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 27 articles )

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  1. Dachman-Soled, Dana; Gong, Huijing; Kulkarni, Mukul; Shahverdi, Aria: (In)security of ring-LWE under partial key exposure (2021)
  2. Miller, Stephen D.; Narayanan, Bhargav; Venkatesan, Ramarathnam: Coppersmith’s lattices and “focus groups”: an attack on small-exponent RSA (2021)
  3. Nakamura, Satoshi; Yasuda, Masaya: Dynamic self-dual DeepBKZ lattice reduction with free dimensions and its implementation (2021)
  4. Cheon, Jung Hee; Cho, Wonhee; Hhan, Minki; Kim, Jiseung; Lee, Changmin: Algorithms for CRT-variant of approximate greatest common divisor problem (2020)
  5. Yasuda, Masaya: Self-dual DeepBKZ for finding short lattice vectors (2020)
  6. Yasuda, Masaya; Nakamura, Satoshi; Yamaguchi, Junpei: Analysis of DeepBKZ reduction for finding short lattice vectors (2020)
  7. Albrecht, Martin R.; Ducas, Léo; Herold, Gottfried; Kirshanova, Elena; Postlethwaite, Eamonn W.; Stevens, Marc: The general sieve kernel and new records in lattice reduction (2019)
  8. Aono, Yoshinori; Nguyen, Phong Q.; Seito, Takenobu; Shikata, Junji: Lower bounds on lattice enumeration with extreme pruning (2018)
  9. Divasón, Jose; Joosten, Sebastiaan; Thiemann, René; Yamada, Akihisa: A formalization of the LLL basis reduction algorithm (2018)
  10. Draziotis, Konstantinos A.; Papadopoulou, Anastasia: Improved attacks on knapsack problem with their variants and a knapsack type ID-scheme (2018)
  11. Hurst, Greg: Computations of the Mertens function and improved bounds on the Mertens conjecture (2018)
  12. Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge: Handbook of floating-point arithmetic (2018)
  13. Albrecht, Martin R.: On dual lattice attacks against small-secret LWE and parameter choices in HElib and SEAL (2017)
  14. 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_\mathbbK|\left(\frac12\right)) and application to the cryptanalysis of a FHE scheme (2017)
  15. Bi, Jingguo; Liu, Jiayang; Wang, Xiaoyun: Cryptanalysis of a homomorphic encryption scheme over integers (2017)
  16. Kimura, Keiji; Waki, Hayato; Yasuda, Masaya: Application of mixed integer quadratic program to shortest vector problems (2017)
  17. Neumaier, Arnold: Bounding basis reduction properties (2017)
  18. Albrecht, Martin; Bai, Shi; Ducas, Léo: A subfield lattice attack on overstretched NTRU assumptions. Cryptanalysis of some FHE and graded encoding schemes (2016)
  19. Raum, Martin: Computing genus 1 Jacobi forms (2016)
  20. Marboe, Christian; Velizhanin, Vitaly; Volin, Dmytro: Six-loop anomalous dimension of twist-two operators in planar ( \mathcalN=4 ) SYM theory (2015)

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