrane consisting of n–octanol or n–decanol (n–AlcM). The comparative study performed for the transport of 4–nitrophenol (NP) showed that the module based on spheres (Ms) was more performant than the one with phase dispersion under the form of droplets (Md). The sphere material influenced the transport of 4–nitrophenol (NP). The transport module with glass spheres (Gl) was superior to the one using copper spheres (Cu), but especially with the one with steel spheres (St). In all the studied cases, the sphere-based module (Ms) had superior transport results compared to the module with droplets (Md). The extraction efficiency (EE) and the transport of 2,4–dichlorophenol (DCP) and 2,4–dinitrophenol (DNP), studied in the module with glass spheres, showed that the two phenolic derivatives could be separated by adjusting the pH of the source phase. At the acidic pH of the source phase (pH = 2), the two derivatives were extracted with good results (EE > 90%), while for pH values ranging from 4 to 6, they could be separated, with DCP having doubled separation efficiency compared to DNP. At a pH of 8 in the source phase, the extraction efficiency halved for both phenolic compounds.

Error-Correction Coding Using Polynomial Residue Number System

There has been a tendency to use the theory of finite Galois fields, or GF(2n), in cryptographic ciphers (AES, Kuznyechik) and digital signal processing (DSP) systems. It is advisable to use modular codes of the polynomial residue number system (PRNS). Modular codes of PRNS are arithmetic codes in which addition, subtraction and multiplication operations are performed in parallel on the bases of the code, which are irreducible polynomials. In this case, the operands are small-bit residues. However, the independence of calculations on the bases of the code and the lack of data exchange between the residues can serve as the basis for constructing codes of PRNS capable of detecting and correcting errors that occur during calculations. The article will consider the principles of constructing redundant codes of the polynomial residue number system. The results of the study of codes of PRNS with minimal redundancy are presented. It is shown that these codes are only able to detect an error in the code combination of PRNS. It is proposed to use two control bases, the use of which allows us to correct an error in any residue of the code combination, in order to increase the error-correction abilities of the code of the polynomial residue number system. Therefore, the development of an algorithm for detecting and correcting errors in the code of the polynomial residue number system, which allows for performing this procedure based on modular operations that are effectively implemented in codes of PRNS, is an urgent task.

GIS-AHP Approach in Forest Logging Planning to Apply Sustainable Forest Operations

This study represents the first attempt of integration, within a Forest Management Plan (FMP), of a Geographic Information System (GIS) and an Analytic Hierarchy Process (AHP) approach for the selection of the most suitable logging method. It is important to underline that the developed methodology is applicable worldwide in each environmental context in which there is a need for planning the intervention and selecting from among several possible logging methods or harvesting systems. Schematically, the main aims of this study were: (i) to develop a GIS-AHP method based on open-access GIS software; (ii) to compare the results of the simulations developed from the statements of two different groups of experts from around the world, to determine the reliability of the predictive probability of the method. The selection of the extraction methods performed with RTS (experts from research and technical sector) input data showed that the most suitable option in the major part of the study area was the cable skidder, followed by the cable yarder, and finally the forwarder. The extraction system selection performed with OS (people from the operative sector) input data revealed limited differences. Thus, considering what was reported above, it is possible to assert that the applied GIS-AHP methodology showed good performance and high consistency in the selection of the best alternatives among different extraction methods. The idea of comparing the results obtained from a survey based on a pool of researchers and forest engineers (RTS) was taken as a target simulation to be evaluated. The method based on data derived from a pool of expert forest operators (OS) was used to check for the results of the other simulation. This is an innovation in these kinds of studies. The results from the consistency check were encouraging, considering that for 51 sub-compartments, only two changed the selected extraction system between RTS and OS.

