Permutation Operations Research Articles

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

We present an implementation of Kuang and Bettenburg’s Quantum Permutation Pad (QPP) used to encrypt superposition states. The project was conducted on currently available IBM quantum systems using the Qiskit development kit. This work extends previously reported implementation of QPP used to encrypt basis states and demonstrates that application of the QPP scheme is not limited to the encryption of basis states. For this implementation, a pad of 56 2-qubit Permutation matrices was used, providing 256 bits of entropy for the QPP algorithm. An image of a cat was used as the plaintext for this experiment. The plaintext was randomized using a classical XOR function prior to the state preparation procedure. To create corresponding superposition states, we applied a novel operator defined in this paper. These superposition states were then encrypted using QPP, with 2-qubit Permutation Operators, producing superposition ciphertext states. Due to the lack of a quantum channel, we omitted the transmission and executed the decryption procedure on the same IBM quantum system. If a quantum channel existed, the superposition ciphertext states could be transmitted as qubits, and be directly decrypted on a different quantum system. We provide a brief discussion of the security, although the focus of the paper remains on the implementation. Previously we have demonstrated QPP operating in both classical and quantum computers, offering an interesting opportunity to bridge the security gap between classical and quantum systems. This work broadens the applicability of QPP for the encryption of basis states as well as superposition states. We believe that quantum encryption schemes that are not limited to basis states will be integral to a secure quantum internet, to reduce vulnerabilities introduced by using two separate algorithms for secure communication between a quantum and a classical computer.

A novel encryption algorithm using multiple semifield S-boxes based on permutation of symmetric group

There is a need of secure and robust encryption algorithm that can be implemented on each and diverse software and hardware platforms. In this paper, we investigate semifield substitution boxes using permutation of symmetric group on a set of size 8 S_8 and establish an effective procedure for generating S_8 semifield substitution boxes having same algebraic properties. Further, the strength analysis of the generated substitution boxes is carried out using the well-known standards, namely bijectivity, non-linearity, strict avalanche criterion, bit independence criterion, XOR table and differential invariant. As application, an encryption algorithm is proposed that can be employed to strengthen any kind of secure communication. The presented algorithm is mainly based on the Shannon idea of substitution–permutation network where the process of substitution is performed by the proposed S_8 semifield substitution boxes and permutation operation is performed by the binary cyclic shift of substitution box transformed data. In addition, the proposed encryption algorithm utilizes two different chaotic maps. To ensure the appropriate utilization of these chaotic maps, we carry out in-depth analyses of their behavior in the context of secure communication and apply the pseudo-random sequences of chaotic maps in the proposed image encryption algorithm accordingly.

Secure frequency-domain image compressed sensing with matrix-inversion-free recovery

Image encryption should be performed prior to image compression in many real-world applications. This results in the requirement of compressing the encrypted image. Compressed sensing (CS) is an attractive tool for compressing encrypted images. Unfortunately, most existing CS-based image encryption-then-compression (ETC) schemes face several critical challenges, such as low security, high-complexity sampling and recovery. Therefore, this paper presents a secure frequency-domain image CS scheme with matrix-inversion-free (MIF) recovery for ETC applications to address the above challenges. More specifically, the bilateral permutation and nonzero entry diffusion encryption operations are utilized to encrypt the frequency-domain image orderly. Surprisingly, the above two encryption operations do not compromise recovery performance with proper parameters. Then, the encrypted frequency-domain image is simultaneously compressed and sampled with low complexity by an untrusted bandwidth-constrained channel provider. Additionally, we design an accompanying access password as a defence layer, and it can further enhance security. Finally, an extension orthogonal matching pursuit (OMP) recovery algorithm is investigated by avoiding pseudo-inverse and multiple encryption and decryption to reduce computational complexity, named MIF OMP (MIFOMP). Theoretical analyses and simulation results demonstrate the proposed scheme can achieve high security, low-complexity sampling and recovery, and satisfy the expected recovery performance.

A Color Image Encryption Algorithm Based on Hash Table, Hilbert Curve and Hyper-Chaotic Synchronization

Chaotic systems, especially hyper-chaotic systems are suitable for digital image encryption because of their complex properties such as pseudo randomness and extreme sensitivity. This paper proposes a new color image encryption algorithm based on a hyper-chaotic system constructed by a tri-valued memristor. The encryption process is based on the structure of permutation-diffusion, and the transmission of key information is realized through hyper-chaotic synchronization technology. In this design, the hash value of the plaintext image is used to generate the initial key the permutation sequence with the Hash table structure based on the hyper-chaotic sequence is used to implement pixel-level and bit-level permutation operations. Hilbert curves combining with the ciphertext feedback mechanism are applied to complete the diffusion operation. A series of experimental analyses have been applied to measure the novel algorithm, and the results show that the scheme has excellent encryption performance and can resist a variety of attacks. This method can be applied in secure image communication fields.

