Bit String Research Articles

A Problem on the Amounts of the Same Consecutive Pairs in Boolean Collections

In this paper, the set of Boolean vectors is mapped onto the set of non-negative integer quartets, octets of numbers, where the elements of the set are the numbers of three consecutive or similar cyclically adjacent pairs of triples. The properties of the images of such representations are studied, and the values of their cardinalities are given.

Tight Error Analysis in Fixed-point Arithmetic

We consider the problem of estimating the numerical accuracy of programs with operations in fixed-point arithmetic and variables of arbitrary, mixed precision, and possibly non-deterministic value. By applying a set of parameterised rewrite rules, we transform the relevant fragments of the program under consideration into sequences of operations in integer arithmetic over vectors of bits, thereby reducing the problem as to whether the error enclosures in the initial program can ever exceed a given order of magnitude to simple reachability queries on the transformed program. We describe a possible verification flow and a prototype analyser that implements our technique. We present an experimental evaluation on a particularly complex industrial case study, including a preliminary comparison between bit-level and word-level decision procedures.

A novel method for lung nodule detection in computed tomography scans based on Boolean equations and vector of filters techniques

This work presents a novel method that uses a Vector of Pre-processing Filters combined with simple relational and Boolean equations for pulmonary nodule detection. To isolate nodules from other lung structures, we propose a 16 filter scheme endowed with multiscale median masks, statistical-based thresholds, and 3-D morphological operations. In the Boolean False Positive Reduction stage, relational and Boolean equations select nodule candidates from pre-processing filters using our descriptor with 20 attributes. Finally, a Convolutional Neural Network (CNN) classifies the remaining structures into nodule or no nodule. The method reached 92.75% sensitivity for an average of 8 false positives per exam using all exams in the public Lung Image Database Consortium (LIDC) with a slice thickness of less than 2 mm that contains lesions larger than 3 mm marked “nodule” by at least 3 radiologists. For a less consensual gold standard, our method reaches the highest sensitivity levels among listed results.

Dropping diversity of products of large US firms: Models and measures.

It is widely assumed that in our lifetimes the products available in the global economy have become more diverse. This assumption is difficult to investigate directly, however, because it is difficult to collect the necessary data about every product in an economy each year. We solve this problem by mining publicly available textual descriptions of the products of every large US firms each year from 1997 to 2017. Although many aspects of economic productivity have been steadily rising during this period, our text-based measurements show that the diversity of the products of at least large US firms has steadily declined. This downward trend is visible using a variety of product diversity metrics, including some that depend on a measurement of the similarity of the products of every single pair of firms. The current state of the art in comprehensive and detailed firm-similarity measurements is a Boolean word vector model due to Hoberg and Phillips. We measure diversity using firm-similarities from this Boolean model and two more sophisticated variants, and we consistently observe a significant dropping trend in product diversity. These results make it possible to frame and start to test specific hypotheses for explaining the dropping product diversity trend.

Composably secure data processing for Gaussian-modulated continuous-variable quantum key distribution

Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data is post-processed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime which requires the use of high-rate (non-binary) low-density parity check codes. We implement all these steps in a Python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.

Improving Parameter Optimization in Decoy-State Quantum Key Distribution

Quantum key distribution (QKD) enables two remote users to share a string of key bits with information-theoretical security. Parameter optimization is a crucial step in achieving optimal performance in practical QKD systems. In general, such optimization is implemented using a local search algorithm (LSA). However, LSAs inevitably fail to find out the optimal values when the searched key rate function is nonconvex or has a discontinuity of first-order derivatives and a narrow parameter search space. This paper proposes a genetic algorithm-based method to overcome the limitations of LSAs for QKD parameter optimization. We tested the proposed method with various types of common QKD protocols and found that it has very high parameter optimization performance for QKD with a time consumption comparable to that using a standard LSA. We expect our method to be a valuable optimization tool for quantum information processing tasks.

