In this paper, we study the security of multi-prime RSA whose modulus is N = p1p2 · · · pr for r ≥ 3 with small prime difference of size N . In ACISP 2013, Zhang and Takagi showed a Fermat-like factoring attack, which can directly factor N for γ < 1 r2 . We improve this bound to theoretically achieve γ < 2 r(r+2) by a new factoring attack. Furthermore, we also analyse specific MPRSA with imbala...

Representations of nite languages as a product (catenation) of languages are investigated, where the factor languages are \prime", that is, cannot be decomposed further in a nontrivial manner. In general, such prime decompositions are not unique even the number of factors can vary exponentially. The paper investigates the uniqueness of prime decompositions, as well as the commuting of the facto...

For a prime power q, let ERq denote the Erdős-Rényi orthogonal polarity graph. We prove that if q is an even power of an odd prime, then χ(ERq) 6 2 √ q + O( √ q/ log q). This upper bound is best possible up to a constant factor of at most 2. If q is an odd power of an odd prime and satisfies some condition on irreducible polynomials, then we improve the best known upper bound for χ(ERq) substan...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...

The configuration-space topology in canonical General Relativity depends on the choice of the initial data 3-manifold. If the latter is represented as a connected sum of prime 3-manifolds, the topology receives contributions from all configuration spaces associated to each individual prime factor. There are by now strong results available concerning the diffeomorphism group of prime 3-manifolds...

in order to study of hydropriming, planting depth and nitrogen split application effect on yield and yield components of double cross hybrid of corn, an experiment was carried out as factorial based on randomized complete block design (rcbd) with four replications. nitrogen split application included (400 kg/ha at sowing date, 100 kg/ha at sowing date and 300 kg/ha 25 to 50 days after sowing da...

Following an idea of Kronecker, we describe a method for factoring prime ideal extensions in number rings. The method needs factorization of polynomials in many variables over finite fields, but it works for any prime and any number field extension. Introduction Let F c K be number fields, let ¿fp c <?* be their corresponding number rings, i.e., the integral closures of Z in F and K, respective...

A 520 VOLUME 116 | NUMBER 12 | December 2008 • Environmental Health Perspectives OBESITY Childhood BMI Rises with Prenatal Exposure to Hexachlorobenzene A prospective study published in the October 2008 issue of Acta Paediatrica has found an association between prenatal exposure to hexachlorobenzene (HCB) and being overweight or obese in childhood. The study was the first prospective look at pr...