Description
Groups of prime order with a bilinear structure are interesting objects for public key cryptography. In the first part of the lecture we shall explain how the pairing on points of the Jacobian variety which is usually called "Tate-pairing" can be got in a p- adic setting by the Lichtenbaum pairing. On the one hand side this setting gives us more freedom for its computation which leads to more efficiency if the genus of the underlying curve is larger than 1.<br/> On the other side it shows that the Brauer groups of local fields arises in a natural way in the world of discrete logarithms based on ideal class groups. This, and the great importance of Brauer groups for number theory, motivates that one should try to investigate them computationally. In the second part of the lecture we shall present index-calculus methods for Brauer groups with applications to the classical discrete logarithm and to the computation of Euler's totient function.
Next sessions
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TBA
Speaker : Eran Lambooij - Inria
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Cryptography
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Key Attack on the ACDGV Matrix Encryption Scheme
Speaker : Anmoal Porwal - Technical University of Munich
I will present our key-recovery attack on the ACDGV public-key encryption scheme proposed at ASIACRYPT 2024 by Aragon, Couvreur, Dyseryn, Gaborit, and Vinçotte. The secret key is a Gabidulin code hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack exploits the resulting algebraic structure to recover an equivalent secret key. It[…]-
Cryptography
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Asymmetric primitive
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