Invariant of Enhanced AES Algorithm Implementations Against Power Analysis Attacks

The security of Internet of Things (IoT) is a challenging task for researchers due to plethora of IoT networks. Side Channel Attacks (SCA) are one of the major concerns. The prime objective of SCA is to acquire the information by observing the power consumption, electromagnetic (EM) field, timing analysis, and acoustics of the device. Later, the attackers perform statistical functions to recover the key. Advanced Encryption Standard (AES) algorithm has proved to be a good security solution for constrained IoT devices. This paper implements a simulation model which is used to modify the AES algorithm using logical masking properties. This invariant of the AES algorithm hides the array of bits during substitution byte transformation of AES. This model is used against SCA and particularly Power Analysis Attacks (PAAs). Simulation model is designed on MATLAB simulator. Results will give better solution by hiding power profiles of the IoT devices against PAAs. In future, the lightweight AES algorithm with false key mechanisms and power reduction techniques such as wave dynamic differential logic (WDDL) will be used to safeguard IoT devices against side channel attacks by using Arduino and field programmable gate array (FPGA).

On bases of all closed classes of Boolean vector functions

Рассматривается функциональная система вектор-функций алгебры логики с естественным образом определенной операцией суперпозиции. Показано, что в каждом замкнутом классе вектор-функций существует конечный базис.

Signed domination number of hypercubes

The [Formula: see text]-cube graph or hypercube [Formula: see text] is the graph whose vertex set is the set of all [Formula: see text]-dimensional Boolean vectors, two vertices being joined if and only if they differ in exactly one co-ordinate. The purpose of the paper is to investigate the signed domination number of this hypercube graphs. In this paper, signed domination number [Formula: see text]-cube graph for odd [Formula: see text] is found and the lower and upper bounds of hypercube for even [Formula: see text] are found.

Boolean analogues of the Pascal triangle with maximal possible number of ones

Abstract The aim of the paper is to find the maximal possible number ξ of units in Boolean triangular array Ts formed by $\begin{array}{} \displaystyle \frac{s(s+1)}{2} \end{array}$ elements of the field GF(2) defined by the top row of s elements. Each element of each row except the top one is the sum (as in the Pascal’s triangle) of two elements of the above row. It is proved that ξ ⩽ ⌈ $\begin{array}{} \displaystyle \frac{s(s+1)}{3} \end{array}$ ⌉ and this value is attained only on triangles having the upper row as the Fibonacci series mod 2.

Compression of MRI brain images based on automatic extraction of tumor region

In the compression of medical images, region of interest (ROI) based techniques seem to be promising, as they can result in high compression ratios while maintaining the quality of region of diagnostic importance, the ROI, when image is reconstructed. In this article, we propose a set-up for compression of brain magnetic resonance imaging (MRI) images based on automatic extraction of tumor. Our approach is to first separate the tumor, the ROI in our case, from brain image, using support vector machine (SVM) classification and region extraction step. Then, tumor region (ROI) is compressed using Arithmetic coding, a lossless compression technique. The non-tumorous region, non-region of interest (NROI), is compressed using a lossy compression technique formed by a combination of discrete wavelet transform (DWT), set partitioning in hierarchical trees (SPIHT) and arithmetic coding (AC). The classification performance parameters, like, dice coefficient, sensitivity, positive predictive value and accuracy are tabulated. In the case of compression, we report, performance parameters like mean square error and peak signal to noise ratio for a given set of bits per pixel (bpp) values. We found that the compression scheme considered in our setup gives promising results as compared to other schemes.

Parametrically driven Kerr cavity solitons

Temporal cavity solitons are optical pulses that propagate indefinitely in nonlinear resonators. They are currently attracting a lot of attention, both for their many potential applications and for their connection to other fields of science. Cavity solitons are phase locked to a driving laser. This is what distinguishes them from laser dissipative solitons and the main reason why they are excellent candidates for precision applications such as optical atomic clocks. To date, the focus has been on driving Kerr solitons close to their carrier frequency, in which case a single stable localised solution exists for fixed parameters. Here we experimentally demonstrate, for the first time, Kerr cavity solitons excitation around twice their carrier frequency. In that configuration, called parametric driving, two solitons of opposite phase may coexist. We use a fibre resonator that incorporates a quadratically nonlinear section and excite stable solitons by scanning the driving frequency. Our experimental results are in excellent agreement with a seminal amplitude equation, highlighting connections to hydrodynamic and mechanical systems, amongst others. Furthermore, we experimentally confirm that two different phase-locked solitons may be simultaneously excited and harness this multiplicity to generate a string of random bits, thereby extending the pool of applications of Kerr resonators to random number generators and Ising machines.

