The hardness of the learning with errors (LWE) problem is one of the most fruitful resources of modern cryptography. In particular, it is one of the most prominent candidates for secure post-quantum cryptography. Understanding its quantum complexity is therefore an important goal. We show that under quantum polynomial time reductions, LWE is equivalent to a relaxed version of the dihedral coset...

Reactive oxygen species (ROS)-induced pancreatic β cell death affects insulin secretion and is important in the pathogenesis of diabetes. Lagerstroemia speciosa, a traditional folk medicine, has been used for t he prevention and treatment of diabetes. However, whether Lagerstroemia speciosa has a cytoprotective effect on pancreatic β cells remains to be elucidated. The present study aimed to in...

Leveled authentication allows resource-constrained IoT devices to be authenticated at different strength levels according to the particular types of communication. To achieve efficient leveled authentication, we propose a lightweight public key encryption scheme that can produce very short ciphertexts without sacrificing its security. The security of our scheme is based on the Learning With Sec...

Abstract The main purpose of this chapter is to give an extension on learning with errors problem (LWE)-based cryptosystem about the probability decryption error more general disturbance. In first section, we introduce LWE its application and some previous research results. Then a precise estimation based independent identical Gaussian disturbances any disturbances. This upper bound could be cl...

In this paper we present a new attack on the polynomial version of the Ring-LWE assumption, for certain carefully chosen number fields. This variant of RLWE, introduced in [BV11] and called the PLWE assumption, is known to be as hard as the RLWE assumption for 2-power cyclotomic number fields, and for cyclotomic number fields in general with a small cost in terms of error growth. For general nu...

This work describes the design and implementation of Λ◦λ, a general-purpose software library for lattice cryptography, written in the functional and strongly typed language Haskell. In comparison with several prior implementations of lattice-based cryptographic schemes, Λ◦λ has several novel and distinguishing features, which include: • Generality and modularity: Λ◦λ defines simple but general ...

We introduce a new concept, called multiplicative learning with errors (MLWE), which is a corresponding multiplicative version of the additive learning with errors (LWE), and show the equivalence between the decisional version and the search version for MLWE such that p is a product of sufficiently large smoothing prime factors. Then we construct the MLWE-based private-key and public-key encryp...

In this study, the dispersal caused by transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using nonlinear longitudinal wave equation (LWE), mathematical physics problem. Using generalized exp-function method, we investigate families of solitary solutions one-dimensional LWE. computer program Wolfram Mathematica 10, these new exact and LWE are...