Related papers: Generating Boolean lattices by few elements and ex…
For every integer $n$ with $n \geq 6$, we prove that the Boolean dimension of a poset consisting of all the subsets of $\{1,\dots,n\}$ equipped with the inclusion relation is strictly less than $n$.
We demonstrate a post-quantum key-exchange with the nanosatellite SpooQy-1 in low Earth orbit using Kyber-512, a lattice-based key-encapsulation mechanism and a round three finalist in the NIST PQC standardization process. Our firmware…
Until recently, techniques for obtaining lower bounds for kernelization were one of the most sought after tools in the field of parameterized complexity. Now, after a strong influx of techniques, we are in the fortunate situation of having…
One-time-pad (OTP) encryption simply cannot be cracked, even by a quantum computer. The need of sharing in a secure way supplies of symmetric random keys turned the method almost obsolete as a standing-alone method for fast and large volume…
Post-Quantum cryptography is about to substitute current cryptographic schemes as being resilient in attacks from quantum computers. McEleiece and Bit Flip Key Encapsulation (BIKE) are two delight representatives based on coding theory…
We present a theoretical analysis of Beat-Note Superlattices (BNSLs), a recently demonstrated technique for generating periodic trapping potentials for ultracold atomic clouds, with arbitrarily large lattice spacings while maintaining…
Pre-tokenization, the initial step in many modern tokenization pipelines, segments text into smaller units called pretokens, typically splitting on whitespace and punctuation. While this process encourages having full, individual words as…
The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a…
We study the complexity of lattice problems in a world where algorithms, reductions, and protocols can run in superpolynomial time, revisiting four foundational results: two worst-case to average-case reductions and two protocols. We also…
In this work we study Invertible Bloom Lookup Tables (IBLTs) with small failure probabilities. IBLTs are highly versatile data structures that have found applications in set reconciliation protocols, error-correcting codes, and even the…
We consider the algorithmic problem of generating each subset of $[n]:=\{1,2,\ldots,n\}$ whose size is in some interval $[k,l]$, $0\leq k\leq l\leq n$, exactly once (cyclically) by repeatedly adding or removing a single element, or by…
P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic…
We propose the use of intra-particle entanglement to enhance the security of a practical implementation of the Bennett-Brassard-1984 (BB84) quantum key distribution scheme. Intra-particle entanglement is an attractive resource since it can…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
Using polarization-entangled photons from spontaneous parametric downconversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties.…
We show that replacing the usual sifting step of the standard quantum-key-distribution protocol BB84 by a one-way reverse reconciliation procedure increases its robustness against photon-number-splitting (PNS) attacks to the level of the…
We propose a simple yet complete lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves strong secret key rates up to 1/2 nat from the optimal in the case of…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any…
The linear subspaces of a multiresolution analysis (MRA) and the linear subspaces of the wavelet analysis induced by the MRA, together with the set inclusion relation, form a very special lattice of subspaces which herein is called a…