In a seminal work at EUROCRYPT '96, Coppersmith showed how to nd all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysis and in a few security proofs. However, the running time of the algorithm is a high-degree polynomial, which limits experiments: the bottleneck is an LLL reduction of a high-dimensional matrix with ...

The Lenstra, Lenstra, and Lovász (abbreviated as LLL) basis reduction algorithm computes a basis of a lattice consisting of short, and near orthogonal vectors. The quality of an LLL reduced basis is expressed by three fundamental inequalities, and it is natural to ask, whether these have a common generalization. In this note we find unifying inequalities. Our main result is Theorem 1. Let b1, ....

This paper introduces a number of modifications that allow for significant improvements of parallel LLL reduction. Experiments show that these modifications result in an increase of the speed-up by a factor of more than 1.35 for SVP challenge type lattice bases in comparing the new algorithm with the state-of-the-art parallel LLL algorithm.

Rice bran is a simple item that delivers fantastic health benefits in our daily diet. This study delivers the importance of utilising all parts of the whole grain, including the bran. The objective was to develop the recipes incorporated with rice bran and evaluate their organoleptic properties and estimate their glycemic index. Ten standard Indian subcontinent recipes namely, chapati, mixed ve...

The Lovász Local Lemma (LLL) is a probabilistic tool which shows that, if a collection of “bad” events B in a probability space are not too likely and not too interdependent, then there is a positive probability that no bad-events in B occur. Moser & Tardos (2010) gave sequential and parallel algorithms which transformed most applications of the variable-assignment LLL into efficient algorithms...

lll

???? ??????????? – ????????? ? ???????????? ?????????? ???????? ???????? ???????????? ???????? ???????? ?????? ???????? ???????????. ???????? ??????. ? ?????? ??????????? ???????? ?????? ??????????? 12-13 ????? ?????????????? ????????–????????? ????? l-lll ???????? (9 ??????????? ?????? ???????????????? ?????, 9 ??????????). ??? ?????????? ?????????????? ??????????? ??????????????? ???????? ???...

The Lovász local lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid collection ℬ $$ \mathcal{B} “bad” events are mostly independent and have low probability. A seminal algorithm Moser Tardos (J. ACM, 2010, 57, 11) (which we call MT algorithm) gives nearly-automatic randomized algorithms for most constructions based on LLL. However...

This chapter introduces Inductive Logic Programming (ILP) and Learning Language in Logic (LLL). No previous knowledge of logic programming, ILP or LLL is assumed. Elementary topics are covered and more advanced topics are discussed. For example, in the ILP section we discuss subsumption, inverse resolution, least general generalisation, relative least general generalisation, inverse entailment,...

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.