本综述中,我们描述了带错误的学习 (LWE) 问题,讨论了它的性质、困难性及其密码应用。 关键词:错误学习;格密码 一、引言 近年来,[Reg05] 中引入的带错误学习 (LWE) 问题,已被证明是密码构造的通用基础。 它主要名声来自于与最坏情况的格问题一样困难,因此在最坏情况的格问题困难性的假设下,使所有基于它的密码构造都是安全的。 本次综述的目标
4.4 Learning with errors problem The work [11] introduced the Learning with Errors (LWE) problem, which is the “encryption-enabling” analog of the SIS problem. These two problems are syntactically similar, and can be viewed seen as duals of each other. The difficult problem of public encryp...
假设我们可以访问使用模数 q 和误差参数 α 解决 LWE 问题的预言机,那么给定任何格 Λ 作为输入,来自离散高斯分布DΛ∗,r 的足够大的多项式样本数,对于某些(不是太小)r,以及离 Λ 的距离 αq/2r 内的点 x,我们可以在多项式时间内得到(唯一)最接近 x 的格点。 r不能太小的要求是很温和的;精确的条件...
TheLearningWithErrorsProblem The Learning With Errors Problem;Overview;A secret vector s in ?174 We are given an arbitrary number of equations, each correct up to ?1 Can you find s? ;LWE’s Claim to Fame;LWE’s Origins;LWE – More Precisely;LWE – Parameters: n, q, ?;Algorithms;...
The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones. The problem has been shown to be as hard as worst-case lattice problems, and in recent years it has served as the foundation...
This C library implementsFrodoKEM, an IND-CCA secure key encapsulation (KEM) protocol based on the well-studied Learning with Errors (LWE) problem [1,3], which in turn has close connections to conjectured-hard problems on generic, "algebraically unstructured" lattices. This package also includes...
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography Oded Regev September 8, 2007 Abstract Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from...
Interleaved practice enhances memory and problem-solving ability in undergraduate physics. npj Sci. Learn. 6, 32 (2021). This study demonstrates significant benefits of distributing homework problems on retention and transfer of university students’ physics knowledge over an academic term. Article Pub...
Problem You wantto rescale the feature values of observations to have unit norm (a total length of 1). Solution UseNormalizerwith anormargument: # Load librariesimportnumpyasnpfromsklearn.preprocessingimportNormalizer# Create feature matrixfeatures=np.array([[0.5,0.5],[1.1,3.4],[1.5,20.2],[1.63...
Overcoming the preferred-orientation problem in cryo-EM with self-supervised deep learning spIsoNet is an end-to-end self-supervised deep learning-based software to address the reconstruction and misalignment challenge in single-particle cryo-EM caused by the preferred-orientation problem. spIsoNet can...