Planning for modular-vehicle transit service system: Model formulation and solution methods

This paper studies the optimal planning of public transit services with modular vehicles. In the modular service operation, the vehicle is comprised of smaller modular units/pods, which can be assembled/dissembled at some specially designed transit stations. The planning decisions are to determine the locations of the specially constructed stations enabling station-wise assembling/dissembling of modular units. Meanwhile, the capacity of these stations, i.e., the maximum number of modular units that can be accommodated, will also be determined. The optimal vehicle formation at these stations will be considered for the multi-period passenger demand to evaluate the system performance. Aiming to minimize the total cost of the operator and passengers, we formulate this problem into a mixed-integer nonlinear program (MINLP). Two solution methods are proposed to solve the problem. One is to transform the formulated MINLP into a mixed-integer linear program (MILP) using various linearization reformulation techniques, which can be solved by using many existing solution methods for MILP. Despite that this method ensures exact solutions, its solution efficiency is compromised. To solve a practical large-size problem, we propose another solution method applying surrogate model-based optimization approaches. A case study in the context of a proposed Singapore dynamic autonomous road transit (DART) line is conducted. Numerical experiments have been carried out to test the validity of the model formulation and the solution performance of the proposed solution methods. The advantage of the modular-vehicle transit service in significantly reducing the operating cost and passengers’ travel time costs has been demonstrated as well. This study offers the public transportation planners a useful tool for determining optimal operation strategies for the future transit service system with modular vehicles.

The Legendre Symbol and the Modulo-2 Operator in Symmetric Schemes over Fnp

Motivated by modern cryptographic use cases such as multi-party computation (MPC), homomorphic encryption (HE), and zero-knowledge (ZK) protocols, several symmetric schemes that are efficient in these scenarios have recently been proposed in the literature. Some of these schemes are instantiated with low-degree nonlinear functions, for example low-degree power maps (e.g., MiMC, HadesMiMC, Poseidon) or the Toffoli gate (e.g., Ciminion). Others (e.g., Rescue, Vision, Grendel) are instead instantiated via high-degree functions which are easy to evaluate in the target application. A recent example for the latter case is the hash function Grendel, whose nonlinear layer is constructed using the Legendre symbol. In this paper, we analyze high-degree functions such as the Legendre symbol or the modulo-2 operation as building blocks for the nonlinear layer of a cryptographic scheme over Fnp.Our focus regards the security analysis rather than the efficiency in the mentioned use cases. For this purpose, we present several new invertible functions that make use of the Legendre symbol or of the modulo-2 operation.Even though these functions often provide strong statistical properties and ensure a high degree after a few rounds, the main problem regards their small number of possible outputs, that is, only three for the Legendre symbol and only two for the modulo-2 operation. By fixing them, it is possible to reduce the overall degree of the function significantly. We exploit this behavior by describing the first preimage attack on full Grendel, and we verify it in practice.

Modular Single-Stage Three-Phase Flyback Differential Inverter for Medium/High-Power Grid Integrated Applications.

This paper proposes a single-stage three-phase modular flyback differential inverter (MFBDI) for medium/high power solar PV grid-integrated applications. The proposed inverter structure consists of parallel modules of flyback DC-DC converters based on the required power level. The MFBDI offers many features for renewable energy applications, such as reduced components, single-stage power processing, high-power density, voltage-boosting property, improved footprint, flexibility with modular extension capability, and galvanic isolation. The proposed inverter has been modelled, designed, and scaled up to the required application rating. A new mathematical model of the proposed MFBDI is presented and analyzed with a time-varying duty-cycle, wide-range of frequency variation, and power balancing in order to display its grid current harmonic orders for grid-tied applications. In addition, an LPF-based harmonic compensation strategy is used for second-order harmonic component (SOHC) compensation. With the help of the compensation technique, the grid current THD is reduced from 36% to 4.6% by diminishing the SOHC from 51% to 0.8%. Moreover, the SOHC compensation technique eliminates third-order harmonic components from the DC input current. In addition, a 15% parameters mismatch has been applied between the flyback parallel modules to confirm the modular operation of the proposed MFBDI under modules divergence. In addition, SiC MOSFETs are used for inverter switches implementation, which decrease the inverter switching losses at high-switching frequency. The proposed MFBDI is verified by using three flyback parallel modules/phase using PSIM/Simulink software, with a rating of 5 kW, 200 V, and 50 kHz switching frequency, as well as experimental environments.

