Single Permutation Research Articles

A Tweakable Key Alternating Lightweight Cipher for Internet of Things

Internet of things (IoT) is a global network of uniquely addressable interconnected things, based on standard communication protocols. As the number of devices connected to the IoT escalates, they are becoming a likely target for hackers. Also, the limited resources of IoT devices makes the security on top of the actual functionality of the device. Therefore, the cryptographic algorithm for such devices has to be devised as small as possible. To tackle the resource constrained nature of IoT devices, this article presents a lightweight cryptography algorithm based on a single permutation and iterated Even-Mansour construction. The proposed algorithm is implemented in low cost microcontrollers, thus making it suitable for a wide range of IoT nodes.

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry.

We introduce the notion of combinatorial gauge symmetry-a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)-that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

SMfinder: Small Molecules Finder for Metabolomics and Lipidomics Analysis.

Metabolomics and lipidomics studies are becoming increasingly popular but available tools for automated data analysis are still limited. The major issue in untargeted metabolomics is linked to the lack of efficient ranking methods allowing accurate identification of metabolites. Herein, we provide a user-friendly open-source software, named SMfinder, for the robust identification and quantification of small molecules. The software introduces an MS2 false discovery rate approach, which is based on single spectral permutation and increases identification accuracy. SMfinder can be efficiently applied to shotgun and targeted analysis in metabolomics and lipidomics without requiring extensive in-house acquisition of standards as it provides accurate identification by using available MS2 libraries in instrument independent manner. The software, downloadable at www.ifom.eu/SMfinder, is suitable for untargeted, targeted, and flux analysis.

The Doubly Stochastic Single Eigenvalue Problem: A Computational Approach

The problem of determining DSn, the complex numbers that occur as an eigenvalue of an n-by-n doubly stochastic matrix, has been a target of study for some time. The Perfect-Mirsky region, PMn, is contained in DSn and is known to be exactly DSn for but strictly contained within DSn for n = 5. Here, we present a Boundary Conjecture that asserts that the boundary of DSn is achieved by eigenvalues of convex combinations of pairs of (or single) permutation matrices. We present a method to efficiently compute a portion of DSn and obtain computational results that support the Boundary Conjecture. We also give evidence that DSn is equal to PMn for certain n > 5.

Globally simple Heffter arrays [formula omitted] when [formula omitted

Square Heffter arrays are n×n arrays such that each row and each column contains k filled cells, each row and column sum is divisible by 2nk+1 and either x or −x appears in the array for each integer 1⩽x⩽nk. Archdeacon noted that a Heffter array, satisfying two additional conditions, yields a face 2-colourable embedding of the complete graph K2nk+1 on an orientable surface, where for each colour, the faces give a k-cycle system. Moreover, a cyclic permutation on the vertices acts as an automorphism of the embedding. These necessary conditions pertain to cyclic orderings of the entries in each row and each column of the Heffter array and are: (1) for each row and each column the sequential partial sums determined by the cyclic ordering must be distinct modulo 2nk+1; (2) the composition of the cyclic orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. We construct Heffter arrays that satisfy condition (1) whenever (a) k≡0(mod4); or (b) n≡1(mod4) and k≡3(mod4); or (c) n≡0(mod4), k≡3(mod4) and n≫k. As corollaries to the above we obtain pairs of orthogonal k-cycle decompositions of K2nk+1.

Graphical representations of cyclic permutation groups

In this paper we prove that a permutation group A generated by a single permutation σ is an automorphism group of an edge-colored graph if and only if for every orbit O of σ with cardinality |O|≥3 there exists another orbit O′ of σ such that gcd(|O|,|O′|)≥3. We prove also that every such permutation group is an automorphism group of a 3-colored graph. This is a step towards a characterization of cyclic permutation groups that are automorphism groups of simple graphs.

Cyclic Permutation Groups that are Automorphism Groups of Graphs

In this paper we establish conditions for a permutation group generated by a single permutation to be an automorphism group of a graph. This solves the so called concrete version of König’s problem for the case of cyclic groups. We establish also similar conditions for the symmetry groups of other related structures: digraphs, supergraphs, and boolean functions.

