- Explicit Relation between Low|Dimensional LLL|Reduced Bases ...🔍
- Example of bad basis for lattices 🔍
- A Formalization of the LLL Basis Reduction Algorithm🔍
- LLL Algorithm for Lattice Basis Reduction🔍
- Formalizing the LLL Basis Reduction Algorithm and the LLL ...🔍
- An application of the LLL algorithm to integer factorization🔍
- Floating|Point LLL🔍
- Lattice Basis Reduction🔍
Explicit Relation between Low|Dimensional LLL|Reduced ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases ...
In particular, we construct explicit representations of the shortest vector by using the LLL-reduced basis. Our analysis yields a necessary and sufficient ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases and Shortest Vectors. Kotaro MATSUDA†a), Atsushi TAKAYASU†,††b), Nonmembers, and Tsuyoshi TAKAGI ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases ...
Download Citation | Explicit Relation between Low-Dimensional LLL-Reduced Bases and Shortest Vectors | The Shortest Vector Problem (SVP) is one of the most ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases and Shortest Vectors. Kotaro MATSUDA†a), Atsushi TAKAYASU†,††b), Nonmembers, and ...
Explicit Relation between Low-Dimensional LLL-Reduced Bases ...
In particular, we construct explicit representations of the shortest vector by using the LLL-reduced basis. Our analysis yields a necessary and ...
(PDF) A 3-Dimensional Lattice Reduction Algorithm - ResearchGate
We prove that to find a nontrivial integer linear relation between vectors of a lattice L ⊂ℝn, whose euclidean length is at most M, one needs O (n 5+ε(ln Mn/λ)1 ...
Example of bad basis for lattices (worst-case for LLL)
... explicit (nor very clear to me...). lattice-crypto · lenstra ... Then at least p% of n-dimensional (1,1/2)-LLL bases have. ∀1≤i≤n−1: ...
A Formalization of the LLL Basis Reduction Algorithm
That formalization uses an explicit carrier set to enforce that all vectors are of the same dimension. ... work, namely the connection between the matrix-to- ...
A Formalization of the LLL Basis Reduction Algorithm - SpringerLink
That formalization uses an explicit carrier set to enforce that all vectors are of the same dimension. ... connection between the matrix-to-vector ...
LLL Algorithm for Lattice Basis Reduction - arXiv
It is similar in process to Gram-Schmidt orthogonalization, which produces vectors that are exactly orthogonal to one another, though at the cost of those ...
Formalizing the LLL Basis Reduction Algorithm and the LLL ...
The connection between a reduced basis and short ... That formalization uses an explicit carrier set to enforce that all vectors are of the same dimension.
An application of the LLL algorithm to integer factorization
αibi |αi ∈ Z. ) . L is called a lattice and the vectors bi are called a basis for L. Let us define the dimension of L, denoted by ...
Floating-Point LLL: Theoretical and Practical Aspects
Other LLL-reduction algorithms. Some LLL-type algorithms have lower complexity upper bounds than the ones described below, with respect to the lattice dimension ...
17.1.1 Connection Between Lagrange-Gauss Reduction and Eu- clid's ... Of course, in the two-dimensional case of LLL then µ2,1 is the same.
... of LLL as a synonym to lattice reduction. As an unfortunate consequence ... It emphasizes a somewhat overlooked connection between lattice algorithms ...
Faster LLL-type Reduction of Lattice Bases - ACM Digital Library
We describe an asymptotically fast variant of the LLL lattice reduction algorithm. It takes as input a basis B ∈ Zn x n and returns a (reduced) basis C of ...
Explicit approximate relation between reduced two- and one-particle ...
A class of approximation of the two-particle density matrix d 2 resembling the Hartree-Fock dependence on the one-particle density matrix d 1 is suggested.
Low-Dimensional Lattice Basis Reduction Revisited
2002]), following Ajtai's discovery [1996] of a connection between the worst-case and average-case complexities of certain lattice problems. Lattice reduction ...
Some lower dimensional quantum field theories reduced from Chern ...
We establish relations at the semiclassical regime between pure Chern-Simons theories on S 3 and the reduced Quantum Field Theories, based on ...
高安 敦 (Atsushi Takayasu) - 論文 - researchmap - researchmap
Explicit Relation between Low-Dimensional LLL-Reduced Bases and Shortest Vectors. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. Kotaro Matsuda ...