Building the Business Platform by Modularization Strategies: Cases of Taiwan Social Networking Vendors

Firms achieve their competitive advantage quickly through the concept framework of open innovation by integrating external inspiration with internal endowment when facing hyper-competition in the digital era. This paper deploys open innovation into building platform blocks by modular operators. These eight modular operators are splitting, augmenting, deleting, substituting, inversing, porting, configuring, and integrating. By means of case studies of two Taiwan Internet vendors, the results depict the manipulation strategies between eight modular operators to fit seven functional requirements for weaving social media, which are presence, identity, sharing, reputation, groups, conversations, and relationship. Finally, this paper advances propositions about the deployment of modularization strategies to develop a competitive platform.

University of Library Studies and Information Technologies

This paper provides implementations of three well-known ciphers – Caesar Cipher, Vigenere Cipher and Hill Cipher in Microsoft Excel. It is shown how the ciphers can be broken by using Brute-force Attack, Frequency Analysis Attack and Known-plaintext Attack. For the purpose of the cryptanalysis the relative occurrence frequencies of the letters and the index of coincidence (κ ) in Bulgarian language are determined. The classical Frequency Analysis Attack is modified using the cross-correlation between frequencies of letters in the natural language and the cipher text. Modular matrix operations in MS Excel are shown.

Operation potential evaluation of multiple hydrogen production and refueling integrated stations under DC interconnected environment

Hydrogen production and refueling integrated station can play an important role in the development of hydrogen transportation and fuel cell vehicles, and actively promote the energy transformation. By using DC system for hydrogen production and refueling, the conversion links can be reduced and the system efficiency can be effectively improved. In this paper, a new scheme of DC interconnection for hydrogen production and refueling integrated station is proposed, and the modular modeling and operation capability evaluation method are proposed, including the characteristic analysis of integrated station, the modular modeling and evaluation method for multiple integrated stations under DC interconnection. The DC interconnection system of five integrated stations is constructed, and operation capability improvement of integrated stations after adopting the innovative DC interconnection scheme is analyzed. On this basis, the system simulation model based on MATLAB/Simulink and physical test platform are built to verify the effectiveness of the theoretical analysis.

Preventing Differential Cryptanalysis Attacks Using a KDM Function and the 32-Bit Output S-Boxes on AES Algorithm Found on the Internet of Things Devices

Many Internet of Things (IoT) devices use an Advanced Encryption Standard (AES) algorithm to secure data stored and transmitted during the communication process. The AES algorithm often suffers DC (DC) attacks. Little has been done to prevent DC attacks, particularly on an AES algorithm. This study focuses on preventing Differential Cryptanalysis attacks. DC attacks are practiced on an AES algorithm that is found on IoT devices. The novel approach of using a Khumbelo Difference Muthavine (KDM) function and changing the 8 × 8 S-Boxes to be the 8 × 32 S-Boxes successfully prevents DC attacks on an AES algorithm. A KDM function is a newly mathematically developed function, coined and used purposely in this study. A KDM function was never produced, defined, or utilized before by any researcher except for in this study. A KDM function makes a new 32-Bit S-Box suitable for the new Modified AES algorithm and confuses the attacker since it comprises many mathematical modulo operators. Additionally, these mathematical modulo operators are irreversible. The study managed to prevent the DC attack of a minimum of 70% on AES and a maximum of 100% on a Simplified DES. The attack on the new Modified AES Algorithm is 0% since no S-Box is used as a building block.

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld’s upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note, we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon–Vonk can be computed in terms of mathcal {L}-invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups.

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem.

In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as , where k equals the number of used moduli. The time complexity is modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.

