IMB > Recherche > Séminaires
Le 3 octobre 2023
à 11:00
salle 2
Jean Gasnier IMB
An Algebraic Point of View on the Generation of Pairing-Friendly Elliptic Curves
In 2010, Freeman, Scott, and Teske published a well-known taxonomy compiling the
best known families of pairing-friendly elliptic curves. Since then, the
research effort mostly shifted from the generation of pairing-friendly curves to
the improvement of algorithms or the assessment of security parameters to resist
the latest attacks on the discrete logarithm problem. Consequently, very few new
families were discovered. However, the need of pairing-friendly curves of prime
order in some new applications such as SNARKs has reignited the interest in the
generation of pairing-friendly curves, with hope of finding families similar to
the one discovered by Barreto and Naehrig.
Building on the work of Kachisa, Schaefer, and Scott, we show that some elements
of extensions of a cyclotomic field have a higher probability of generating a
family of pairing-friendly curves. We present a general framework which embraces
the KSS families and many of the other families in the taxonomy paper. We finally
introduce a new family with embedding degree k=20 which we estimate to provide
a faster Miller loop compared to KSS16 and KSS18 at the 192-bit security level.
Le 10 octobre 2023
à 11:00
salle 2
Wouter Rozendaal IMB
A Renormalisation Decoder for Kitaev's Toric Quantum Code
Kitaev's toric code is expected to be at the core of the first generation of quantum computers that will incorporate error protection. To make full use of the toric code, one requires an efficient decoding scheme that will process the classical information obtained from quantum syndrome measurements, so as to be able to regularly put arrays of qubits back into their intended states. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best trade-offs between efficiency and speed. One feature that remained a mystery however, is their behaviour over adversarial channels, i.e. their worst-case behaviour. In this talk, we introduce a relatively natural and deterministic version of a renormalisation decoder and bound its error-correcting radius.
Le 24 octobre 2023
à 11:00
salle 2
Donghyeok Lim Korea
TBA
Le 7 novembre 2023
à 11:00
salle 2
Maxime Bombar CWI
Pseudorandom Correlation Generators from the Hardness of Decoding Codes over Group Algebras
Le 14 novembre 2023
à 11:00
salle 2
Stefano Marseglia Utrecht University
TBA
Séminaire de Théorie Algorithmique des Nombres
Responsables : Razvan Barbulescu et Wessel Van Woerden
best known families of pairing-friendly elliptic curves. Since then, the
research effort mostly shifted from the generation of pairing-friendly curves to
the improvement of algorithms or the assessment of security parameters to resist
the latest attacks on the discrete logarithm problem. Consequently, very few new
families were discovered. However, the need of pairing-friendly curves of prime
order in some new applications such as SNARKs has reignited the interest in the
generation of pairing-friendly curves, with hope of finding families similar to
the one discovered by Barreto and Naehrig.
Building on the work of Kachisa, Schaefer, and Scott, we show that some elements
of extensions of a cyclotomic field have a higher probability of generating a
family of pairing-friendly curves. We present a general framework which embraces
the KSS families and many of the other families in the taxonomy paper. We finally
introduce a new family with embedding degree k=20 which we estimate to provide
a faster Miller loop compared to KSS16 and KSS18 at the 192-bit security level.
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Institut de Mathématiques de Bordeaux UMR 5251
Université de Bordeaux
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