A Generator for LWE and Ring-LWE Instances
نویسندگان
چکیده
We introduce software for the generation of instances of the LWE and Ring-LWE problems, allowing both the generation of generic instances and also particular instances closely-related to those arising from cryptomania proposals in the literature. Our goal is to allow researchers to attack different instances in order to assess the practical hardness of LWE and Ring-LWE. This will in turn give insight to the practical security of cryptographic systems based on both problems.
منابع مشابه
Provably Weak Instances of Ring-LWE
The ring and polynomial learning with errors problems (Ring-LWE and Poly-LWE) have been proposed as hard problems to form the basis for cryptosystems, and various security reductions to hard lattice problems have been presented. So far these problems have been stated for general (number) rings but have only been closely examined for cyclotomic number rings. In this paper, we state and examine t...
متن کاملA New Ring-Based SPHF and PAKE Protocol On Ideal Lattices
emph{ Smooth Projective Hash Functions } ( SPHFs ) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient cryptographic schemes and protocols. As an application of SPHFs, emph { Password - Based Authenticated Key Exchange } ( PAKE ) protocol is well-studied area in the last few years. In 2009, Katz and Vaikuntanathan described the first lattice-based ...
متن کاملOn the Hardness of LWE with Binary Error: Revisiting the Hybrid Lattice-Reduction and Meet-in-the-Middle Attack
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...
متن کاملInteger Version of Ring-LWE and its Applications
In this work, we describe an integer version of ring-LWE over the polynomial rings and prove that its hardness is equivalent to one of the polynomial ring-LWE. Moreover, we also present a public key cryptosystem using this variant of the polynomial ring-LWE.
متن کاملOn the concrete hardness of Learning with Errors
The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for...
متن کامل