Efficient Single Secret Image Sharing in Resource-Constrained Environment using Counting-Based Secret Sharing over Cloud

This paper presents a novel approach for secure and efficient single-secret image sharing in a resource-constrained environment. Traditional secret-sharing techniques are effective but often resource-intensive, making them less practical in scenarios with limited computational resources and storage overhead. While counting-based Secret-Sharing (CBSS) Schemes have been developed for numeric data, there has been a lack of schemes designed specifically for multimedia images. In response to this gap, our proposed model introduces a single-image sharing scheme based on bit permutation and counting bit operations, distributed over a cloud network. The key components of the proposed scheme include the group generation process, share generation and distribution, and secret reconstruction. In the group generation process, the secret image undergoes bit permutation to generate intermediate shares, which are then grouped into sets. Share generation involves performing counting bit operations on these groups to generate individual shares, which are subsequently distributed over a cloud server. The secret image can be reconstructed by combining all the shares and applying counting bit operations. The experimental findings illustrate that the proposed approach generates almost random shares. An assessment of the scheme's performance, utilizing metrics such as correlation, RMSE, and PSNR, indicates its superior results. The limitation of the scheme is that fewer than the required n shares may reveal the secret information.

Засіб захисту аналогового телефонного зв’язку на основі скремблера зі зміною коефіцієнтів вейвлет-перетворення

The paper proposes a device for providing protection of speech information transmitted over an analog telephone line against unauthorized interception based on a scrambler with modified Latin square wavelet transform coefficients. The developed device consists of hardware and software parts, the hardware part is implemented on the microcontroller platform of the Arduino family, the software part of the device is implemented using the Proteus software environment. As the main part of the functions of the device is performed by a microcontroller, the general structure of the device comprises a microphone, a power supply and an Arduino board. Taking into account the results of the research, it is proposed to modernize the scrambling algorithm by performing permutation operations, matching XOR to the scrambler key, which displays the Latin square itself. A statistical and spectral analysis of the improved method was carried out and a comparison of the execution speed of scrambling algorithms was performed. To improve the security, it was proposed to carry out several stages of permutations of the received coefficients of wavelet transformations. Increasing the variability of the permutations of the wavelet transformation coefficients made it possible to increase the time spent by the attacker on going through all possible combinations. And taking into account that the permutation does not take place in one part of the signal, but in a set of n parts, this in its turn further complicates the procedure of sorting through all possible options. The implementation of the elements of this device with the help of electronic computing equipment and available components makes it an accessible, as well as an effective tool for solving technical information protection tasks, which can ensure the improvement of information protection systems at various business entities.

Efficient Privacy-Preserving Inference Outsourcing for Convolutional Neural Networks

Inference outsourcing enables model owners to deploy their machine learning models on cloud servers to serve users. In this paradigm, the privacy of model owners and users should be considered. Existing solutions focus on Convolutional Neural Networks (CNNs) but their efficiency is much lower than GALA, which is a solution that only protects user privacy. Furthermore, these solutions adopt approximations that reduce the model accuracy and thus require model owners to retrain the models. In this paper, we present an efficient CNN inference outsourcing solution that protects the privacy of both model owners and users. Specifically, we design secure two-party computation protocols based on two non-colluding cloud servers, which calculate with additive secret shares of the model and the user’s input. Our protocols avoid the expensive permutation operations in linear calculations and approximations in non-linear calculations. We implement our solution on realistic CNNs and experimental results show that our solution is even 2–4 times faster than GALA.

Efficient Multi Port-Based Teleportation Schemes

In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob’s side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> systems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n-$ </tex-math></inline-formula> fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary.

Simple Yet Secure Encoder Architecture and Ultralightweight Mutual Authentication Protocol for RFID Tags in IoT

