Further observations on SIMON and SPECK families of block ciphers

SIMON and SPECK families of block ciphers are well-known lightweight ciphers designed by NSA. In this note, based on the previous investigations on SIMON, a closed formula for the squared correlations and differential probabilities of the mapping $\phi(x) = x \odot S^1(x)$ on $\mathbb{F}_2^n$ is given. From the aspects of linear and differential cryptanalysis, this mapping is equivalent to the core quadratic mapping of SIMON via rearrangement of coordinates and EA-equivalence. Based upon the proposed explicit formula, a full description of DDT and LAT of $\phi$ is provided. In the case of SPECK, as the only nonlinear operation in this family of ciphers is, addition mod $2^n$, after reformulating the formula for linear and differential probabilities of addition mod $2^n$, straightforward algorithms for finding the output masks with maximum squared correlation, given the input masks as well as the output differences with maximum differential probability, given the input differences, are presented

Prevalence and pattern of basal skull fracture in head injury patients in an academic hospital

Background: Basal skull fractures (BSFs) have been reported to be a major cause of morbidity and mortality in the literature, particularly in young male patients. However, there are limited data available on the aetiology, prevalence and patterns of such observed in South Africa. Objectives: To evaluate the prevalence and pattern of BSF in head injury patients referred to Dr George Mukhari Academic Hospital, Gauteng, South Africa. Methods: Patients of all ages with head injuries were considered for the study, and those who met the inclusion criteria were scanned using a 128-slice multidetector helical computed tomography (CT) machine after obtaining consent. Data were prospectively obtained over a 6-month period, interpreted on an advanced workstation by two readers and statistically analysed. Results: The prevalence of BSF in this study was found to be 15.2%. The majority of patients (80.5%) were under 40 years old, with a male to female ratio of 3:1. The most common aetiology of BSF was assault, which accounted for 46% of cases. The middle cranial fossa was the most frequently fractured compartment, while the petrous bone was the most commonly fractured bone. There was a statistically significant association between head injury severity and BSF, and between the number of fracture lines and associated signs of BSF (p < 0.001). The sensitivity of clinical signs in predicting BSF was 31%, while specificity was 89.3% (p = 0.004). Conclusion: The prevalence and pattern of BSF found were consistent with data from previously published studies, although, dissimilarly, assault was found to be the most common aetiology in this study

Lai-Massey Scheme Revisited

Lai-Massey scheme is a well-known block cipher structure which has been used in the design of the ciphers PES, IDEA, WIDEA, FOX and MESH. Recently, the lightweight block cipher FLY applied this structure in the construction of a lightweight $8 \times 8$ S-box from $4 \times 4$ ones. In the current paper, firstly we investigate the linear, differential and algebraic properties of the general form of S-boxes used in FLY, mathematically. Then, based on this study, a new cipher structure is proposed which we call generalized Lai-Massey scheme or GLM. We give upper bounds for the maximum average differential probability (MADP) and maximum average linear hull (MALH) of GLM and after examination of impossible differentials and zero-correlations of one round of this structure, we show that two rounds of GLM do not have any structural impossible differentials or zero-correlations. As a measure of structural security, we prove the pseudo-randomness of GLM by the H-coefficient method

Insulin-Like Growth Factor I and II mRNA Levels in Rumen Wall of Calves Fed with Different Physical Forms of Diets

This study was designed to investigate the effects of physical forms and hay contents of diets on gene expression of insulin-like growth factor (IGF) I and II in rumen epithelium of Holstein calves. Twelve male calves were assigned to 4 treatments: ground (GR), texturized (TX), pellet (PL), and ground+10% forage (GF). Calves were weaned on day 50 of age and then slaughtered on day 70 after birth. Rumen epithelial tissue samples were immediately collected for quantification of mRNA abundance. Results indicated that only IGF I expression was influenced by the dietary treatments. A significant (pIGF I expression and each of histological parameters denoted as length of rumen villi and diameter of keratinocyte layer was observed. No significant correlation between IGF II expression and rumen histological parameters was found (p&gt;0.05). Regarding the results, higher 0.05). Regarding the results, higher IGF I expression in PL and TX treatments despite the low growth rate might be due to the challenging condition of developing rumen in calves. In fact, the rumen tissue attempted to maintain rumen pH at least by induction of a higher IGF I expression