Efficient and Privacy-Preserving Decision Tree Classification for Health Monitoring Systems

Due to the increasing healthcare costs and the advance of wireless technology, health monitoring systems have been widely adopted recently. In health monitoring systems, a hospital outsources a clinical decision model to a cloud service provider, which receives biomedical data from remote clients and produces clinical decisions based on the outsourced model. Due to critical privacy concerns, both the clinical decision model and biomedical data should be protected. In this article, we propose an efficient and privacy-preserving decision tree (PPDT) classification scheme for health monitoring systems. Specifically, we first transform a decision tree classifier (i.e., the clinical decision model) into the Boolean vectors. Then, we leverage symmetric key encryption to encrypt the Boolean vectors as encrypted indices. The PPDT classification is achieved by searching the encrypted indices with encrypted tokens. We formulate a leakage function and provide the security definition and simulation-based proof for PPDT. The performance analyses demonstrate that PPDT is very efficient in terms of computation, communication, and storage. Experimental evaluations show that PPDT only requires microsecond-level execution time, kilobyte-level communication costs, and kilobyte-level storage costs on the test data set.

Mutually unbiased balanced functions and generalized random access codes

Quantum resources and protocols are known to outperform their classical counterparts in variety of communication and information processing tasks. Random Access Codes (RACs) are one such cryptographically significant family of bipartite communication tasks, wherein, the sender encodes a data set (typically a string of input bits) onto a physical system of bounded dimension and transmits it to the receiver, who then attempts to guess a randomly chosen part of the sender's data set (typically one of the sender's input bits). In this work, we introduce a generalization of this task wherein the receiver, in addition to the individual input bits, aims to retrieve randomly chosen functions of sender's input string. Specifically, we employ sets of mutually unbiased balanced functions (MUBS), such that perfect knowledge of any one of the constituent functions yields no knowledge about the others. We investigate and bound the performance of (i.) classical, (ii.) quantum prepare and measure, and (iii.) entanglement assisted classical communication (EACC) protocols for the resultant generalized RACs (GRACs). Finally, we detail the case of GRACs with three input bits, find maximal success probabilities for classical, quantum and EACC protocols, along with the effect of noisy quantum channels on the performance of quantum protocols. Moreover, with the help of this case study, we reveal several characteristic properties of the GRACs which deviate from the standard RACs.

Два ритуальных клада эпохи Митридатовых войн из Нижнего Подонья

The article is about two ritual deposits of the 2nd—1st centuries BC from the Lower Don region. The first votive hoard was found in 2018 in the inter-mound space of Turbuta III burial ground and transferred to the NovocherkasskMuseum of the History of Don Cossacks. The complex consisted of a crumpled bronze situla and helmet, a set of silver phalerae and a frontlet, as well as six sets of bits and cheekpieces. In 2016, information about another ritual deposit from illegal excavations in the Rostov region got on the Internet. Both complexes are very similar in composition, the nature of ritual damage, and the way things are placed. Phalerae and the frontlet from Turbuta III find close analogies in the well-known Starobelsk hoard. Obviously, in the Lower Don region, the same pattern can be traced as in the Northern Black Sea region — the connection of sets of phalerae with votive hoards. The helmets from both hoards are later versions of the Celtic helmets with a reinforced crown. It is difficult to determine unambiguously whether these helmets were made by Celtic armourer, or in a workshop of one of the Hellenistic kingdoms according to Celtic patterns. Situlae are believed to have been part of Roman military equipment. Probably, objects from both ritual deposits reflect participation of the Sarmatians in the Mithridatic wars, recorded in written sources.

Efficient boolean SSE: A novel encrypted database (EDB) for biometric authentication

Biometric authentication is up-and-coming to replace the traditional identity authentication method (e.g., passwords, PIN, identification cards) for its convenience and intelligence. With more and more users using this method, the database becomes more extensive, and the functions are seriously challenged. Data outsourcing has advantages in terms of convenience and cost savings, so it has attracted much research effort. However, due to the biometric's immutability of the whole life, it is extremely sensitive, and disclosing it to a third party is undesirable. In this paper, we address the issue of securely outsourcing biometric database. We propose a novel boolean searchable symmetric encryption (SSE) to construct a secure interactive protocol when outsourcing. A new encrypted database construction method was proposed, using the more efficient boolean vectors. Based on this, We suggest three kinds of expressive SSE, supporting disjunctive query, boolean query, and lightweight settings. We prove the schemes' correctness and security theoretically. Our constructions use simple cryptographic tools, such as symmetric cryptography and pseudo-random functions. They are straightforward to understand and easy to implement. The experiments show that all our schemes are practical and more efficient than the existing methods.

