In this paper, we propose a fast iterative modular multiplication algorithm for calculating the product AB modulo N , where N is a large modulus in number-theoretic cryptosystems, such as RSA cryptosystems. Our algorithm requires ( 3 − 1 4k ) nk + 5 3 4 k − 3 2k − 17 6 additions on average for an n-bit modulus if k carry bits are dealt with in each loop. For a 512-bit modulus, the known fastest...

Given knowledge of one or more of the primes in a multiprime RSA modulus we show that the private exponent can be recovered provided it is sufficiently small. In particular, we present a simple and efficient method that given v of the u primes dividing the modulus N recovers any private exponent d satisfying d < Nv/u− . When only one prime is known, this bound can be increased to approximately ...

static deformation modulus is recognized as one of the most important parameters governing the behavior of rock masses. predictive models for the mechanical properties of rock masses have been used in rock engineering because direct measurement of the properties is difficult due to time and cost constraints. in this method the deformation modulus is estimated indirectly from classification syst...

In this paper, we introduce parameters slε(X) and sl0(X) based on slices of Banach space X . Using these parameters we describe some new properties of Banach spaces related to normal structure, uniformly non-squareness and others. In particular, we prove that if sl 2 3 (X) < 2, then X has normal structure, and sl0(X) = ε0(X) where ε0(X) is the characteristic of convexity of X . In addition, we ...

Computer simulations showed that the elastic modulus of the cell layer relative to the elastic modulus of the extracellular layers predicted the effectiveness of different force-generating mechanisms for sea urchin primary invagination [L. A. Davidson, M. A. R. Koehl, R. Keller, and G. F. Oster (1995) Development 121, 2005-2018]. Here, we measured the composite elastic modulus of the cellular a...

There was employed the density functional theory plane-wave pseudopotential method with local density approximation and generalized gradient approximation to investigate the structural, elastic and mechanical properties of the intermetallic compound Ni3Ga. The calculated equilibrium lattice constant and bulk modulus are in good agreement with the experimental values. The elastic constants were ...

This paper analyzes the usability of different dynamic moduli of elasticity and wood density for the prediction of mechanical properties – static modulus of elasticity and modulus of rupture – in samples with grain deflection from the longitudinal direction. Five tropical hardwoods (Afzelia bipindensis, Intsia bijuga, Millettia laurentii, Astronium graveolens and Microberlinia brazzavillensis) ...

This study evaluated nanohardness, elastic modulus and surface roughness of human enamel after contact with citric beverages. Human enamel samples were assigned to 3 groups according to the type of beverage used: carbonated drink, orange juice and tap water (control). Surface roughness was assessed using a profilometer, and nanohardness and elastic modulus were recorded using a nanoindenter. Th...

Available data on critical energies for ffostained ignition of black alpha-cellulose paper in the absence of forced convective heat losses are correlated against exposure time on a nondimenslonal basis. Investigations cover a range of irradiance from 2 to 25 cal/cm^sec, exposure time from 0.1 to ^ seconds, and paper thickness from 2 to 30 mils. Ignition energies for papers of two nominal densit...