The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and therefore to prove the security of numerous cryptographic schemes and protocols — including key-exchange, digital signatures, public-key encry...

NTRUEncrypt is a fast and standardized lattice-based public key encryption scheme, but it lacks a solid security guarantee. In 2011, Stehlé and Steinfeld first proposed a provably secure variant of NTRUEncrypt, denoted by pNE, over power-of-2 cyclotomic rings. The IND-CPA security of pNE is based on the worst-case quantum hardness of classical problems over ideal lattices. Recently, Yu, Xu and ...

In this work, we give a partial overview of lattice attacks in cryptography. While different kinds of attacks are considered, the emphasis of this work is given to attacks that are based on Coppersmith’s results for solving low degree multivariate modular equations and bivariate integer equations.

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 broad lattice manipulation technique for expressive cryptography, and use it to realize functional encryption for access structures from post-quantum hardness assumptions. Specifically, we build an efficient key-policy attribute-based encryption scheme, and prove its security in the selective sense from learningwith-errors intractability in the standard model.

This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between ...

My research is dedicated to developing new, stronger mathematical foundations for cryptography, with a particular focus on geometric objects called lattices. Informally, a lattice is a periodic ‘grid’ of points in n-dimensional real space Rn. Lattices have been studied since the early 1800s, and their apparent simplicity belies many deep connections and applications across mathematics, physics,...

Lattice-based cryptography, as an active branch of post-quantum cryptography (PQC), has drawn great attention from side-channel analysis researchers in recent years. Despite the various targets examined previous studies, detail on revealing secret-dependent information efficiently is less studied. In this paper, we propose adaptive EM attacks with carefully constructed ciphertexts Kyber, which ...