We describe a comparatively simple fully homomorphic encryption (FHE) scheme based on the learning with errors (LWE) problem. In previous LWE-based FHE schemes, multiplication is a complicated and expensive step involving “relinearization”. In this work, we propose a new technique for building FHE schemes that we call the approximate eigenvector method. In our scheme, for the most part, homomor...

We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the “learning with errors” (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple distinguishing attack considered in prior analyses...

The problem of blind source separation is usually solved by optimizing a contrast function that measures either the independence of several variables or the non-gaussianity of a single variable. If the problem involves bounded sources, this knowledge can be exploited and the solution can be found with a customized contrast that relies on a simple endpoint estimator. The minimization of the leas...

One of the most attractive problems for post-quantum secure cryptographic schemes is the LWE problem. Beside combinatorial and algebraic attacks, LWE can be solved by a lattice-based Bounded Distance Decoding (BDD) approach. We provide the first parallel implementation of an enumeration-based BDD algorithm that employs the Lindner-Peikert and Linear Length pruning strategies. We ran our algorit...

GPU based computing has made significant strides in recent years. Unfortunately, GPU program optimizations can introduce subtle concurrency errors, and so incisive formal bug-hunting methods are essential. This paper presents a new formal bug-hunting method for GPU programs that combine barriers and atomics. We present an algorithm called conflict-directed delay-bounded scheduling algorithm (CD...

In this report we describe a fully homomorphic encryption (FHE) scheme based on the learning with errors (LWE) problem. Firstly we introduce some definitions related to lattices and some operators which will be needed to build an efficient fully homomorphic encryption system base on LWE. The main focus in this report is to explain the new technique to building FHE schemes that is called the app...

The security of many cryptographic schemes has been based on special instances of the Learning with Errors (LWE) problem, e.g., Ring-LWE, LWE with binary secret, or LWE with ternary error. However, recent results show that some subclasses are weaker than expected. In this work we show that LWE with binary error, introduced by Micciancio and Peikert, is one such subclass. We achieve this by appl...

In previous papers authors have considered agents as inertia-less self driven particles and designed a flocking algorithm. Application of this algorithm to agents with considerable inertial characteristics needs a behavioural controller. The controller uses the local information and helps every agent to imitate the desired behaviour as a member of the flocking frame which covers the main is...

In this paper we propose a new algorithm for solving the Learning With Errors (LWE) problem based on the steps of the famous Blum-Kalai-Wasserman (BKW) algorithm. The new idea is to introduce an additional procedure of mapping subvectors into codewords of a lattice code, thereby increasing the amount of positions that can be cancelled in each BKW step. The procedure introduces an additional noi...