The Shortest lattice Vector Problem is central in lattice-based cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 and space 2, where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris ...

Nowadays, most smartphones come pre-equipped with location (GPS) sensing capabilities, allowing developers to create a wide variety of location-aware applications and services. While location awareness provides novel features and functionality, it opens the door to many privacy nightmares. In many occasions, however, users do not need to share their actual location, but to determine whether the...

The shortest vector problem (SVP) is one of the lattice problems and mathematical basis for lattice-based cryptography, which expected to be post-quantum cryptography. SVP can mapped onto Ising problem, in principle solved by quantum annealing (QA). However, issue solving using QA that solution corresponds first excited state Hamiltonian. Therefore, QA, searches ground states, cannot provide a ...

The security of lattice-based cryptography relies on the hardness of problems based on lattices, such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). This paper presents two parallel implementations for the SE++ with and without extreme pruning. The SE++ is an enumeration-based CVP-solver, which can be easily adapted to solve the SVP. We improved the SVP version of th...

In this work we consider the closest vector problem (CVP) —a problem also known as maximum-likelihood decoding— in the tensor of two root lattices of type A (Am⊗An), as well as in their duals (Am⊗An). This problem is mainly motivated by lattice based cryptography, where the cyclotomic rings Z[ζc] (resp. its co-different Z[ζc]) play a central role, and turn out to be isomorphic as lattices to te...

We propose a fully private fingerprint matching protocol that compares two fingerprints based on the most widely-used minutia-based fingerprint matching algorithm. The protocol enables two parties, each holding a private fingerprint, to find out if their fingerprints belong to the same individual. Unlike previous works, we do not make any simplifying assumption on the matching algorithm or use ...

The Rényi divergence is a measure of divergence between distributions. It has recently found several applications in lattice-based cryptography. The contribution of this paper is twofold. First, we give theoretic results which renders it more efficient and easier to use. This is done by providing two lemmas, which give tight bounds in very common situations – for distributions that are tailcut ...

Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how much space they can spare to store pr...

A well-known cryptographic scenario is the following: a smart card wishes to compute an RSA signature with the help of an untrusted powerful server. Several protocols have been proposed to solve this problem , and many have been broken. There exist two kinds of attacks against such protocols: passive attacks (where the server follows the instructions) and active attacks (where the server may re...

Building cryptographic schemes upon as many fundamentally different hard problems as possible, seems to be the best way to hedge against future threats such as quantum computers. Being mainly based on the hardness of factoring and computing discrete logarithms, the present security landscape is at risk. In contrast, problems in lattices, such as finding short non-zero vectors, seem to withstand...