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

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

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

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

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

Efficient MDS Diffusion Layers Through Decomposition of Matrices

Diffusion layers are critical components of symmetric ciphers. MDS matrices are diffusion layers of maximal branch number which have been used in various symmetric ciphers. In this article, we examine decomposition of cyclic matrices from mathematical viewpoint and based on that, we present new cyclic MDS matrices. From the aspect of implementation, the proposed matrices have lower implementation costs both in software and hardware, compared to what is presented in cryptographic literature, up to our knowledge

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th Laguerre polynomial. The two key problems (viz., the one of the ambiguity and the one of the closed-form construction of all of the eligible inner products which make $H$ Hermitian in the respective {\em ad hoc} Hilbert spaces) are discussed. Then, for illustration, the first four simplest, $k-$parametric definitions of inner products with $k=0,k=1,k=2$ and $k=3$ are explicitly displayed. In mathematical terms these alternative inner products may be perceived as alternative Hermitian conjugations of the initial N-plet of Laguerre polynomials. In physical terms the parameter $k$ may be interpreted as a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p

Demographic parameters of two spotted ladybird Adalia bipunctata L. (Col.: Coccinellidae) on pomegranate aphid Aphis punicae (Hem.: Aphididae) under controlled conditions

Abstract Demographic parameters of Adalia bipunctata on Aphis punicae under controlled conditions were studied. Life table parameters of predator were studied on 100 newly laid A. bipunctata eggs. Daily larvae and adults of ladybirds were fed on fresh leaves of pomegranate which were infected by A. punicae. Fifteen pairs of A. bipunctata (24h-old) were selected to study the reproductive life history of A. bipunctata. The reproduction data were analyzed according to jackknife method. The results indicated that the incubation period was 30.22 days and adults emerged after 24.85 days. L x was estimated 0.69 and the specific mortality age of larvae and adults of coccinellid increased gradually from day 46. Reproductive parameters of A.bipunctata showed that the gross fecundity rate, gross fertility rate, gross hatch rate, net fecundity rate and net fertility rate were 462.4±22.1, 405.3±23.4, 0.78651±1.058, 228.4±11 and 189.49±9.11 days, respectively. The mean numbers of eggs was estimated 11.8 egg/female/day and 13.21 egg/day. The net reproductive rate (R 0 ), mean generation time (T c ), doubling time (DT) and Finite rate of increase (λ) of A.bipunctata were 133.796, 25.27, 3.57, 1.21 days, respectively and intrinsic rate of natural increase (r m ) was 0.193 female/female/days. Also intrinsic rate of birth (b) and intrinsic rate of dead (d) were 0.2047 and 0.02851 female/ female/ day respectively. Hence, our findings may provide important information towards designing a comprehensive IPM program to control the pomegranate aphid in Iran. Up to date, no other published data are available concerning the demographic parameters of A. bipunctata on A. punicae