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 ...

This paper examines the recently developed p-shift iterative unbiased Kalman-like algorithm intended for filtering (p = 0), prediction (p > 0), and smoothing (p < 0) of linear discrete time-varying state-space models in non Gaussian environment with uncertainties. The algorithm is designed to have no requirements for noise and initial conditions and becomes optimal on large averaging intervals....

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...

we consider the following problem min x2R n min kEk 2 k(A + E)x ? bk 2 where A is an m n real matrix and b is an n-dimensional real column vector, when it has multiple global minima. An eecient algorithm is presented to nd the global solution of minimum Euclidean norm.

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation LWE . The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of t...

We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the iterates to its neighbors. Then, each agent combines weighted averages of the received iterates with its own iterate, and adjusts the iterate by using subgradi...

Predictable interprocessor synchronization and fast interrupt response are important for real-time systems constructed using asymmetric shared-memory multiprocessors. This paper points out the problem that existing spin lock algorithms cannot satisfy both requirements at the same time, and proposes a new algorithm to solve this problem. The algorithm, an extension of queueing spin locks modi ed...