By Charles R. Kolb (auth.), Charles W. Finkl (eds.)
The Encyclopedia of utilized Geology is a world compendium of engineering geology issues ready by way of specialists from many nations. the amount comprises greater than 80 major entries in alphabetical order, facing hydrology, rock constitution tracking and soil mechanics as well as engineering geology. targeted themes specialize in earth technology info and resources, electrokinetics, forensic geology, geocryology, nuclear plant siting, photogrammetry, tunnels and tunnelling, city geomorphology and good info systems.
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Extra info for Applied Geology
This paper introduces inverted Edwards coordinates. Inverted Edwards coordinates (X1 : Y1 : Z1 ) represent the aﬃne point (Z1 /X1 , Z1 /Y1 ) on an Edwards curve; for comparison, standard Edwards coordinates (X1 : Y1 : Z1 ) represent the aﬃne point (X1 /Z1 , Y1 /Z1 ). This paper presents addition formulas for inverted Edwards coordinates using only 9M + 1S. The formulas are not complete but still are strongly uniﬁed. Dedicated doubling formulas use only 3M + 4S, and dedicated tripling formulas use only 9M + 4S.
ASIACRYPT 2007. LNCS, vol. 4833. ie Abstract. We will discuss two diﬀerent but related topics. We ﬁrst give a connection between the Fourier spectrum of Boolean functions and subspaces of skew-symmetric subspaces where each nonzero element has a lower bound on its rank. Secondly, we discuss some connections between bent and near-bent functions. 1 Introduction Let Vn denote any n-dimensional vector space over F2 . The Fourier transform of a function f : Vn −→ Vm is deﬁned by f (a, b) := (−1) b,f (x) + a,x x∈Vn for a ∈ Vn and b ∈ Vm , b = 0.
We showed in  that, when curve parameters are chosen properly, the addition law is even complete: it works for all inputs, with no exceptional cases. Our fast addition formulas in  have the same features. See Section 2 of this paper for a more detailed review of Edwards curves. In , together with Birkner and Peters, we showed that tripling on Edwards curves could be performed using only 9M + 4S. We also analyzed the optimal combinations of additions, doublings, triplings, windowing methods, on-the-ﬂy precomputations, curve shapes, and curve formulas, improving upon the analysis in  by Doche and Imbert.