A square root (SQRT) algorithm inGF (p) (m=r0r1 · · · rn−12, ri: odd prime, d>0: integer) is proposed in this paper. First, the TonelliShanks algorithm is modified to compute the inverse SQRT in GF (p d ), where most of the computations are performed in the corresponding subfields GF (p i ) for 0 i d − 1. Then the Frobenius mappings with an addition chain are adopted for the proposed SQRT algor...

Let f(x) be a mapping f : GF(p) → GF(p), where p is prime and GF(p) is the finite field with p elements. A mapping f is called differentially k-uniform if k is the maximum number of solutions x ∈ GF(p) of f(x + a) − f(x) = b, where a, b ∈ GF(p) and a = 0. A 1-uniform mapping is called perfect nonlinear (PN). In this paper, we propose an approach for assurance of perfect nonlinearity which invol...

"Black" pigment gallstones form in sterile gallbladder bile in the presence of excess bilirubin conjugates ("hyperbilirubinbilia") from ineffective erythropoiesis, hemolysis, or induced enterohepatic cycling (EHC) of unconjugated bilirubin. Impaired gallbladder motility is a less well-studied risk factor. We evaluated the spontaneous occurrence of gallstones in adult germfree (GF) and conventio...

GF (Grammatical Framework) is a grammar formalism based on the distinction between abstract and concrete syntax. An abstract syntax is a free algebra of trees, and a concrete syntax is a mapping from trees to nested records of strings and features. These mappings are naturally defined as functions in a functional programming language; the GF language provides the customary functional programmin...

Computing the inverse of a number in finite fields GF(p) or GF(2) is equally important for cryptographic applications. This paper proposes a novel scalable and unified architecture for a Montgomery inverse hardware that operates in both GF(p) and GF(2) fields. We adjust and modify a GF(2) Montgomery inverse algorithm to accommodate multi-bit shifting hardware, making it very similar to a previo...

Recently, there has been a lot of interest on cryptographic applications based on fields GF (p), for p > 2. This contribution presents GF (p) multipliers architectures, where p is odd. We present designs which trade area for performance based on the number of coefficients that the multiplier processes at one time. Families of irreducible polynomials are introduced to reduce the complexity of th...

Abstract syntax is a tectogrammatical tree representation, which can be shared between languages. It is used for programming languages in compilers, and has been adapted to natural languages in GF (Grammatical Framework). Recent work has shown how GF trees can be converted to UD trees, making it possible to generate parallel synthetic treebanks for those 30 languages that are currently covered ...

Granuloma faciale (GF) is an uncommon inflammatory dermatosis that usually presents on the face as reddish brown or violaceous papules and nodules that may coalesce into plaques. Eosinophilic angiocentric fibrosis (EAF) is a rare fibrosing condition that shares many histologic characteristics with GF and is regarded by some authors as a mucosal counterpart of GF. We present a case of GF with co...

In this study, methodologies were developed for the determination of metals (Cu, Mn, Ni, Sn and Zn) in sediments prepared as slurries, which were maintained homogeneous by the introduction of air supplied by an aquariam pump by GF AAS (Graphite Furnace Atomic Absorption Spectrometry). The optimization of the pyrolysis and atomization temperatures were done through pyrolysis and atomization temp...

The grafted-graphene oxide/glass fiber/epoxy resin (grafted-GO/GF/EP) and dispersed-graphene (dispersed-GO/GF/EP) composites were successfully prepared by grafting graphene oxide (GO) on glass fiber (GF) with coupling agent random dispersion of GO. A scanning electron microscope (SEM) was employed to characterize the micro structure. heat transfer RVE models grafted-GO/GF/EP dispersed-GO/GF/EP ...