The Maiorana-McFarland structure based cryptanalysis of Simon

In this paper we propose the linear hull construction for block ciphers with quadratic Maiorana-McFarland structure round functions. The search for linear trails with high squared correlations from our Maiorana-McFarland structure based constructive linear cryptanalysis is linear algebraic. Hence from this linear algebraic essence, the space of all linear trails has the structure such that good linear hulls can be constructed. Then for the Simon2n and its variants, we prove the lower bound $\frac{1}{2^n}$ on the potential of the linear hull with the fixed input and output masks at arbitrary long rounds, under independent assumptions. We argue that for Simon2n the potential of the realistic linear hull of the Simon2n with the linear key-schedule should be bigger than $\frac{1}{2^{2n}}$.\\ On the other hand we prove that the expected differential probability (EDP) is at least $\frac{1}{2^n}$ under the independence assumptions. It is argued that the lower bound of EDP of Simon2n of realistic differential trails is bigger than $\frac{1}{2^{2n}}$. It seems that at least theoretically the Simon2n is insecure for the key-recovery attack based on our new constructed linear hulls and key-recovery attack based on our constructed differential trails.\

The Security of SIMON-like Ciphers Against Linear Cryptanalysis

In the present paper, we analyze the security of SIMON-like ciphers against linear cryptanalysis. First, an upper bound is derived on the squared correlation of SIMON-like round function. It is shown that the upper bound on the squared correlation of SIMON-like round function decreases with the Hamming weight of output mask increasing. Based on this, we derive an upper bound on the squared correlation of linear trails for SIMON and SIMECK, which is $2^{-2R+2}$ for any $R$-round linear trail. We also extend this upper bound to SIMON-like ciphers. Meanwhile, an automatic search algorithm is proposed, which can find the optimal linear trails in SIMON-like ciphers under the Markov assumption. With the proposed algorithm, we find the provably optimal linear trails for $12$, $16$, $19$, $28$ and $37$ rounds of SIMON$32/48/64/96/128$. To the best of our knowledge, it is the first time that the provably optimal linear trails for SIMON$64$, SIMON$96$ and SIMON$128$ are reported. The provably optimal linear trails for $13$, $19$ and $25$ rounds of SIMECK$32/48/64$ are also found respectively. Besides the optimal linear trails, we also find the $23$, $31$ and $41$-round linear hulls for SIMON$64/96/128$, and $13$, $21$ and $27$-round linear hulls for SIMECK$32/48/64$. As far as we know, these are the best linear hull distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers in \cite{KolblLT15}, our search algorithm is more efficient and practical to evaluate the security against linear cryptanalysis in the design of SIMON-like ciphers

Monte Carlo study of the hull distribution for the q=1 Brauer model

We study a special case of the Brauer model in which every path of the model has weight q=1. The model has been studied before as a solvable lattice model and can be viewed as a Lorentz lattice gas. The paths of the model are also called self-avoiding trails. We consider the model in a triangle with boundary conditions such that one of the trails must cross the triangle from a corner to the opposite side. Motivated by similarities between this model, SLE(6) and critical percolation, we investigate the distribution of the hull generated by this trail (the set of points on or surrounded by the trail) up to the hitting time of the side of the triangle opposite the starting point. Our Monte Carlo results are consistent with the hypothesis that for system size tending to infinity, the hull distribution is the same as that of a Brownian motion with perpendicular reflection on the boundary.Comment: 21 pages, 9 figure

Network Models in Class C on Arbitrary Graphs

We consider network models of quantum localisation in which a particle with a two-component wave function propagates through the nodes and along the edges of an arbitrary directed graph, subject to a random SU(2) rotation on each edge it traverses. The propagation through each node is specified by an arbitrary but fixed S-matrix. Such networks model localisation problems in class C of the classification of Altland and Zirnbauer, and, on suitable graphs, they model the spin quantum Hall transition. We extend the analyses of Gruzberg, Ludwig and Read and of Beamond, Cardy and Chalker to show that, on an arbitrary graph, the mean density of states and the mean conductance may be calculated in terms of observables of a classical history-dependent random walk on the same graph. The transition weights for this process are explicitly related to the elements of the S-matrices. They are correctly normalised but, on graphs with nodes of degree greater than 4, not necessarily non-negative (and therefore interpretable as probabilities) unless a sufficient number of them happen to vanish. Our methods use a supersymmetric path integral formulation of the problem which is completely finite and rigorous.Comment: 17 pages, 3 figure

Quantum and classical localisation and the Manhattan lattice

We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A mapping exists between problems belonging to this symmetry class and certain classical random walks which are self-avoiding and have attractive interactions; we exploit this equivalence, using a study of the classical random walks to gain information about the corresponding quantum problem. In a field-theoretic approach, we show that the interactions may flow to one of two possible strong coupling regimes separated by a transition: however, using Monte Carlo simulations we show that the walks are in fact always compact two-dimensional objects with a well-defined one-dimensional surface, indicating that the corresponding quantum system is localised.Comment: 11 pages, 8 figure

A semi-supervised approach to visualizing and manipulating overlapping communities

When evaluating a network topology, occasionally data structures cannot be segmented into absolute, heterogeneous groups. There may be a spectrum to the dataset that does not allow for this hard clustering approach and may need to segment using fuzzy/overlapping communities or cliques. Even to this degree, when group members can belong to multiple cliques, there leaves an ever present layer of doubt, noise, and outliers caused by the overlapping clustering algorithms. These imperfections can either be corrected by an expert user to enhance the clustering algorithm or to preserve their own mental models of the communities. Presented is a visualization that models overlapping community membership and provides an interactive interface to facilitate a quick and efficient means of both sorting through large network topologies and preserving the user's mental model of the structure. © 2013 IEEE

A Human-Environment Systems Approach to Outdoor Recreation, Human Biological Stress, and Landscape Aesthetics

Outdoor recreation, as the intersection between physical exercise and nature, provides a multitude of psychological and physiological benefits to human well-being. Though many studies have reported qualitative stress reduction from outdoor recreation, few have focused on quantitative measurements of stress across recreational activity types, intrapersonal differences, and environmental variables. To determine whether outdoor recreation affects physiology, we collected 190 paired salivary cortisol and testosterone samples and 157 surveys from 88 hikers, 81 mountain bikers, and 44 off-highway vehicle (OHV) motorists. After recreation, cortisol concentrations were significantly reduced in hikers and OHV motorists, but cortisol and testosterone concentrations increased in mountain bikers. These three recreational activity types also significantly differed in motivation and wildlife observations, which could be additional mechanisms of physiological change. Out of all three recreation types, hikers were most motivated by environmental variables. To test how the environment could be affecting hikers, we evaluated the impact of landscape aesthetic perceptions and land cover types on hiker spatial movement and stress relief. Using data from 58 GPS tracks, we found that salivary cortisol was significantly reduced when hikers walked through riparian areas. Hiker cortisol also decreased after recreating in areas they perceived as aesthetically pleasing. Aesthetic quality influenced hiker spatial movement, with hikers choosing to recreate in high-aesthetic high-wildlife observance riparian areas. Though hiker movement and stress were not related to the intensity of visitor use, wildlife observations decreased with greater recreational utilization. Hikers, however, did not perceive any negative impact from their recreational activities. Despite the different forms of recreational activity, outdoor recreation has potential to benefit human well-being. In addition, managing recreational land for ecosystem health and wildlife may enhance well-being benefits, as well as serving a role in the conservation of wildlands