Three constructions of perfect authentication codes from projective geometry over finite fields

We propose a construction of full-rank q-ary 1-perfect codes. This is a generalization of the construction of full-rank binary 1-perfect codes by Etzion and Vardy (1994). The properties of the i-components of q-ary Hamming codes are investigated, and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1-perfect codes is generalized to the q-ary case. We propose a generalization of the notion of an i-component of a 1-perfect code and introduce the concept of an (i, σ)-component of a q-ary 1-perfect code. We also present a generalization of the Lindström–Schönheim construction of q-ary 1-perfect codes and provide a lower bound for the number of pairwise distinct q-ary 1-perfect codes of length n.

A construction of authentication codes with arbitration from subspace of vector space over finite fields is presented, and the parameters of the code are computed. Assuming that the probability distribution of source state and encoding rules are uniform, the probabilities of successful attacks are also computed. In some condition, the construction is perfect.

A construction of perfect binary codes is presented. It is shown that this construction gives rise to perfect codes that are nonequivalent to any of the previously known perfect codes. Furthermore, perfect codes C 1 and C 2 are constructed such that their intersection C 1∩C 2 has the maximum possible cardinality. The latter result is then employed to explicitly construct 22cn nonequivalent perfect codes of length n, for sufficiently large n and some constant c slightly less than 0.5.KeywordsParity CheckParity Check MatrixCoset RepresentativePerfect CodePerfect SegmentationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To build safe and reliable distributed decentralized systems using blockchain technology, a continuous chain of blocks is created, the unauthorized modification of which is not allowed by the applied cryptographic mechanisms. This is achieved by using unidirectional, collision resistant and search prototypes of cryptographic functions whose hash values from previous blocks are included in subsequent blocks. As a result, an unauthorized change in at least one bit of data in the previous blocks will be immediately detected. However, in the case of distributed storage of information, there is an additional requirement of synchronization of individual chains of blocks that are stored by various nodes. These and other issues are resolved by applying consensus building mechanisms, through which, after a certain sequence of actions, a continuous sequence of blocks (blockchain chain) becomes the same on all nodes of a decentralized network. This work examines one of the main vulnerabilities of blockchain systems built by consensus with probabilistic completion, namely, a double-spend attack. Based on the model of “independent players”, an analytical expression is obtained for calculating the probability of an attacker's successful double-spending attack. The quantitative values of the probability of a successful attack are given for various abilities of an attacker, a different number of generated blocks and a different race duration. Using computer simulation, the calculated values are experimentally verified. All empirical estimates were obtained with high accuracy (relative error not higher than 1%) and reliability (confidence level of at least 99%). To confirm the adequacy of the results obtained, a comparison of empirical results with theoretical calculations is given.

Contemporary social science has produced little research on connections between climate change and crime. Nonetheless, much prior research suggests that economic insecurity may affect individual calculations of the cost and benefit of engaging in criminal behavior, and climate change is likely to have important economic consequences for professions like fishing that depend directly on the environment. In this paper, we test the possibility that climate change affects participation in maritime piracy, depending on the specific ways that it impacts regional fish production. Our analysis is based on piracy in East Africa and the South China Sea. These two regions are strategic in that both areas have experienced a large amount of piracy; however, rising sea temperatures have been associated with declines in fish production in East Africa but increases in the South China Sea. We treat sea surface temperature as an instrument for fish output and find that in East Africa higher sea surface temperature is associated with declining fish production, which in turn increases the risk of piracy, whereas in the South China Sea higher sea surface temperature is associated with increasing fish production, which in turn decreases the risk of piracy. Our results also show that decreases in fish production bring about a larger number of successful piracy attacks in East Africa and that increases in fish production are associated with fewer successful attacks in the South China Sea. We discuss the theoretical and policy implications of the findings and point out that as climate change continues, its impact on specific crimes will likely be complex, with increases and decreases depending on context. Significance Statement There is little evidence on the effect of climate change on criminal behavior. This study seeks to quantify the impact of a specific type of climate change—rising sea temperature—on maritime piracy, a type of crime that is linked exclusively to the ocean. The risk of piracy attacks and the probability of successful attacks are higher with declines in fish production in East Africa and lower with increases in fish production in the South China Sea. These results suggest that climate change does affect maritime piracy rates and that its effect depends on the specific situational context and the rational choices that changing sea temperatures generate.

