Related papers: Generating cryptographically-strong random lattice…
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…
The theory underlying a proposed random number generator for numerical simulations in elementary particle physics and statistical mechanics is discussed. The generator is based on an algorithm introduced by Marsaglia and Zaman, with an…
High quality random numbers are necessary in the modern world. Ranging from encryption keys in cyber security to models and simulations for scientific use: it's important that these random numbers are of high quality and quickly attainable.…
We construct a strong PUF with provable security against ML attacks on both classical and quantum computers. The security is guaranteed by the cryptographic hardness of learning decryption functions of public-key cryptosystems, and the…
The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors…
S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
In this paper, we propose a lattice-based robust distributed source coding system for two correlated sources and provide a detailed performance analysis under the high resolution assumption. It is shown, among other things, that, in the…
Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries…
A recent proposal has shown that it is possible to perform linear-optics quantum computation using a ballistic generation of the lattice. Yet, due to the probabilistic generation of its cluster state, it is not possible to use the…
When searching for new gravitational-wave or electromagnetic sources, the $n$ signal parameters (masses, sky location, frequencies,...) are unknown. In practice, one hunts for signals at a discrete set of points in parameter space, called a…
In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Gr\"obner bases. Ideal lattices are ideals in the residue class ring, $\mathbb{Z}[x]/\langle f \rangle$ (here $f$ is a monic…
The "Ring Learning with Errors" (RLWE) problem was formulated as a variant of the "Learning with Errors" (LWE) problem, with the purpose of taking advantage of an additional algebraic structure in the underlying considered lattices; this…
Low density generator matrix (LDGM) codes have an acceptable performance under iterative decoding algorithms. This idea is used to construct a class of lattices with relatively good performance and low encoding and decoding complexity. To…
With the widespread use of communication technologies, cryptosystems are therefore critical to guarantee security over open networks as the Internet. Pseudo-random number generators (PRNGs) are fundamental in cryptosystems and information…
Quantum mechanics provides means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a self-testing manner that is independent of…
Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit…
We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…