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113 results on '"DUCAS, LÉO"'

2. Asymptotics and Improvements of Sieving for Codes

Author

Ducas, Léo, Esser, Andre, Etinski, Simona, Kirshanova, Elena, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Joye, Marc, editor, and Leander, Gregor, editor

Published
2024
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3. Smoothing Codes and Lattices: Systematic Study and New Bounds

Author

Debris-Alazard, Thomas, Ducas, Léo, Resch, Nicolas, and Tillich, Jean-Pierre

Subjects
Computer Science - Information Theory, Computer Science - Cryptography and Security
Abstract

In this article we revisit smoothing bounds in parallel between lattices $and$ codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many lattice-based cryptosystems. Unencumbered by direct application concerns, we provide a systematic study of how these bounds are obtained for both lattices $and$ codes, transferring techniques between both areas. We also consider multiple choices of spherically symmetric noise distribution. We found that the best strategy for a worst-case bound combines Parseval's Identity, the Cauchy-Schwarz inequality, and the second linear programming bound, and this holds for both codes and lattices and all noise distributions at hand. For an average-case analysis, the linear programming bound can be replaced by a tight average count. This alone gives optimal results for spherically uniform noise over random codes and random lattices. This also improves previous Gaussian smoothing bound for worst-case lattices, but surprisingly this provides even better results with uniform ball noise than for Gaussian (or Bernoulli noise for codes). This counter-intuitive situation can be resolved by adequate decomposition and truncation of Gaussian and Bernoulli distributions into a superposition of uniform noise, giving further improvement for those cases, and putting them on par with the uniform cases.

Published
2022

4. Finding Short Integer Solutions When the Modulus Is Small

Author

Ducas, Léo, Espitau, Thomas, Postlethwaite, Eamonn W., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Handschuh, Helena, editor, and Lysyanskaya, Anna, editor

Published
2023
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5. Does the Dual-Sieve Attack on Learning with Errors Even Work?

Author

Ducas, Léo, Pulles, Ludo N., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Handschuh, Helena, editor, and Lysyanskaya, Anna, editor

Published
2023
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6. Hull Attacks on the Lattice Isomorphism Problem

Author

Ducas, Léo, Gibbons, Shane, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Boldyreva, Alexandra, editor, and Kolesnikov, Vladimir, editor

Published
2023
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7. Hawk: Module LIP Makes Lattice Signatures Fast, Compact and Simple

Author

Ducas, Léo, Postlethwaite, Eamonn W., Pulles, Ludo N., Woerden, Wessel van, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Agrawal, Shweta, editor, and Lin, Dongdai, editor

Published
2022
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12. NTRU Fatigue: How Stretched is Overstretched?

Author

Ducas, Léo, van Woerden, Wessel, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Tibouchi, Mehdi, editor, and Wang, Huaxiong, editor

Published
2021
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13. Advanced Lattice Sieving on GPUs, with Tensor Cores

Author

Ducas, Léo, Stevens, Marc, van Woerden, Wessel, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Canteaut, Anne, editor, and Standaert, François-Xavier, editor

Published
2021
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17. Random Self-reducibility of Ideal-SVP via Arakelov Random Walks

Author

de Boer, Koen, Ducas, Léo, Pellet-Mary, Alice, Wesolowski, Benjamin, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Micciancio, Daniele, editor, and Ristenpart, Thomas, editor

Published
2020
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18. LWE with Side Information: Attacks and Concrete Security Estimation

Author

Dachman-Soled, Dana, Ducas, Léo, Gong, Huijing, Rossi, Mélissa, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Micciancio, Daniele, editor, and Ristenpart, Thomas, editor

Published
2020
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19. Integral Matrix Gram Root and Lattice Gaussian Sampling Without Floats

Author

Ducas, Léo, Galbraith, Steven, Prest, Thomas, Yu, Yang, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Canteaut, Anne, editor, and Ishai, Yuval, editor

Published
2020
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20. On the Quantum Complexity of the Continuous Hidden Subgroup Problem

Author

de Boer, Koen, Ducas, Léo, Fehr, Serge, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Canteaut, Anne, editor, and Ishai, Yuval, editor

Published
2020
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21. The Randomized Slicer for CVPP: Sharper, Faster, Smaller, Batchier

Author

Ducas, Léo, Laarhoven, Thijs, van Woerden, Wessel P. J., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Kiayias, Aggelos, editor, Kohlweiss, Markulf, editor, Wallden, Petros, editor, and Zikas, Vassilis, editor

Published
2020
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22. On the Shortness of Vectors to Be Found by the Ideal-SVP Quantum Algorithm

Author

Ducas, Léo, Plançon, Maxime, Wesolowski, Benjamin, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Boldyreva, Alexandra, editor, and Micciancio, Daniele, editor

Published
2019
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23. The General Sieve Kernel and New Records in Lattice Reduction

Author

Albrecht, Martin R., Ducas, Léo, Herold, Gottfried, Kirshanova, Elena, Postlethwaite, Eamonn W., Stevens, Marc, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Ishai, Yuval, editor, and Rijmen, Vincent, editor