Internet of things (IoT) has evolved as the internet of everything, and it has grabbed the interest of all the researchers in recent days. Almost all the objects, including nonelectronics devices, can also be connected with the internet through radio frequency identification (RFID) technology. The security of the perception layer is crucial to secure the entire IoT network. RFID-enabled IoT perception layer has secured reader-to-server channel and unsecured tag to reader channel. Hence, securing the unsecured communication channel between the reader and the tag is the need of the hour. This work proposes a simple yet secure permutation approximate adder (SYSPXA)-based RFID mutual authentication protocol to address the need. The proposed protocol dramatically reduces the tag’s storage and computational overhead. It needs 40% less storage and 66.7% less permutation operation in comparison with the existing protocols. Nondisclosure of the key and freshness of key, IDS and random numbers at every mutual authentication process gives resistance to the protocol against de-synchronization attack, disclosure attack, tag tracking, replay attack. The SYSPXA protocol is validated for its security features using Burrows–Abadi–Needham (BAN) logic formal verification. The performance and security of the proposed protocol are contrasted with various futuristic permutation-based protocols, and its superiority over other protocols is highlighted. We have simulated the SYSPXA protocol with ModelSim tool for verifying its functionality. The protocol encoder architecture is implemented in the Intel cyclone IV Field Programmable Gate Array (FPGA) EP4CE115F29C7 device.

A recursive formulation of one‐electron coupling coefficients for spin‐adapted configuration interaction calculations featuring many unpaired electrons

AbstractThis work reports on a novel computational approach to the efficient evaluation of one‐electron coupling coefficients as they are required during spin‐adapted electronic structure calculations of the configuration interaction type. The presented approach relies on the equivalence of the representation matrix of excitation operators in the basis of configuration state functions and the representation matrix of permutation operators in the basis of genealogical spin eigenfunctions. After the details of this connection are established for every class of one‐electron excitation operator, a recursive scheme to evaluate permutation operator representations originally introduced by Yamanouchi and Kotani is recapitulated. On the basis of this scheme we have developed an efficient algorithm that allows the evaluation of all nonredundant coupling coefficients for systems with 20 unpaired electrons and a total spin of within only a few hours on a simple Desktop‐PC. Furthermore, a full‐CI implementation that utilizes the presented approach to one‐electron coupling coefficients is shown to perform well in terms of computational timings for CASCI calculations with comparably large active spaces. More importantly, however, this work paves the way to spin‐adapted and configuration driven selected configuration interaction calculations with many unpaired electrons.

Efficient Implementation of SPEEDY Block Cipher on Cortex-M3 and RISC-V Microcontrollers

The SPEEDY block cipher family announced at the CHES 2021 shows excellent performance on hardware architectures. Due to the nature of the hardware-friendly design of SPEEDY, the algorithm has low performance for software implementations. In particular, 6-bit S-box and bit permutation operations of SPEEDY are inefficient in software implementations, where it performs word-wise computations. We implemented the SPEEDY block cipher on a 32-bit microcontroller for the first time by applying the bit-slicing techniques. The optimized encryption performance results on ARM Cortex-M3 for SPEEDY-5-192, SPEEDY-6-192, and SPEEDY-7-192 are 65.7, 75.25, and 85.16 clock cycles per byte (i.e., cpb), respectively. It showed better performance than AES-128 constant-time implementation and GIFT constant-time implementation in the same platform. In RISC-V, the performance showed 81.9, 95.5, and 109.2 clock cycles per byte, which outperformed the previous works. Finally, we conclude that SPEEDY can show efficient software implementation on low-end embedded environments.

Order recognition by Schubert polynomials generated by optical near-field statistics via nanometre-scale photochromism

Irregular spatial distribution of photon transmission through a photochromic crystal photoisomerized by a local optical near-field excitation was previously reported, which manifested complex branching processes via the interplay of material deformation and near-field photon transfer therein. Furthermore, by combining such naturally constructed complex photon transmission with a simple photon detection protocol, Schubert polynomials, the foundation of versatile permutation operations in mathematics, have been generated. In this study, we demonstrated an order recognition algorithm inspired by Schubert calculus using optical near-field statistics via nanometre-scale photochromism. More specifically, by utilizing Schubert polynomials generated via optical near-field patterns, we showed that the order of slot machines with initially unknown reward probability was successfully recognized. We emphasized that, unlike conventional algorithms, the proposed principle does not estimate the reward probabilities but exploits the inversion relations contained in the Schubert polynomials. To quantitatively evaluate the impact of Schubert polynomials generated from an optical near-field pattern, order recognition performances were compared with uniformly distributed and spatially strongly skewed probability distributions, where the optical near-field pattern outperformed the others. We found that the number of singularities contained in Schubert polynomials and that of the given problem or considered environment exhibited a clear correspondence, indicating that superior order recognition is attained when the singularity of the given situations is presupposed. This study paves way for physical computing through the interplay of complex natural processes and mathematical insights gained by Schubert calculus.

