Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic constructions. Attractive features of lattice cryptography include: apparent resistance to quantum attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and...

How to deal with large tightness gaps in security proofs is a vexing issue in cryptography. Even when analyzing protocols that are of practical importance, leading researchers often fail to treat this question with the seriousness that it deserves. We discuss nontightness in connection with complexity leveraging, HMAC, lattice-based cryptography, identity-based encryption, and hybrid encryption.

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...

Cryptography based on lattices is the use of conjectured hard problems on point lattices in Rn as the basis for security in cryptosystems. In this report, firstly we introduce lattices and some hard problems based on lattice then present some of the major developments in lattice-based cryptography. The main focus in this report is on the fundamental learning with errors (LWE) problems, Ring-LWE...

One essential quest in cryptography is the search for hard instances of a given computational problem that is known to be hard in the worst-case. In lattice cryptography we are in the unique situation that we have found a way of picking random instances which are at least as hard as well-studied lattice problems in the worst-case. At the same time, no attack running in subexponential time is kn...

Creation of smart spaces and scaling of devices to achieve miniaturization in pervasive computing environments has put forth a question on the degree of security of such devices. Security being a unique challenge in such environments, solution demands scalability, access control, heterogeneity, trust. Most of the existing cryptographic solutions widely in use rely on the hardness of factorizati...

Lattice-based cryptography is one of the candidates in the area of post-quantum cryptography. Cryptographic schemes with security reductions to hard lattice problems (like the Shortest Vector Problem SVP) offer an alternative to recent number theory-based schemes. In order to guarantee asymptotic efficiency, most lattice-based schemes are instantiated using polynomial rings over integers. These...

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 ...

In this paper, we first critically analyze two existing latticebased cryptosystems, namely GGH and Micciancio, and identify their drawbacks. Then, we introduce a method for improving the implementation of GGH using the Chinese Remainder Theorem (CRT). Furthermore, we also propose another cryptosystem optimized for CRT, drawing on the strengths of both cryptosystems. We provide a fair comparison...

In this paper, we report that we have solved the SVP Challenge over a 128-dimensional lattice in Ideal Lattice Challenge from TU Darmstadt, which is currently the highest dimension in the challenge that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the shortest vector problem (SVP) in lattices. In 2010, Micciancio and Voulgaris proposed a G...