Published
2019
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25. Large FHE Gates from Tensored Homomorphic Accumulator

Author

Bonnoron, Guillaume, Ducas, Léo, Fillinger, Max, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Joux, Antoine, editor, Nitaj, Abderrahmane, editor, and Rachidi, Tajjeeddine, editor

Published
2018
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26. Attacks on the AJPS Mersenne-Based Cryptosystem

Author

de Boer, Koen, Ducas, Léo, Jeffery, Stacey, de Wolf, Ronald, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Lange, Tanja, editor, and Steinwandt, Rainer, editor

Published
2018
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27. Shortest Vector from Lattice Sieving: A Few Dimensions for Free

Author

Ducas, Léo, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Nielsen, Jesper Buus, editor, and Rijmen, Vincent, editor

Published
2018
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28. Hash Proof Systems over Lattices Revisited

Author

Benhamouda, Fabrice, Blazy, Olivier, Ducas, Léo, Quach, Willy, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Abdalla, Michel, editor, and Dahab, Ricardo, editor

Published
2018
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29. Second Order Statistical Behavior of LLL and BKZ

Author

Yu, Yang, Ducas, Léo, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Adams, Carlisle, editor, and Camenisch, Jan, editor

Published
2018
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30. Learning Strikes Again: The Case of the DRS Signature Scheme

Author

Yu, Yang, Ducas, Léo, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Peyrin, Thomas, editor, and Galbraith, Steven, editor

Published
2018
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31. On the Statistical Leak of the GGH13 Multilinear Map and Some Variants

Author

Ducas, Léo, Pellet-Mary, Alice, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Peyrin, Thomas, editor, and Galbraith, Steven, editor

Published
2018
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33. Short Stickelberger Class Relations and Application to Ideal-SVP

Author

Cramer, Ronald, Ducas, Léo, Wesolowski, Benjamin, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Coron, Jean-Sébastien, editor, and Nielsen, Jesper Buus, editor

Published
2017
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40. A Subfield Lattice Attack on Overstretched NTRU Assumptions : Cryptanalysis of Some FHE and Graded Encoding Schemes

Author

Albrecht, Martin, Bai, Shi, Ducas, Léo, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Robshaw, Matthew, editor, and Katz, Jonathan, editor

Published
2016
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41. Recovering Short Generators of Principal Ideals in Cyclotomic Rings

Author

Cramer, Ronald, Ducas, Léo, Peikert, Chris, Regev, Oded, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Fischlin, Marc, editor, and Coron, Jean-Sébastien, editor

Published
2016
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42. Sanitization of FHE Ciphertexts

Author

Ducas, Léo, Stehlé, Damien, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Fischlin, Marc, editor, and Coron, Jean-Sébastien, editor

Published
2016
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43. FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second

Author

Ducas, Léo, Micciancio, Daniele, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Oswald, Elisabeth, editor, and Fischlin, Marc, editor

Published
2015
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46. Efficient Identity-Based Encryption over NTRU Lattices

Author

Ducas, Léo, Lyubashevsky, Vadim, Prest, Thomas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Sarkar, Palash, editor, and Iwata, Tetsu, editor

Published
2014
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47. Enhanced Lattice-Based Signatures on Reconfigurable Hardware

Author

Pöppelmann, Thomas, Ducas, Léo, Güneysu, Tim, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Batina, Lejla, editor, and Robshaw, Matthew, editor

Published
2014
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48. Improved Short Lattice Signatures in the Standard Model

Author

Ducas, Léo, Micciancio, Daniele, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Garay, Juan A., editor, and Gennaro, Rosario, editor

Published
2014
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49. Lattice Signatures and Bimodal Gaussians

Author

Ducas, Léo, Durmus, Alain, Lepoint, Tancrède, Lyubashevsky, Vadim, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Canetti, Ran, editor, and Garay, Juan A., editor

Published
2013
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50. Mildly Short Vectors in Cyclotomic Ideal Lattices in Quantum Polynomial Time.

Author

CRAMER, RONALD, DUCAS, LÉO, and WESOLOWSKI, BENJAMIN

Subjects
OPTICAL lattices, POLYNOMIAL time algorithms, APPROXIMATION algorithms, POLYNOMIAL rings, CYCLOTOMIC fields, CURRICULUM, HARDNESS, ALGORITHMS
Abstract

In this article, we study the geometry of units and ideals of cyclotomic rings and derive an algorithm to find a mildly short vector in any given cyclotomic ideal lattice in quantum polynomial time, under some plausible number-theoretic assumptions. More precisely, given an ideal lattice of the cyclotomic ring of conductor m, the algorithm finds an approximation of the shortest vector by a factor exp(-õ (vm)). This result exposes an unexpected hardness gap between these structured lattices and general lattices: The best known polynomial time generic lattice algorithms can only reach an approximation factor exp(-O (m)). Following a recent series of attacks, these results call into question the hardness of various problems over structured lattices, suchas Ideal-SVP and Ring-LWE, upon which relies the security of a number of cryptographic schemes. [ABSTRACT FROM AUTHOR]

Published
2021
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