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An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
The Coppersmith method, proposed by Don Coppersmith, is a method to find small integer zeroes of univariate or bivariate polynomials, or small zeros modulo a given integer. The method uses the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller ...
Lattice reduction algorithms aim, given a basis for a lattice, to output a new basis consisting of relatively short, nearly orthogonal vectors. The Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL) was an early efficient algorithm for this problem which could output an almost reduced lattice basis in polynomial time. [33]
Lattice reduction algorithms are used in a number of modern number theoretical applications, including in the discovery of a spigot algorithm for . Although determining the shortest basis is possibly an NP-complete problem, algorithms such as the LLL algorithm [ 2 ] can find a short (not necessarily shortest) basis in polynomial time with ...
Lenstra has worked principally in computational number theory. He is well known for: Co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982); Developing an polynomial-time algorithm for solving a feasibility integer programming problem when the number of variables is fixed (in 1983); [3]
Please share your opinion at Talk:Lenstra-Lenstra-Lovász lattice reduction algorithm. Nuesken 17:24, 18 May 2006 (UTC) There are likely thousands of papers which talk about "lattice reduction"; it's a commonly accepted term. I think an appropriate title for the article is "Lenstra–Lenstra–Lovász lattice reduction".
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The lattice reduction attack is one of the best known and one of the most practical methods to break the NTRUEncrypt. In a way it can be compared to the factorization of the modulus in RSA. The most used algorithm for the lattice reduction attack is the Lenstra-Lenstra-Lovász algorithm.