Description
Les couplages interviennent dans des protocoles cryptographiques de plus en plus nombreux tel que le chiffrement basé sur l'identité ou la signature courte. Dès lors, fournir une implémentation efficace des couplages cryptographique pour un grand nombre de supports, et plus spécialement les systèmes embarqués, devient un chalenge intéressant. Nous présentons une nouvel méthode pour concevoir des accélérateurs matériels compacts pour le cacul du couplage de Tate sur des courbes supersingulières de petite caractéristique. Du fait de leur degré de plongement (embedding degree) limité, ces courbes ne sont généralement pas utilisées pour atteindre la sécurité standard de 128 bits. En effet, la taille du corps fini de définition d'une courbe à ce niveau de sécurité est très grande. Afin de palier cet effet, nous considérons des courbes supersingulières définies sur des corps finis de de degré d'extension modérément composé ($\F{p}{nm}$ avec $n$ «petit» et $m$ premier). Ces courbes deviennent alors vulnérables aux attaques basées sur la descente de Weil mais une analyse fine de celles-ci nous permet de montrer que leur impact reste limité et que nous pouvons maintenir la sécurité au-dessus de 128 bits.<br/> Nous appliquons alors cette méthode à une courbe supersingulière définie sur $\F{3}{5\cdot97}$ et décrivons ainsi une implémentation FPGA d'un accélérateur pour le calcul de couplage à 128 bits de sécurité. Sur FPGA de gamme moyenne (Xilinx Virtex-4 FPGA), cet accélérateur cacule le couplage en 2.2 ms sur une surface limitée à 4755 slices.
Next sessions
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Combining Partial Sums and FFT for the Fastest Known Attack on 6‑Round AES
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
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
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
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Some applications of linear programming to Dilithium
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^∞
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
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CryptoVerif: a computationally-sound security protocol verifier
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
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Structured-Seed Local Pseudorandom Generators and their Applications
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
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