We descibe a new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a speci ed eigenvec tor of the Laplacian This Laplacian eigenvector solves a continuous relaxation of a related discrete problem called the minimum sum problem The permutation ...

In 2011, B.B.Brumley and N.Tuveri found a remote timing attack on OpenSSL’s ECDSA implementation for binary curves. We will study if the title of their paper was indeed relevant (Remote Timing Attacks are Still Practical). We improved on their lattice attack using the Embedding Strategy that reduces the Closest Vector Problem to the Shortest Vector Problem so as to avoid using Babai’s procedure...

The two classical hard problems underlying the security of lattice-based cryptography are the shortest vector problem (SVP) and the closest vector problem (CVP). For SVP, lattice sieving currently has the best (heuristic) asymptotic time complexity: in high dimensions d, sieving can solve SVP in time 2, using 2 memory [Becker– Ducas–Gama–Laarhoven, SODA’16]. The best heuristic time complexity t...

We provide unconditional constructions of concurrent statistical zero-knowledge proofs for a variety of non-trivial problems (not known to have probabilistic polynomial-time algorithms). The problems include Graph Isomorphism, Graph Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a restricted version of Statistical Difference, and approximate versions of the (coNP forms of the)...

This paper introduces a novel RBF model – Transductive Radial Basis Function Neural Network with Weighted Data Normalization (TWRBF). In transductive systems a local model is developed for every new input vector, based on some closest to this vector data from the training data set. The Weighted Data Normalization method (WDN) optimizes the data normalization range individually for each input va...

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

In this paper, we propose approximate lattice algorithms for solving the shortest vector problem (SVP) and the closest vector problem (CVP) on an n-dimensional Euclidean integral lattice L. Our algorithms run in polynomial time of the dimension and determinant of lattices and improve on the LLL algorithm when the determinant of a lattice is less than 2 2/4. More precisely, our approximate SVP a...

As we saw in the previous lecture, solving this optimization recovers a linear classifier of the form y = sign(w ·h(x)+w0) that minimizes the hinge loss for all misclassified points and maximizes the size of the margin (the distance to the closest point to the decision boundary). The term “support vector” refers to the vectors from the decision boundary to the closest points. Note that moving a...