A Proposal of a New Chaotic Map for Application in the Image Encryption Domain

Several chaos-based image encryption schemes have been proposed in the last decade. Each encryption scheme has pros and cons regarding its speed, complexity, and security. This paper proposes a new chaotic map called Power-Chaotic Map (PCM). Characteristics of the proposed PCM, such as chaotic behaviour, randomness, sensitivity, and s-unimodality, are investigated. As an application of the proposed chaotic map, an image encryption scheme is proposed to encrypt greyscale and text images. The proposed three-phase image encryption scheme performs a series of substitution and permutation operations. The Pixel-Level phase utilises the PCM’s generated keystreams to perform the substitution operation of image pixels. The Row-Level phase permutates, via a proposed pseudorandom number generator, pixel locations of each row and then shuffles row locations. Finally, the Column-Level phase performs a substitution operation on pixels of each column. Performance of the proposed PCM-based image encryption scheme is investigated through histogram analysis, statistical correlation analysis, key sensitivity, encryption performance of text images, and permutation and substitution properties. Experimental results indicate that the PCM has a wider range of chaotic behaviour than well-known one-dimensional maps, meets the s-unimodality property, has high sensitivity, and generates keystreams with random-like behaviour. Furthermore, results indicate that the PCM-based image encryption scheme provides high encryption security for text images, high key sensitivity, immunity against brute-force attacks, strong statistical correlation results, strong encryption performance, and low computational complexity.

Hidden Bethe states in a partially integrable model

We present a one-dimensional multi-component model, known to be partially integrable when restricted to the subspaces made of only two components. By constructing fully anti-symmetrized bases, we find integrable excited eigenstates corresponding to the totally anti-symmetric irreducible representation of the permutation operator in the otherwise non-integrable subspaces. We establish rigorously the breakdown of integrability in those subspaces by showing explicitly the violation of the Yang-Baxter's equation. We further solve the constraints from Yang-Baxter's equation to find exceptional momenta that allows Bethe Ansatz solutions of solitonic bound states. These integrable eigenstates have distinct dynamical consequence from the embedded integrable subspaces previously known, as they do not span their separate Krylov subspaces, and a generic initial state can partly overlap with them and therefore have slow thermalization. However, this novel form of weak ergodicity breaking contrasts that of quantum many-body scars in that the integrable eigenstates involved do not have necessarily low entanglement. Our approach provides a complementary route to arrive at quantum many-body scars since, instead of solving towers of single mode excited states based on a solvable ground state in a non-integrable model, we identify the integrable eigenstates that survive in a deformation of the Hamiltonian away from its integrable point.

Fast quantum image encryption scheme based on multilayer short memory fractional order Lotka-Volterra system and dual-scale triangular map

The Caputo fractional order Lotka-Volterra system is time-consuming in practical applications, since its starting point is fixed. To tackle this problem, a short memory fractional order Lotka-Volterra system (SMFrLVS) is proposed, where the chaotic attractor of the short memory fractional order Lotka-Volterra system is achieved by the predictor-corrector method. Then, a multilayer fractional order Lotka-Volterra system with short memory (MSMFrLVS) is introduced, whose chaotic behaviors are explored via Poincare sections and frequency power spectra. A quantum image encryption algorithm is proposed by combining MSMFrLVS with quantum dual-scale triangular map. A quantum circuit of the dual-scale triangular map is designed with ADDER-MOD2n. At the permutation stage, the plaintext image is transformed into quantum form with the generalized quantum image representation model. The resulting quantum image is divided into sub-blocks and scrambled by the quantum dual-scale triangular map. Subsequently, the intra and the inter permutation operations on bit-planes are realized by sorting pseudo-random sequence and by quantum Gray code, respectively. At the diffusion stage, the initial values of the MSMFrLVS are generated with a plaintext correlation mechanism. The ciphertext image can be acquired by carrying out three-level diffusion operations. It is demonstrated that the proposed quantum image encryption algorithm performs better than some typical image encryption algorithm in terms of security, robustness, computational complexity and encryption speed.

Autonomous Service Robots for Urban Waste Management - Multiagent Route Planning and Cooperative Operation

A sustainable approach towards smart waste management means reduced impact on the health of the workers, lower greenhouse gas emissions and low operational costs. Incorporating fleets of the robot MARBLE (Mobile Autonomous RoBot for Litter Emptying) effectuates these requirements for autonomously emptying the dustbins on the streets of Berlin. The dedicated waypoints for the route formulation are the global positions of the dustbins, and the garbage emptying position from the robots after reaching the maximum compressed-garbage storage capacity. In this paper, we provide a cost function efficient solution for providing global routes to the robots. The cost function includes operational energy expenditure. After conducting numerous experiments with varying algorithm parameter values, the specific weightage of route permutation operators and the initial temperature for a simulated annealing method with nearest neighbour approach was narrowed down as a well-performing set. This set was used in three different operation scenarios. The results of the cost function on the basis of the chosen parameters show an improvement of average 28% for two different exemplary datasets, and 30% improvement for an implementation in an actual existing park in Berlin for operation scenarios as compared to results from a nearest neighbour heuristic.

