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The LLL algorithm takes as input a basis of a Euclidean lattice, and, within a polynomial number of operations, it outputs another basis of the same lattice but consisting of rather short vectors. We ...
We introduce stochastic sandpile models which imitate numerous aspects of the practical behavior of the LLL algorithm with compelling accuracy. In addition, we argue that the physics and mathematics o...
In this work we analyze the impact of translating the well-known LLL algorithm for lattice reduction into the quantum setting. We present the first (to the best of our knowledge) quantum circuit repre...
The LLL algorithm (from Lenstra, Lenstra and Lovász) and its generalization BKZ (from Schnorr and Euchner) are widely used in cryptanalysis, especially for lattice-based cryptography. Precisely unders...
We describe an asymptotically fast variant of the LLL lattice reduction algorithm. It takes as input a basis B∈Zn×nB∈Zn×n and returns a (reduced) basis CC of the Euclidean lattice LL spanned by BB, wh...
Lattice reduction is fundamental in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra–Lenstra–Lovász reduction algorithm (called LLL or L3) has be...
In this paper, we give an attack against a public key cryptosystem based on Diophantine equations of degree increasing type (DEC) proposed by the third author ([Oku15]). We show that the security of...
In a seminal work at EUROCRYPT '96, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysi...
In a seminal work at EUROCRYPT '96, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysi...
Given a matrix A 2 Zm×n satisfying certain regularity assumptions,a well-known integer programming problem asks to find an integer point in the associated knapsack polytope P(A, b) = {x 2 Rn 0 : Ax ...
模糊度降相关技术可以有效提高模糊度求解的效率及成功率,LLL( A . K. Lenstra , H. W. Lenstra ,L. Lovasz) 算法是新出现的模糊度降相关方法。详细分析LLL 算法, 针对该算法中存在的缺陷, 提出逆整数乔勒斯基、整数高斯算法和升序调整矩阵辅助的改进LLL 算法。利用谱条件数及平均相关系数为准则, 以300个随机模拟的对称正定矩阵作为模糊度方差- 协方差矩阵,...
THE course of our narrative now takes us back to the regions beyond the mountains, to dispose of the parties that set out from Astoria, in company with Mr. Robert Stuart, and whom he left on the banks...
A female patient with a skeletal Class III severe anterior openbite was treated using miniplates as the anchorage. The patient was 15 years and 10 months of age when she reported to our university hos...
该焚烧炉依据内核烧结法的原理研制而成,即先在堆放于炉膛内的垃圾之下引燃,形成热核,该热核由料堆的下部向外、向上逐渐缓慢地扩张燃烧,最后将垃圾中的有机物全部烧尽。该炉采用链条炉排传送,连续运行,垃圾进入炉内经预热、干燥、燃烧及燃尽四个阶段,形成烧结渣排出炉外,产生的废渣可作建材及水泥辅料;烟气经余热锅炉及空气预热器后,进入多管除尘器和喷雾式脱酸器进行处理,达标排放。该技术解决了厚床层、不搅动、燃烧强...

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