Composable security for practical quantum key distribution with two way classical communication

We present a theory for the composable security of sending-or-not-sending (SNS) protocol of twin field quantum key distribution (TF-QKD). We present methods to strictly calculate the finite-key effects in QKD with error rejection through two-way classical communication (TWCC) for SNS TF-QKD protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. With explicit formulas, we show that simply applying Chernoff bound in the calculation gives correct key rate, but the failure probability changes a little bit. We calculate the key rate with strict bounds and security, and obtain key rates by far breaking the PLOB (Pirandola, Laurenza, Ottaviani, and Banchi) bound with composable security.

Weak Convex Domination in Hypercubes

The n-cube Qn is the graph whose vertex set is the set of all n-dimensional Boolean vectors, two vertices being joined if and only if they differ in exactly one coordinate. The n-star graph Sn is a simple graph whose vertex set is the set of all n! permutations of {1, 2, · · · , n} and two vertices α and β are adjacent if and only if α(1)≠β(1) and α(i) ≠β(i) for exactly one i, i≠ 1.
 In this paper we determine weak convex domination number for hypercubes. Also convex, weak convex, m - convex and l1-convex numbers of star and hypercube graphs are determined.

SAVINGS TIME EXECUTION PRIMA NUMBERS GENERATOR USING BIT-ARRAY STRUCTURE

Prime number in growth computer science of number theory and very need to yield an tool which can yield an hardware storey level effectiveness use efficiency and Existing Tools can be used to awaken regular prime number sequence pattern, structure bit-array represent containing subdividing variables method of data aggregate with every data element which have type of equal, and also can be used in moth-balls the yielded number sequence. Prime number very useful to be applied by as bases from algorithm kriptografi key public creation, hash table, best algorithm if applied hence is prime number in order to can minimize collision (collisions) will happen, in determining pattern sequence of prime number which size measure is very big is not an work easy to, so that become problems which must be searched by the way of quickest to yield sequence of prime number which size measure is very big Serial use of prosesor in seeking sequence prime number which size measure is very big less be efficient remember needing of computing time which long enough, so also plural use prosesor in seeking sequence of prime number will concerning to price problem and require software newly. So that by using generator of prime number use structure bit-array expected by difficulty in searching pattern sequence of prime number can be overcome though without using plural processor even if, as well as time complexity minimization can accessed. Execution time savings gained from the research seen from the research data, using the algorithm on the input Atkins 676,999,999. 4235747.00 execution takes seconds. While the algorithm by using an array of input bits 676,999,999. 13955.00 execution takes seconds. So that there is a difference of execution time for 4221792.00 seconds.

Masking Circuit Faults and Trojan Circuit Injections Using Sat Solvers

Combinational circuit C composed of gates and its sub-circuit with set V of output nodes and set U of input nodes are considered. The set V consists of output nodes of fault gates of the circuit C (only logical faults are examined) and fault free gates, the inputs of which are at the same time lines in that Trojan circuit payloads are injected. A procedure of forming the set U, as a rule, depends on circuit C fabrication technology and is out of our consideration. We suggest recovering the circuit C behavior by using as much as possible simple masking circuits (patch circuits). Masking circuit inputs are connected with nodes from the set U, and outputs are united either with nodes that are fed by nodes from the set V or directly with nodes from the set V. The conventional way of recovering the circuit C behavior (in the frame of Engineering Change Order (ECO) technologies) is based on using results of circuit C simulation. This way guarantees correct circuit C behavior only on a set of Boolean vectors applied during simulation. We suggest using incompletely specified Boolean functions of nodes from V in the frame of ECO technologies, which allows guaranteeing correct behavior of the circuit C among all its input Boolean vectors. Deriving the incompletely specified Boolean functions is connected with applying SAT solvers. Having got these functions, we then obtain the masking circuit (patch circuit) using ESPRESSO and ABC systems.