Blockchain technology is being studied in many innovative applications, such as: cryptocurrencies, smart contracts, communication systems, healthcare, Internet of Things, financial systems, software development, electronic voting and many others. Using a transparent and fully distributed peer-to-peer blockchain architecture, applications benefit from a data-only model, in which “transactions” are accepted into the blockchain ledger and, if the system is functioning properly, cannot be modified or deleted. The transparency of blockchain systems makes it possible to store publicly available and irrefutable records. A peer-to-peer blockchain system provides verifiable ledger maintenance without centralized management, which solves the problems of a single point of failure and a single point of trust. The article deals with the issue of the security of application of accounting systems built on decentralized principles using blockchain technology. Particular attention is paid to the problem of the possibility of double spending in such accounting systems. The article exemplifies the reorganization of records in blockchain ledgers, performed by successfully carrying out a 51% attack on consensus algorithms based on proof of work. Given refinement of analytical expressions of 51% attack probability obtained in the works of S. Nakamoto and M. Rosenfeld using a more general model, namely, the model of independent players, where the probability of block formation by attackers and an honest network are independent events. The results of comparing of the success probability of a double-spending attack on the blockchain systems calculated according to different models are presented.

Coded Caching is a promising solution to reduce the peak traffic in broadcast networks by prefetching the popular content close to end users and using coded transmissions. One of the chief issues of most coded caching schemes in literature is the issue of large subpacketization, i.e., they require each file to be divided into a large number of subfiles. In this work, we present a coded caching scheme using line graphs of bipartite graphs in conjunction with projective geometries over finite fields. The presented scheme achieves a rate Θ(K/log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> K) (K being the number of users, q is some prime power) with subexponential subpacketization q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O((logq K)^2)</sup> when cached fraction is upper bounded by a constant (M/N ≤ 1/q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> , for some positive integer α). Compared to earlier schemes, the presented scheme has a lower subpacketization (albeit possessing a higher rate). We also present a new subpacketization dependent lower bound on the rate for caching schemes in which each subfile is cached in the same number of users. Compared to the previously known bounds, this bound seems to perform better for a range of parameters of the caching system.

A new self-embedding and fragile watermarking technique which was used for image integrity authentication was brought up. The assured function of the composite chaotic iterative dynamic system and its initial parameter was put forward. The method using the single pixel value for self-authentication that authenticating bit embedded in the lowest significant bit of the pixel value was brought up. It brought up the prime decomposition function of the pixel value, making the adjacent pixel value completely separated in chaotic calculation. It led up to the facts that no additional information was needed when authenticating, and the algorithm could prevent the safety danger caused by parameter transmission, and it could ascertain the position accurately to a single pixel when tamper occurs, the probability of successful attack was 50%.

Let PG be the ‐dimensional projective space over and let be a simple graph of order for some . A design over is a collection of graphs (blocks) isomorphic to with the following properties: the vertex set of every block is a subspace of PG; every two distinct points of PG are adjacent in exactly blocks. This new definition covers, in particular, the well‐known concept of a design over corresponding to the case that is complete. In this study of a foundational nature we illustrate how difference methods allow us to get concrete nontrivial examples of ‐decompositions over or for which is a cycle, a path, a prism, a generalized Petersen graph, or a Moebius ladder. In particular, we will discuss in detail the special and very hard case that is complete and , that is, the Steiner 2‐designs over a finite field. Also, we briefly touch the new topic of near resolvable designs over . This study has led us to some (probably new) collateral problems concerning difference sets. Supported by multiple examples, we conjecture the existence of infinite families of Γ‐decompositions over a finite field that can be obtained by suitably labeling the vertices of Γ with the elements of a Singer difference set.

In this paper, a construction of Cartesian authentication codes from vector space over finite fields is presented and its size parameters are computed. Under the assumption that the choose of encoding rules and source states obeys uniform probability distribution, the probabilities P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</sub> of a successful impersonation attack and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> of a successful substitution attack of these codes are also computed.

Perfect binary codes: bounds and properties

We present a few new constructions for perfect linear single byte-correcting codes. These constructions generate some perfect single byte-correcting codes with new parameters, and some perfect single byte-correcting codes with known parameters and simpler presentation and implementation over the known codes. It is also shown that nonequivalent perfect linear single byte-correcting codes exist when all the bytes have the same size.

In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or, in the ω-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity.The proof necessitated an extension of the model-theoretic framework to includealmost hyperimaginaries, and the study ofpolygroups.

A new definition for the dimension of a combinatorial t- (v,k,\lambda) design over a finite field is proposed. The complementary designs of the hyperplanes in a finite projective or affine geometry, and the finite Desarguesian planes in particular, are characterized as the unique (up to isomorphism) designs with the given parameters and minimum dimension. This generalizes a well-known characterization of the binary hyperplane designs in terms of their minimum 2-rank. The proof utilizes the q-ary analogue of the Hamming code, and a group-theoretic characterization of the classical designs.

New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the \textit {Hamming number-theoretic transform} and the \textit {Golay number-theoretic transform}. A few properties of these new transforms are presented.