A high speed processor for elliptic curve cryptography over NIST prime field

Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) operation which has the highest computational complexity in ECC. In this study, we propose a hardware processor which achieves high speed and high security for ECC. We first present a three-clock cycle, divide-and-conquer multiplication algorithm which greatly reduces the number of execution cycles of multiplication. We then propose a dedicated multiplication hardware structure which reuses the multiplier and optimizes data path delay. To keep multiplication running in non-idle status and executing in parallel with other modular operations, the operation scheduling of point addition and point doubling has been re-designed and optimized based on an effective segmentation and pipeline strategy. Finally, under the premise of similar computing and hardware overhead, we propose an improved high-security SM algorithm which involves random points to resist side-channel attacks. On a 55 nm complementary metal oxide semiconductor application specific integrated circuit platform, the processor costs 463k gates and requires 0.028 ms for one SM. Our results indicate that the ECC processor is superior to other state-of-the-art designs reported in the literature in terms of speed and area-time product metrics.

Modular reduction with step-by-step using of several bits of the reducible number

Although public key cryptography is known to solve the problem of physically secure key exchange, the main drawback of this system is its low performance during encrypting and decrypting data. One of the ways to solve this issue is to increase the speed of the modular reduction operation, one of the basic operations of asymmetric cryptoalgorithms. A new method of step-by-step reduction by the N-bit module P using several bits of the 2Nbit reducible number A in one step is proposed in this paper. The method is based on using multiples of the P and reducing modulo at each step not the entire initial number, but its parts (A1, A2… Ai), which allows to reduce the bit capacity of A. A structural diagram of the hardware implementation of this method are developed. The main unit of the modular reduction device is a block of partial remainder formers, in which the partial remainder is computed using multiples of the P. The circuits are modeled in the Vivado Design Suite computer aided design (CAD) on base Artix-7 Fieldprogrammable gate array (FPGA) device from Xilinx. Optimization of hardware costs is achieved by applying the same comparison circuits to compare different multiples of P with Ai

Memory-Saving and High-Speed Privacy Amplification Algorithm Using LFSR-Based Hash Function for Key Generation

Privacy amplification is an indispensable procedure for key generation in the quantum key distribution system and the physical layer key distribution system. In this paper, we propose a high-speed privacy amplification algorithm that saves hardware memory and improves the key randomness performance. Based on optimizing the structure of the Toeplitz matrix generated by a linear feedback shift register, the core of our algorithm is a block-iterative structure hash function that is used to generate a secure key of arbitrary length. The proposed algorithm adopts multiple small Toeplitz matrices to compress the negotiation key for convenient implementation. The negotiated key is equally divided into multiple small blocks, and the multiplication operation of the negotiated key with the Toeplitz matrix is converted into a modular addition operation through an accumulator. The analysis results demonstrate that the algorithm has the advantages of saving memory and running quickly. In addition, the NIST randomness test and avalanche effect test on the key sequences indicate that the proposed algorithm has a favorable performance.

Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

A variant RSA acceleration with parallelisation

The standard RSA relies on multiple big-number modular exponentiation operations and a longer key-length is required for better protection. This imposes a hefty time penalty for encryption and decryption. In this study, we analysed and developed an improved parallel algorithm (PMKRSA) based on the idea of splitting the plaintext into multiple chunks and encrypt the chunks using multiple key-pairs. The algorithm in our new scheme is so natural for parallelised implementation that we also investigated its parallelisation in a GPU environment. In the following, the structure of our new scheme is outlined and its correctness is proved mathematically. Then, with the algorithm implemented and optimised on both CPU and CPU+GPU platforms, we showed that our algorithm shortens the computational time considerably, and it has a security advantage over the standard RSA as it is invulnerable to the common attacks. Finally, we also proved the feasibility of using our algorithm to encrypt large files through simulation. The results show that over the set of file size: 1 MB, 10 MB, 25 MB, 50 MB, 100 MB, the average encryption and decryption time of the CPU version is 0.2476 and 9.4476 s, and for the CPU+GPU version, it is 0.0009 and 0.0618 s, respectively.