Autistic traits, resting-state connectivity, and absolute pitch in professional musicians: shared and distinct neural features

BackgroundRecent studies indicate increased autistic traits in musicians with absolute pitch and a higher proportion of absolute pitch in people with autism. Theoretical accounts connect both of these with shared neural principles of local hyper- and global hypoconnectivity, enhanced perceptual functioning, and a detail-focused cognitive style. This is the first study to investigate absolute pitch proficiency, autistic traits, and brain correlates in the same study.Sample and methodsGraph theoretical analysis was conducted on resting-state (eyes closed and eyes open) EEG connectivity (wPLI, weighted phase lag index) matrices obtained from 31 absolute pitch (AP) and 33 relative pitch (RP) professional musicians. Small-worldness, global clustering coefficient, and average path length were related to autistic traits, passive (tone identification) and active (pitch adjustment) absolute pitch proficiency, and onset of musical training using Welch two-sample tests, correlations, and general linear models.ResultsAnalyses revealed increased path length (delta 2–4 Hz), reduced clustering (beta 13–18 Hz), reduced small-worldness (gamma 30–60 Hz), and increased autistic traits for AP compared to RP. Only clustering values (beta 13–18 Hz) were predicted by both AP proficiency and autistic traits. Post hoc single connection permutation tests among raw wPLI matrices in the beta band (13–18 Hz) revealed widely reduced interhemispheric connectivity between bilateral auditory-related electrode positions along with higher connectivity between F7–F8 and F8–P9 for AP. Pitch-naming ability and pitch adjustment ability were predicted by path length, clustering, autistic traits, and onset of musical training (for pitch adjustment) explaining 44% and 38% of variance, respectively.ConclusionsResults show both shared and distinct neural features between AP and autistic traits. Differences in the beta range were associated with higher autistic traits in the same population. In general, AP musicians exhibit a widely underconnected brain with reduced functional integration and reduced small-world property during resting state. This might be partly related to autism-specific brain connectivity, while differences in path length and small-worldness reflect other ability-specific influences. This is further evidenced for different pathways in the acquisition and development of absolute pitch, likely influenced by both genetic and environmental factors and their interaction.

Beyond-birthday secure domain-preserving PRFs from a single permutation

This paper revisits the fundamental cryptographic problem of building pseudorandom functions (PRFs) from pseudorandom permutations (PRPs). We prove that, SUMPIP, i.e. $$P \oplus P^{-1}$$P?P-1, the ...

A Hardware and Secure Pseudorandom Generator for Constrained Devices

Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the N-cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term effects of a slight modification of the seed (proven to be sensitive to the initial conditions) or of the inputted generator cannot be predicted. The proposal has been fully deployed on a FPGA and 65 nm ASIC, it runs completely in parallel while consuming as low resources as possible, and achieving: (a) 11.5 Gb/s for FPGA and 9.4 Gb/s for ASIC random bit throughput, (b) 3.3 μW (LF) to 7.8 mW (UHF) total power consumption with 5% leakage power, measured at 1.32 V, and (c) able to successfully pass the statistical tests of NIST and TestU01 (BigCrush).

Genome-wide analysis of nucleotide binding site-leucine-rich repeats (NBS-LRR) disease resistance genes in Gossypium hirsutum

Nucleotide binding site-leucine-rich repeats (NBS-LRR) disease resistance genes (R genes) are the main class of R genes in plants. In order to fully understand the structure characteristic and composition of NBS-LRR R genes in upland cotton, and further reveal their roles in against to various pathogens, all NBS-LRR R genes in upland cotton were gathered, then their physical located distribution on chromosomes were analyzed. Next, all these upland cotton NBS-LRR R genes were performed by homologous comparison analysis compared with Arabidopsis thaliana (A. thaliana) NBS-LRR R genes. The results showed that cotton NBS-LRR R genes are distributed on 26 chromosomes with clustered or single permutation characters. These R genes can be divided into two subfamilies of group CC-NBS-LRR (315 genes) and TIR-NBS-LRR (122 genes). The CC-NBS-LRR subtype can be further classified into five groups: A, B, C, D and NL-A. The TIR-NBS-LRR subtype contains seven groups: B, C, D, E, G, TN-A and putative genes. Some cotton NBS-LRR R genes have homologous genes with those of A. thaliana, but most of them presented obvious differences compared with Arabidopsis NBS-LRR R genes. The basic information on the classification of cotton NBS-LRR R genes would be helpful for further ongoing their functional exploration and finally revealing their roles in against to various pathogens.

