fplll contains several algorithms on lattices that rely on floating-point computations. This includes implementations of the floating-point LLL reduction algorithm, offering different speed/guarantees ratios. It contains a ’wrapper’ choosing the estimated best sequence of variants in order to provide a guaranteed output as fast as possible. In the case of the wrapper, the succession of variants is oblivious to the user. It also includes a rigorous floating-point implementation of the Kannan-Fincke-Pohst algorithm that finds a shortest non-zero lattice vector, and the BKZ reduction algorithm.

References in zbMATH (referenced in 12 articles )

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  1. Hurst, Greg: Computations of the mertens function and improved bounds on the mertens conjecture (2018)
  2. Biasse, Jean-François; Espitau, Thomas; Fouque, Pierre-Alain; Gélin, Alexandre; Kirchner, Paul: Computing generator in cyclotomic integer rings. A subfield algorithm for the principal ideal problem in $L_|\varDelta_\mathbb K|\left(\frac12\right)$ and application to the cryptanalysis of a FHE scheme (2017)
  3. Bi, Jingguo; Liu, Jiayang; Wang, Xiaoyun: Cryptanalysis of a homomorphic encryption scheme over integers (2017)
  4. Albrecht, Martin; Bai, Shi; Ducas, Léo: A subfield lattice attack on overstretched NTRU assumptions. Cryptanalysis of some FHE and graded encoding schemes (2016)
  5. Raum, Martin: Computing genus 1 Jacobi forms (2016)
  6. van de Pol, Joop; Smart, Nigel P.; Yarom, Yuval: Just a little bit more (2015)
  7. Albrecht, Martin R.; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic; Todo, Yosuke; Xagawa, Keita: Practical cryptanalysis of a public-key encryption scheme based on new multivariate quadratic assumptions (2014)
  8. Plantard, Thomas; Susilo, Willy; Zhang, Zhenfei: Lattice reduction for modular knapsack (2013)
  9. Hanrot, Guillaume; Pujol, Xavier; Stehlé, Damien: Algorithms for the shortest and closest lattice vector problems (2011)
  10. Schneider, Michael: Analysis of Gauss-sieve for solving the shortest vector problem in lattices (2011)
  11. Pujol, Xavier; Stehlé, Damien: Rigorous and efficient short lattice vectors enumeration (2008)
  12. Roune, Bjarke Hammersholt: Solving thousand-digit Frobenius problems using Gröbner bases (2008)