Related papers: On the practicality of quantum sieving algorithms …
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…
Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring $ \Z[x]/(x^{2^n} + 1) $, a popular choice in the design of ideal lattice based…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective…
Grover's search algorithm gives a quantum attack against block ciphers by searching for a key that matches a small number of plaintext-ciphertext pairs. This attack uses $O(\sqrt{N})$ calls to the cipher to search a key space of size $N$.…
Traditional cryptography, rooted in problems, e.g., integer factorisation or discrete log, is inevitably vulnerable to a fully operational quantum computer. Although it remains an engineering frontier, the looming threat extends to…
The discrete Gaussian $D_{L- t, s}$ is the distribution that assigns to each vector $x$ in a shifted lattice $L - t$ probability proportional to $e^{-\pi \|x\|^2/s^2}$. It has long been an important tool in the study of lattices. More…
The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high…
A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
$ \newcommand{\problem}[1]{\ensuremath{\mathrm{#1}} } \newcommand{\SVP}{\problem{SVP}} \newcommand{\ensuremath}[1]{#1} $We prove the following quantitative hardness results for the Shortest Vector Problem in the $\ell_p$ norm ($\SVP_p$),…
We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time…
Discrete Gaussian Sampling on lattices is a fundamental problem in lattice-based cryptography. It appears both in basic cryptographic primitives such as digital signatures and as an important cryptanalysis building block for solving hard…
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
In recent years, establishing secure visual communications has turned into one of the essential problems for security engineers and researchers. However, only limited novel solutions are provided for image encryption, and limiting the…
Lattices have many significant applications in cryptography. In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem…
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…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
This review examines how quantum computing and artificial intelligence challenge current cryptographic systems. We analyze the literature to assess the resilience of algorithms against quantum attacks (Shor's and Grover's algorithms) and…