Analysis of the single-permutation encrypted Davies–Meyer construction

We consider the so-called Encrypted Davies–Meyer (EDM) construction, which turns a permutation P on $$\{0,1\}^n$$ into a function from $$\{0,1\}^n$$ to $$\{0,1\}^n$$ defined as $$P(P(x)\oplus x)$$ . A similar construction using two independent permutations, namely $$P'(P(x)\oplus x)$$ , was previously analyzed by Cogliati and Seurin (Advances in cryptology—CRYPTO 2016 (Proceedings, Part I). LNCS, vol 9814, pp. 121–149, 2016) who showed that when P and $$P'$$ are secret and random, then any black-box adversary needs at least roughly $$2^{2n/3}$$ queries to distinguish the construction from a uniformly random function from $$\{0,1\}^n$$ to $$\{0,1\}^n$$ . In this paper, we focus on the single-permutation variant of the construction. Our main result is that the PRF-security of the single-permutation EDM construction is also (at least) roughly $$2^{2n/3}$$ , in the sense that any black-box adversary needs at least this number of queries to distinguish the construction from a uniformly random function. This yields the first PRP-to-PRF conversion method which uses a single permutation, does not shrink the original domain nor range of the permutation, and provides security beyond the birthday bound.

Opposition-Based Memetic Algorithm and Hybrid Approach for Sorting Permutations by Reversals.

Sorting unsigned permutations by reversals is a difficult problem; indeed, it was proved to be -hard by Caprara ( 1997 ). Because of its high complexity, many approximation algorithms to compute the minimal reversal distance were proposed until reaching the nowadays best-known theoretical ratio of 1.375. In this article, two memetic algorithms to compute the reversal distance are proposed. The first one uses the technique of opposition-based learning leading to an opposition-based memetic algorithm; the second one improves the previous algorithm by applying the heuristic of two breakpoint elimination leading to a hybrid approach. Several experiments were performed with one-hundred randomly generated permutations, single benchmark permutations, and biological permutations. Results of the experiments showed that the proposed OBMA and Hybrid-OBMA algorithms achieve the best results for practical cases, that is, for permutations of length up to 120. Also, Hybrid-OBMA showed to improve the results of OBMA for permutations greater than or equal to 60. The applicability of our proposed algorithms was checked processing permutations based on biological data, in which case OBMA gave the best average results for all instances.

Genome sequence and analysis of Escherichia coli production strain LS5218

Escherichia coli strain LS5218 is a useful host for the production of fatty acid derived products, but the genetics underlying this utility have not been fully investigated. Here, we report the genome sequence of LS5218 and a list of large mutations and single nucleotide permutations (SNPs) relative to E. coli K-12 strain MG1655. We discuss how genetic differences may affect the physiological differences between LS5218 and MG1655. We find that LS5218 is more closely related to E. coli strain NCM3722 and suspect that small genetic differences between K-12 derived strains may have a significant impact on metabolic engineering efforts.

Nine classes of permutations enumerated by binomial transform of Fine’s sequence

The problem of avoidance of a single permutation pattern or of a pair of patterns of length four has been well studied. Less is known concerning the avoidance of three 4-letter patterns. In this paper, we determine up to symmetry all triples of 4-letter patterns such that the number of members of Sn avoiding any one of them is given by the binomial transform of Fine’s sequence (see A033321 in OEIS). We make use of both algebraic and combinatorial proofs in order to establish our results. In a couple of cases, we introduce certain auxiliary statistics on Sn which give rise to a system of functional equations that can be solved using the kernel method. In another case, a direct bijection is defined between members of the avoidance class in question and the set of skew Dyck paths.

