Related papers: Generating Boolean lattices by few elements and ex…
In theory, quantum key distribution (QKD) allows secure communications between two parties based on physical laws. However, most of the security proofs of QKD today make unrealistic assumptions and neglect many relevant device…
We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate's inputs. A recent result by Kalai et al. (FOCS 2012) converts any boolean formula into a resilient formula of polynomial…
The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…
In the Element Distinctness problem, one is given an array $a_1,\dots, a_n$ of integers from $[poly(n)]$ and is tasked to decide if $\{a_i\}$ are mutually distinct. Beame, Clifford and Machmouchi (FOCS 2013) gave a low-space algorithm for…
Long-distance quantum communication in quantum networks faces significant challenges due to the constraints imposed by the no-cloning theorem. Most existing quantum communication protocols rely on the a priori distribution of entanglement…
Our main result is a quantum public-key encryption scheme based on the Extrapolated Dihedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number…
Let $L\subset \mathbb{Z}^n$ be a lattice and $I_L=\langle x^{\bf u}-x^{\bf v}:\ {\bf u}-{\bf v}\in L\rangle$ be the corresponding lattice ideal in $\Bbbk[x_1,\ldots, x_n]$, where $\Bbbk$ is a field. In this paper we describe minimal…
We present scalable parallel algorithms with sublinear per-processor communication volume and low latency for several fundamental problems related to finding the most relevant elements in a set, for various notions of relevance: We begin…
Let $La(n,P)$ be the maximum size of a family of subsets of $[n]=\{1,2,...,n\}$ not containing $P$ as a (weak) subposet. The diamond poset, denoted $B_{2}$, is defined on four elements $x,y,z,w$ with the relations $x<y,z$ and $y,z<w$.…
Given a Boolean formula and a satisfying assignment, a flip is an operation that changes the value of a variable in the assignment so that the resulting assignment remains satisfying. We study the problem of computing the shortest sequence…
We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two…
We introduce a new relativistic orthogonal states quantum key distribution protocol which leverages the properties of both quantum mechanics and special relativity to securely encode multiple bits onto the spatio-temporal modes of a single…
Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in…
Quantum key distribution (QKD) enables two parties to establish a secret key over a potentially hostile channel by exchanging photonic quantum states, relying on the fact that it is impossible for an eavesdropper to tap the quantum channel…
Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|. Then, the sliding token problem is to determine whether there exists a sequence of…
A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a "qualified" subset of parties can efficiently reconstruct the secret while any…
The necessity to secure the communication between hardware components in embedded systems becomes increasingly important with regard to the secrecy of data and particularly its commercial use. We suggest a low-cost (i.e. small logic-area)…
A novel framework for sharing common randomness and generating secret keys in wireless networks is considered. In particular, a network of users equipped with pulse oscillators (POs) and coupling mechanisms in between is considered. Such…
It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize a common secret-key, which can be subsequently used to keep their group messages confidential. As one…
We present Lattice (L, ticker: LAT), a peer-to-peer electronic cash system designed as a post-quantum settlement layer for the era of quantum computing. Lattice combines three independent defense vectors: hardware resilience through RandomX…