A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R n. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these " partial quotients " , so called determinants, are defined. It is pro...

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved t...

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard ...

Complex classical Cayley-Klein categories A(j), B(j), C(j) and D(j) are constructed by the method of categorical extension of the complex classical Cayley-Klein groups SL(2n; j;C), SO(2n + 1; j;C), Sp(2n; j;C) and SO(2n; j;C), respectively. The explicit construction of the irreducible representations of the complex classical Cayley-Klein categories is received. Completeness of lists of the irre...

KLEIN is a family of block ciphers proposed by Zheng Gong et al. at RFIDSec 2011, and its lightweight features are suitable for resource-constrained devices. However, the original design of KLEIN does not consider the potential attacks by power analysis methods. This paper presents power analysis attacks against a FPGA implementation of KLEIN by the authors of KLEIN. The attacking strategy, att...

Abstract. A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly on G/H such that the quotient space Γ\G/H is compact. When n is even, we find every closed connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work reveals ...

KLEIN is a family of lightweight block ciphers presented at RFIDSec 2011 that combines a 4-bit Sbox with Rijndael’s byte-oriented MixColumn. This approach allows compact implementations of KLEIN in both low-end software and hardware. This paper shows that interactions between those two components lead to the existence of differentials of unexpectedly high probability: using an iterative collect...

An analysis of the effects associated with the Kaluza-Klein excitations of the photon and of the W and Z bosons on gμ − 2 for d number of extra dimensions with large radius compactifications is given. The Kaluza-Klein effects on gμ − 2 are found to be very sensitive to the number of extra dimensions. For models where the quarkleptons generations live on the 4D wall, it is shown that when the co...

A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly discontinuously on G/H, such that the quotient space Γ\G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work ...