Description
The talk will be concerned with arithmetic on elliptic and hyperelliptic curves. We show how fast the arithmetic can get by clever choices of the coordinates and present special kinds of curves which allow even faster arithmetic using the Frobenius endomorphism. For elliptic curves this has been used to achieve fast arithmetic for the past years. However, so far arithmetic in the ideal class group of hyperelliptic curves was performed using Cantor's algorithm which needs several inversions per group operation.<br/> Starting with the work of Harley and improved by Miyamoto, Doi, Matsuo, Chao, and Tsuji and by Takahashi efficient explicit formulae are at hand. Meanwhile inversion-free systems have been studied allowing even hardware implementations and depending on the system, hyperelliptic curves can even be faster than elliptic curves. Curve-endomorphisms allow to obtain further speed-up. We shortly present Koblitz curves, the generalized GLV method and trace zero subvarieties.
Prochains exposés
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MIKE: An efficient and compact NIKE Based on a Commutative Monoidal Action
Orateur : Jonathan Komada Eriksen - COSIC, KU Leuven
Robert recently described a powerful correspondence between certain (Hermitian) modules and (polarized) abelian varieties, which simultaneously generalizes both the class-group action underlying protocols such as CSIDH, and the Deuring correspondence, underlying protocols such as SQIsign. Using this correspondence, he also proposed how to construct a post-quantum NIKE, called MIKE, which, at a[…]-
Cryptography
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TBA
Orateur : Anmoal Porwal - Technical University of Munich
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Cryptography
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Asymmetric primitive
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