The ionosphere causes the most difficult error to mitigate in Satellite Based Augmentation Systems (SBAS). The problem has been solved for the mid latitude regions using the thin shell approximation. There, it is very accurate on quiet days and allows the augmentation system so send the information in a two dimensional grid with a five by five degree resolution. However, even during quiet days,...

Models are developed to adjust for measurement errors in Normally distributed predictor and response variables and categorical predictors with misclassification errors. The models allow for a hierarchical data structure and for correlations among the errors and misclassifications. MCMC estimation is used and implemented in a set of MATLAB macros.

Definition 1 (Search problem). In SearchLWE[n, α, q], the goal is, given oracle access to LWEs for some fixed s ∼ UZnq , to find and output s. Definition 2 (Decision problem). In DecisionLWE[n, α, q], given oracle access to some oracle O along with the promise that it either outputs samples (a) from LWEs (for some fixed s ∼ UZnq ) or (b) drawn uniformly at random in Zq ×Zq, the goal is to decid...

• The LWE error distribution Φαq is a continuous one-dimensional Gaussian, which is a projection of the spherical n-dimensional distribution Dαq onto its first coordinate. • The distribution Dαq is smooth in the following sense: If L is some lattice (or coset of a lattice) with λn(L) αq, then if we choose ~x← DL,r and ~y ← Ds such that r2 + s2 = (αq)2 then the induced distribution on ~x+ ~y is ...

To model liquid water correctly and to reproduce its structural, dynamic and thermodynamic properties warrants models that account accurately for electronic polarisation. We have previously demonstrated that polarisation can be represented by fluctuating multipole moments (derived by quantum chemical topology) predicted by multilayer perceptrons (MLPs) in response to the local structure of the ...

The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for...

In this paper, we present a new masking scheme for ring-LWE decryption. Our scheme exploits the additively-homomorphic property of the existing ring-LWE encryption schemes and computes an additivemask as an encryption of a random message. Our solution differs in several aspects from the recent masked ring-LWE implementation by Reparaz et al. presented at CHES 2015; most notably we do not requir...

GGH13, CLT13 and GGH15 of multilinear maps suffer from zeroizing attacks. In this paper, we present a new construction of multilinear maps using a variant of ring-LWE (vRLWE). Furthermore, we also present two new variants of vRLWE, which respectively support the applications of multipartite key exchange and witness encryption. At the same time, we also present a new variant of GGH13 using matri...