Design and Embedded Implementation of Secure Image Encryption Scheme Using DWT and 2D-LASM.

In order to further improve the information effectiveness of digital image transmission, an image-encryption algorithm based on 2D-Logistic-adjusted-Sine map (2D-LASM) and Discrete Wavelet Transform (DWT) is proposed. First, a dynamic key with plaintext correlation is generated using Message-Digest Algorithm 5 (MD5), and 2D-LASM chaos is generated based on the key to obtain a chaotic pseudo-random sequence. Secondly, we perform DWT on the plaintext image to map the image from the time domain to the frequency domain and decompose the low-frequency (LF) coefficient and high-frequency (HF) coefficient. Then, the chaotic sequence is used to encrypt the LF coefficient with the structure of “confusion-permutation”. We perform the permutation operation on HF coefficient, and we reconstruct the image of the processed LF coefficient and HF coefficient to obtain the frequency-domain ciphertext image. Finally, the ciphertext is dynamically diffused using the chaotic sequence to obtain the final ciphertext. Theoretical analysis and simulation experiments show that the algorithm has a large key space and can effectively resist various attacks. Compared with the spatial-domain algorithms, this algorithm has great advantages in terms of computational complexity, security performance, and encryption efficiency. At the same time, it provides better concealment of the encrypted image while ensuring the encryption efficiency compared to existing frequency-domain methods. The successful implementation on the embedded device in the optical network environment verifies the experimental feasibility of this algorithm in the new network application.

Engineering Symmetry-Selective Couplings of a Superconducting Artificial Molecule to Microwave Waveguides.

Tailoring the decay rate of structured quantum emitters into their environment opens new avenues for nonlinear quantum optics, collective phenomena, and quantum communications. Here, we demonstrate a novel coupling scheme between an artificial molecule comprising two identical, strongly coupled transmon qubits and two microwave waveguides. In our scheme, the coupling is engineered so that transitions between states of the same (opposite) symmetry, with respect to the permutation operator, are predominantly coupled to one (the other) waveguide. The symmetry-based coupling selectivity, as quantified by the ratio of the coupling strengths, exceeds a factor of 30 for both waveguides in our device. In addition, we implement a Raman process activated by simultaneously driving both waveguides, and show that it can be used to coherently couple states of different symmetry in the single-excitation manifold of the molecule. Using that process, we implement frequency conversion across the waveguides, mediated by the molecule, with efficiency of about 95%. Finally, we show that this coupling arrangement makes it possible to straightforwardly generate spatially separated Bell states propagating across the waveguides. We envisage further applications to quantum thermodynamics, microwave photodetection, and photon-photon gates.

Diffractive interconnects: all-optical permutation operation using diffractive networks

Abstract Permutation matrices form an important computational building block frequently used in various fields including, e.g., communications, information security, and data processing. Optical implementation of permutation operators with relatively large number of input–output interconnections based on power-efficient, fast, and compact platforms is highly desirable. Here, we present diffractive optical networks engineered through deep learning to all-optically perform permutation operations that can scale to hundreds of thousands of interconnections between an input and an output field-of-view using passive transmissive layers that are individually structured at the wavelength scale. Our findings indicate that the capacity of the diffractive optical network in approximating a given permutation operation increases proportional to the number of diffractive layers and trainable transmission elements in the system. Such deeper diffractive network designs can pose practical challenges in terms of physical alignment and output diffraction efficiency of the system. We addressed these challenges by designing misalignment tolerant diffractive designs that can all-optically perform arbitrarily selected permutation operations, and experimentally demonstrated, for the first time, a diffractive permutation network that operates at THz part of the spectrum. Diffractive permutation networks might find various applications in, e.g., security, image encryption, and data processing, along with telecommunications; especially with the carrier frequencies in wireless communications approaching THz-bands, the presented diffractive permutation networks can potentially serve as channel routing and interconnection panels in wireless networks.

Quantum Tree Search with Qiskit

We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms from IBM. The objects are represented by symbols and adjectives. Two principles are presented. Either the position description (adjective) is fixed and the class descriptors moves (is changed) or, in the reverse interpretation, the class descriptor is fixed and the position descriptor (adjective) moves (is changed). We indicate how to decompose the permutation operator that executes the rules by the two principles. We demonstrate that the the branching factor is reduced by Grover’s amplification to the square root of the average branching factor and not to the maximal branching factor as previously assumed.