mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This...

The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik...

(n)}} ) in the lattice dimension. The former class of algorithms most notably includes lattice enumeration and random sampling reduction, while the latter...

Korkine–Zolotarev (KZ) lattice basis reduction algorithm or Hermite–Korkine–Zolotarev (HKZ) algorithm is a lattice reduction algorithm. For lattices in R n {\displaystyle...

Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or...

Erdős–Faber–Lovász conjecture. He is also one of the eponymous authors of the LLL lattice reduction algorithm. Lovász was born on March 9, 1948, in Budapest, Hungary...

Dimension reduction, the process of reducing the number of random variables under consideration Lattice reduction, given an integer lattice basis as input...

code or assembly Lenstra–Lenstra–Lovász lattice basis reduction algorithm, a polynomial time lattice reduction algorithm Lowest Landau level, wave functions...

Computational lattice problems have many applications in computer science. For example, the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL)...

relies on the difficulty of lattice reduction. The idea included in this trapdoor function is that, given any basis for a lattice, it is easy to generate...

Howgrave-Graham; Whyte. "Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches" (PDF). NTRU. Archived from the original (PDF)...

2}+2{F_{n+1}}^{2}\right)} These can be found experimentally using lattice reduction, and are useful in setting up the special number field sieve to factorize...

vectors of the lattice are reduced using lattice reduction only a set number of lattice points need to be used. In two-dimensions only the lattice points that...

Izabachène, P.Q. Nguyen, and X. Xie Structural Lattice Reduction: Generalized Worst-Case to Average-Case Reductions and Homomorphic Cryptosystems. In EUROCRYPT...

(determinant −1). The unimodular matrix used (possibly implicitly) in lattice reduction and in the Hermite normal form of matrices. The Kronecker product...

related, though not equivalent, to the algorithmic problem of lattice reduction in certain lattices. Careful choice of parameters is necessary to thwart some...

Elsenhans & Jahnel (2009) used a method of Noam Elkies (2000) involving lattice reduction to search for all solutions to the Diophantine equation x 3 + y 3...

discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts...

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge...

rational coefficients in the seminal paper that introduced the LLL lattice reduction algorithm with Hendrik Willem Lenstra and László Lovász. Lenstra is...

Chen, Jiazhe (April 2010). "Bounding the sum of square roots via lattice reduction". Mathematics of Computation. 79 (270): 1109–1122. arXiv:0905.4487...

subposition, reduction and object/attribute generalization, and the manipulation of concept lattices via approximation, projection and selection. Lattice Miner...

The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is...

product on the weight lattice. The connected Dynkin diagrams (corresponding to simple groups) are pictured below. For a split reductive group G over a field...

In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important...

theory of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a...

dipoles forming superposed resonance rings in helical pathways throughout lattices of microtubules. The oscillations are either electric, due to charge separation...

Goldwasser, Shafi; Halevi, Shai (1997). "Public-key cryptosystems from lattice reduction problems". CRYPTO '97: Proceedings of the 17th Annual International...

In Lie theory and related areas of mathematics, a lattice in a locally compact group is a discrete subgroup with the property that the quotient space...

in an ideal lattice. The best method to gauge the practical security of a given set of lattice parameters is the BKZ 2.0 lattice reduction algorithm. According...