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...

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

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

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...

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...

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...

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

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

in 1970, and received her PhD in 1986 at the University of Caen (Lattice reduction algorithms in small dimensions). Her doctoral advisor was Jacques...

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

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

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

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...

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

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...

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

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...

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

In computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine...

cryptosystems, such as Merkle-Hellman, techniques like Euclidean lattice reduction do not apply to this problem. The best known generic attack consists...

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...

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...

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

Veterinarian. The paper provides a general solution to a class of lattice reduction puzzles exemplified by the following one: "Suppose a mad veterinarian...

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