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Research

I am currently working on lattice-based cryptography with a focus on algebraic lattices and their underlying number theoretical structure. More generally, I am interested by computer algebra, algebraic number theory and their applications to cryptography.

PhD thesis

My Ph.D. thesis can be found here.
Please, feel free to contact me if you have any question, remark or if you spot any error/typo.

Preprints

1. Diagonally dominant matrices for cryptography. [HAL, PDF]
   With Kazuhide Fukushima, Thomas Plantard and Arnaud Sipasseuth.
   Follow-up on the note found below.


2. On the Short Principal Ideal Problem over some real Kummer fields. [ePrint]
   With Willy Susilo and Thomas Plantard.
   Code available here

Journal Papers

1. Improved computation of polynomial roots over number fields when using complex embeddings. [DOI]
   With Willy Susilo and Thomas Plantard.
   Accepted for publication to Journal of Computational Algebra.
   Code available here


2. Short Principal Ideal Problem in multicubic fields.
   With Willy Susilo and Thomas Plantard.
   Journal of Mathematical Cryptology, 14(1), 359-392.
   Journal version of the paper below, presented at NutMic 2019.

Conference Papers

1. Computing \(e\)-th roots in number fields. [arXiv]
   With Olivier Bernard and Pierre-Alain Fouque.
   SIAM Symposium on Algorithm Engineering and Experiments (ALENEX24).


2. Log-S-unit lattices using Explicit Stickelberger Generators to solve Approx Ideal-SVP. [ePrint]
   With Olivier Bernard, Tuong-Huy Nguyen, and Adeline Roux-Langlois.
   ASIACRYPT 2022.
   Code available here


3. On ideal lattices in multicubic fields.
   With Willy Susilo and Thomas Plantard.
   Number-Theoretic Methods in Cryptology 2019
   Slides


4. Efficient Leak Resistant Modular Exponentiation in RNS.
   With Christophe Negre and Thomas Plantard.
   Proceedings of ARITH 24. 24th IEEE Symposium on Computer Arithmetic. London, England, July 24-26, 2017, pages 156-163.


5. Efficient Randomized Regular Modular Exponentiation using Combined Montgomery and Barrett Multiplications.
   With Christophe Negre and Thomas Plantard.
   SECRYPT 2016. The 13th International Conference on Security and Cryptography. Lisbon, Portugal, July 26-28, 2016, pages 368-375.

Notes and works in progress

1. Covering Radius and First Minima Bound on Diagonally Dominant Lattices in the l\(_\infty\)-norm, with Thomas Plantard and Arnaud Sipasseuth.
   Accepted for presentation to Number-Theoretic Methods in Cryptology (Nutmic) 2021.


2. A note on the discriminant and prime ramification of some real Kummer extensions.

Andrea Lesavourey