The Learning with Errors (LWE) problem, proposed by Regev in 2005, has become an ever-popular cryptographic primitive, due mainly to its simplicity, flexibility and convincing theoretical arguments regarding its hardness. Among the main proposed approaches to solving LWE instances — namely, lattice algorithms, combinatorial algorithms, and algebraic algorithms — the last is the one that has rec...

Arora & Ge [5] recently showed that solving LWE can be reduced to solve a high-degree non-linear system of equations. They used a linearization to solve the systems. We investigate here the possibility of using Gröbner bases to improve Arora & Ge approach. Introduction The Learning With Errors (LWE) Problem was introduced by Regev in [27, 26]. It is a generalisation for large primes of the well...

Post-quantum cryptography (PQC) has gained significant attention from the community recently as it is proven that existing public-key cryptosystems are vulnerable to attacks launched well-developed quantum computers. The finite field arithmetic $AB+C$ , where A and C integer...

The purpose of this lecture note is to introduce lattice based cryptography, which is thought to be a cryptosystem of post-quantum age. We have tried to give as many details possible specially for novice on the subject. Something may be trivial to an expert but not to a novice. Many fundamental problems about lattice are thought to be hard even against quantum computer, compared to factorizatio...

introduction: screening of patients with anterior abdominal penetrating trauma in need for laparotomy is an important issue in management of these cases. this study aimed to compare the accuracy of abdominal wall ultrasonography (awu) and local wound exploration (lwe) in this regard. methods: this diagnostic accuracy study was conducted on ≥ 18 year-old patients presenting to emergency departme...

Lattice-based cryptography is centered around the hardness of problems on lattices. A lattice a grid points that stretches to infinity. With development quantum computers, existing cryptographic schemes are at risk because underlying mathematical can, in theory, be easily solved by computers. Since lattice-based hard even promising foundation for future schemes. In this paper, we focus public-k...

We introduce a new variant MP-LWE of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer q. We exhibit a reduction from the PolynomialLWE problem (PLWE) parametrized by a polynomial f , to MP-LWE which is defined independently of any such f . The reduction only requires f to be monic with constant coefficient coprime with q. It incurs a ...

The Learning with Errors (LWE) problem has been widely used as a hardness assumption to construct public-key primitives. In this paper, we propose an efficient instantiation of a PKE scheme based on LWE with a sparse secret, named as spLWE. We first construct an IND-CPA PKE and convert it to an IND-CCA scheme in the quantum random oracle model by applying a modified Fujisaki-Okamoto conversion ...

Lattice trapdoors are an important primitive used in a wide range of cryptographic protocols, such as identitybased encryption (IBE), attribute-based encryption, functional encryption, and program obfuscation. In this paper, we present software implementations of the Gentry-Peikert-Vaikuntanathan (GPV) digital signature, IBE and ciphertextpolicy attribute-based encryption (CP-ABE) schemes based...

INTRODUCTION Screening of patients with anterior abdominal penetrating trauma in need for laparotomy is an important issue in management of these cases. This study aimed to compare the accuracy of abdominal wall ultrasonography (AWU) and local wound exploration (LWE) in this regard. METHODS This diagnostic accuracy study was conducted on ≥ 18 year-old patients presenting to emergency departme...