In ARX structures, constants that are not rotational invariant are often injected into the state, in the form of round constants or as a result of using a fixed key. Rotational cryptanalysis cannot deal with such constants. Rotational cryptanalysis in the presence of constants, also known as rotational-XOR cryptanalysis, is a recently proposed statistical technique to attack ARX primitives. The...

In this paper we review some author’s results about Weingarten surfaces in Euclidean space R 3 and hyperbolic space H 3 . We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property. First, we consider Weingarten surfaces in R 3 that are foliated by circles, proving that the surface is rotational, a Riemann example or a generalized cone. Next...

We examine the Toda frame formulation of the SO(3)–invariant hyper–Kahler 4–metrics, namely Eguchi–Hanson, Taub–NUT and Atiyah–Hitchin. Our method exploits the presence of a rotational SO(2) isometry, leading to the explicit construction of all three complex structures as a singlet plus a doublet. The Atiyah–Hitchin metric on the moduli space of BPS SU(2) monopoles with magnetic charge 2 is pur...

In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. An integrable random vector ξ in R is called swap-invariant if E ∣∣∑ j ujξj ∣∣ is invariant under all permutations of the components of ξ for each u ∈ R. Further a random sequence is swap-invariant if its finite-dimensional distributions are swap-invariant. Two characterizations of large classe...

We study supersymmetric domain walls in N=1 supergravity theories, including those with modular-invariant superpotentials arising in superstring compactifications. Such domain walls are shown to saturate the Bogomol’nyi bound of wall energy per unit area. We find static and reflection asymmetric domain wall solutions of the self-duality equations for the metric and the matter fields. Our result...

We are interested in the computability of the invariant measures in a computable dynamical system. We construct two counter-examples. The first one has a unique SRB measure, which is not computable. The second one has no computable invariant measure at all. The systems are topological, i.e. continuous transformations on compact spaces, so they admit invariant measures. A topological dynamical s...

We study sequences of periodic orbits and the associated phase space dynamics in a 4-D symplectic map of interest to the problem of beam stability in circular particle accelerators. The increasing period of these orbits is taken from a sequence of rational approximants to an incommensurate pair of irrational rotation numbers of an invariant torus. We find stable (elliptic– elliptic) periodic or...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...