Table of contents

  • This session has been presented February 27, 2015.

Description

  • Speaker

    Luca De Féo - UVSQ

La recherche de racines dans un corps fini est un problème classique, avec de nombreuses applications en cryptographie et codage. Étant donné un polynôme de degré d à coefficients dans un corps fini GF(q^n), on cherche ses zéros dans GF(q^n).<br/> Cet exposé s'intéresse au cas où q est un petit nombre, et donc notamment au cas de la petite caractéristique. Nous présentons trois algorithmes pour la recherche de racines. Berlekamp's Trace Algorithm (BTA), proposé par Berlekamp en '67, le Affine Refinement Method (ARM), proposé par Menezes, van Oorschot et Vanstone en '89, et le Successive Resultants Algorithm, proposé par Petit en '14. Nous mettons en évidence le lien entre ces trois algorithmes et la géométrie affine de GF(q^n). Le lien entre BTA et ARM a déjà été mis en évidence par Menezes et ses co-auteurs, qui concluaient en faveur de ARM. Nous montrons que leur analyse est trop pessimiste, et qu'une simple modification de ARM est tout à fait compétitive avec BTA pour tout paramètre. Le lien entre BTA et ARM n'a pas été remarqué auparavant. Nous montrons que ces deux algorithmes sont dans un sens *duaux* l'un de l'autre, et que leurs performances sont très proches. Nous donnons une analyse détaillée des trois algorithmes, et comparons leurs implantations avec l'état de l'art. Nous proposons aussi des variantes adaptées à certaines classes de corps finis. Ceci est un travail commun avec Michaël Quisquater et Christophe Petit.

Next sessions

  • Combining Partial Sums and FFT for the Fastest Known Attack on 6‑Round AES

    • October 17, 2025 (13:45 - 14:45)

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Shibam Ghosh - Inria

    The partial-sums technique introduced by Ferguson et al. (2000) achieved a 6‑round AES attack with time complexity 2^{52} S‑box evaluations, a benchmark that has stood since. In 2014, Todo and Aoki proposed a comparable approach based on the Fast Fourier Transform (FFT).  In this talk, I will show how to combine partial sums with FFT to get "the best of both worlds". The resulting attack on 6[…]

    • Cryptography

  • Lie algebras and the security of cryptosystems based on classical varieties in disguise

    • November 07, 2025 (13:45 - 14:45)

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Mingjie Chen - KU Leuven

    In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups.   In this talk, we[…]

    • Cryptography

  • Some applications of linear programming to Dilithium

    • November 14, 2025 (13:45 - 14:45)

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Paco AZEVEDO OLIVEIRA - Thales & UVSQ

    Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases.   During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…]

  • Wagner’s Algorithm Provably Runs in Subexponential Time for SIS^∞

    • November 21, 2025 (13:45 - 14:45)

    • Salle Guernesey à l'ISTIC

    Speaker : Johanna Loyer - Inria Saclay

    At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus q = poly(n) and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner’s algorithm (CRYPTO 2002), run[…]

    • Cryptography

  • CryptoVerif: a computationally-sound security protocol verifier

    • November 28, 2025 (13:45 - 14:45)

    • Batiment 32B salle 12

    Speaker : Bruno Blanchet - Inria

    CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]

    • Cryptography

  • Structured-Seed Local Pseudorandom Generators and their Applications

    • December 05, 2025 (13:45 - 14:45)

    • IRMAR - Université de Rennes - Campus Beaulieu Bat. 22, RDC, Rennes - Amphi Lebesgue

    Speaker : Nikolas Melissaris - IRIF

    We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]

    • Cryptography

Show previous sessions
Page top