The Role of Protein SUMOylation in the Pathogenesis of Atherosclerosis

Atherosclerosis is a progressive, inflammatory cardiovascular disorder characterized by the development of lipid-filled plaques within arteries. Endothelial cell dysfunction in the walls of blood vessels results in an increase in vascular permeability, alteration of the components of the extracellular matrix, and retention of LDL in the sub-endothelial space, thereby accelerating plaque formation. Epigenetic modification by SUMOylation can influence the surface interactions of target proteins and affect cellular functionality, thereby regulating multiple cellular processes. Small ubiquitin-like modifier (SUMO) can modulate NFκB and other proteins such as p53, KLF, and ERK5, which have critical roles in atherogenesis. Furthermore, SUMO regulates leukocyte recruitment and cytokine release and the expression of adherence molecules. In this review, we discuss the regulation by SUMO and SUMOylation modifications of proteins and pathways involved in atherosclerosis

Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions

We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm and a are respectively complex and real parameters and \delta(x) is the Dirac delta function. For regions in the space of coupling constants \zeta_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator \eta and the corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a (perturbatively) bounded operator for the cases that the imaginary part of the coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also calculate the energy expectation values for certain Gaussian wave packets to study the nonlocal nature of \rh or equivalently the non-Hermitian nature of \rH. We show that these physical quantities are not directly sensitive to the presence of PT-symmetry.Comment: 22 pages, 4 figure

Statistical Properties of the Square Map Modulo a Power of Two

The square map is one of the functions that is used in cryptography. For instance, the square map is used in Rabin encryption scheme, block cipher RC6 and stream cipher Rabbit, in different forms. In this paper we study a special case of the square map, namely the square function modulo a power of two. We obtain probability distribution of the output of this map as a vectorial Boolean function. We find probability distribution of the component Boolean functions of this map. We present the joint probability distribution of the component Boolean functions of this function. We introduce a new function which is similar to the function that is used in Rabbit cipher and we compute the probability distribution of the component Boolean functions of this new map

Construction of New Families of ‎MDS‎ Diffusion Layers

Diffusion layers are crucial components of symmetric ciphers&#8206;. &#8206;These components&#8206;, &#8206;along with suitable Sboxes&#8206;, &#8206;can make symmetric ciphers resistant against statistical attacks like linear and differential cryptanalysis&#8206;. &#8206;Conventional &#8206;&#8206;MDS diffusion layers, which are defined as matrices over finite fields, have been used in symmetric ciphers such as AES&#8206;, &#8206;Twofish and SNOW&#8206;. &#8206;In this paper&#8206;, &#8206;we study linear, linearized and nonlinear MDS diffusion layers&#8206;. We investigate linearized diffusion layers, &#8206;which are a generalization of conventional diffusion layers&#8206;; t&#8206;hese diffusion layers are used in symmetric ciphers like SMS4&#8206;, &#8206;Loiss and ZUC&#8206;. W&#8206;e introduce some &#8206;new &#8206;families of linearized MDS diffusion layers &#8206;and as a consequence, &#8206;we &#8206;present a&#8206; &#8206;method &#8206;for &#8206;construction of &#8206;&#8206;&#8206;&#8206;randomized linear &#8206;&#8206;&#8206;&#8206;&#8206;diffusion &#8206;layers over a finite field. Nonlinear MDS diffusion layers are introduced in Klimov\u27s thesis; we investigate nonlinear MDS diffusion layers theoretically, and we present a new family of nonlinear MDS diffusion layers. We show that these nonlinear diffusion layers can be made randomized with a low &#8206;implementatio&#8206;n cost. An important fact about linearized and nonlinear diffusion layers is that they are more resistant against algebraic attacks in comparison to conventional diffusion layers. A &#8206;special case of diffusion layers are &#8206;&#8206;&#8206;(0,1)&#8206;-&#8206;diffusion layers. This type of diffusion layers are used in symmetric ciphers like ARIA&#8206;. &#8206;W&#8206;e examine (0,1)&#8206;-&#8206;diffusion layers and prove a theorem about them&#8206;. &#8206;At last&#8206;, &#8206;we study linearized MDS diffusion layers of symmetric ciphers Loiss, SMS4 and ZUC&#8206;, from the mathematical viewpoint

Cryptographic Properties of Addition Modulo 2n2^n

The operation of modular addition modulo a power of two is one of the most applied operations in symmetric cryptography. For example, modular addition is used in RC6, MARS and Twofish block ciphers and RC4, Bluetooth and Rabbit stream ciphers. In this paper, we study statistical and algebraic properties of modular addition modulo a power of two. We obtain probability distribution of modular addition carry bits along with conditional probability distribution of these carry bits. Using these probability distributions and Markovity of modular addition carry bits, we compute the joint probability distribution of arbitrary number of modular addition carry bits. Then, we examine algebraic properties of modular addition with a constant and obtain the number of terms as well as algebraic degrees of component Boolean functions of modular addition with a constant. Finally, we present another formula for the ANF of the component Boolean functions of modular addition modulo a power of two. This formula contains more information than representations which are presented in cryptographic literature, up to now