Multi-key Analysis of Tweakable Even-Mansour with Applications to Minalpher and OPP

The tweakable Even-Mansour construction generalizes the conventional Even-Mansour scheme through replacing round keys by strings derived from a master key and a tweak. Besides providing plenty of inherent variability, such a design builds a tweakable block cipher from some lower level primitive. In the present paper, we evaluate the multi-key security of TEM-1, one of the most commonly used one-round tweakable Even-Mansour schemes (formally introduced at CRYPTO 2015), which is constructed from a single n-bit permutation P and a function f(k, t) linear in k from some tweak space to {0, 1} n. Based on giant component theorem in random graph theory, we propose a collision-based multi-key attack on TEM-1 in the known-plaintext setting. Furthermore, inspired by the methodology of Fouque et al. presented at ASIACRYPT 2014, we devise a novel way of detecting collisions and eventually obtain a memory-efficient multi-key attack in the adaptive chosen-plaintext setting. As important applications, we utilize our techniques to analyze the authenticated encryption algorithms Minalpher (a second-round candidate of CAESAR) and OPP (proposed at EUROCRYPT 2016) in the multi-key setting. We describe knownplaintext attacks on Minalpher and OPP without nonce misuse, which enable us to recover almost all O(2n/3) independent masks by making O(2n/3) queries per key and costing O(22n/3) memory overall. After defining appropriate iterated functions and accordingly changing the mode of creating chains, we improve the basic blockwiseadaptive chosen-plaintext attack to make it also applicable for the nonce-respecting setting. While our attacks do not contradict the security proofs of Minalpher and OPP in the classical setting, nor pose an immediate threat to their uses, our results demonstrate their security margins in the multi-user setting should be carefully considered. We emphasize this is the very first third-party analysis on Minalpher and OPP.

Improved method for detecting weak abrupt information based on permutation entropy

As a dynamic detecting method for abrupt information, permutation entropy could effectively reflect the subtle change in time series data, which is also simple and can be computed conveniently. Based on the permutation entropy, some improved methods for detecting weak abrupt information hidden in time series data are presented, such as permutation entropy spectrum, second permutation entropy, and second permutation entropy spectrum. Through some simulation examples, these new methods are compared with the existing single permutation entropy and approximate entropy, and the results show that these methods can more effectively detect the much weaker abrupt information. Especially, the second permutation entropy spectrum is very robust even if the periodic abrupt information is very weak.

The effect of response option order on self-rated health: a replication study.

Following calls for replication of research studies, this study documents the results of two studies that experimentally examine the impact of response option order on self-rated health (SRH). Two studies from an online panel survey examined how the order of response options (positive to negative versus negative to positive) influences the distribution of SRH answers. The results of both studies indicate that the distribution of SRH varies across the experimental treatments, and mean SRH is lower (worse) when the response options start with "poor" rather than "excellent." In addition, there are differences across the two studies in the distribution of SRH and mean SRH when the response options begin with "excellent," but not when the response options begin with "poor." The similarities in the general findings across the two studies strengthen the claim that SRH will be lower (worse) when the response options are ordered beginning with "poor" rather than "excellent" in online self-administered questionnaires, with implications for the validity of SRH. The slight differences in the administration of the seemingly identical studies further strengthen the claim and also serve as a reminder of the inherent variability of a single permutation of any given study.

Forward VNS, Reverse VNS, and Multi-VNS Algorithms for Job-Shop Scheduling Problem

This paper proposes a number of forward VNS and reverse VNS algorithms for job-shop scheduling problem. The forward VNS algorithms are the variable neighborhood search algorithms applied to the original problem (i.e., the problem instance with the original precedence constraints). The reverse VNS algorithms are the variable neighborhood search algorithms applied to the reversed problem (i.e., the problem instance with the reversed precedence constraints). This paper also proposes a multi-VNS algorithm which assigns an identical initial solution-representing permutation to the selected VNS algorithms, runs these VNS algorithms, and then uses the best solution among the final solutions of all selected VNS algorithms as its final result. The aim of the multi-VNS algorithm is to utilize each single initial solution-representing permutation most efficiently and thus receive its best result in return.

A linear-time algorithm for the orbit problem over cyclic groups

The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same orbit with respect to a given finite permutation group (represented by their generators) acting on this set of configurations by permuting indices. It is known that the problem is in general as hard as the graph isomorphism problem, whose precise complexity (whether it is solvable in polynomial-time) is a long-standing open problem. In this paper, we consider the restriction of the orbit problem when the permutation group is cyclic (i.e. generated by a single permutation), an important restriction of the problem. It is known that this subproblem is solvable in polynomial-time. Our main result is a linear-time algorithm for this subproblem.