Description
A {\em black-box} secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g.\ the structure of the group or its order. The expansion factor of a BBSSS is the length of a vector of shares (the number of group elements in it) divided by the number of players $n$.<br/> In 2002 Cramer and Fehr proposed a threshold BBSSS with an asymptotically minimal expansion factor $\Theta(\log n)$. We present a BBSSS that is based on a new paradigm, namely, {\em primitive sets in algebraic number fields}. This leads to a new BBSSS with an expansion factor that is absolutely minimal up to an additive term of at most~2, which is an improvement by a constant additive factor. The construction uses techniques from algebraic number theory as well as algebraic geometry.<br/> We provide good evidence that our scheme is considerably more efficient in terms of the computational resources it requires. Indeed, the number of group operations to be performed is $\tilde{O}(n^2)$ instead of $\tilde{O}(n^3)$ for sharing and $\tilde{O}(n^{1.6})$ instead of $\tilde{O}(n^{2.6})$ for reconstruction. Finally, we show that our scheme, as well as that of Cramer and Fehr, has asymptotically optimal randomness efficiency.<br/> This is talk is based on joint work with Serge Fehr, Hendrik Lenstra, and Martijn Stam. An article with these results appears in the Proceedings of the 25th Annual IACR CRYPTO Conference, 2005.
Prochains exposés
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Predicting Module-Lattice Reduction
Orateur : Paola de Perthuis - CWI
Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as `Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens[…]-
Cryptography
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Séminaire C2 à INRIA Paris
Emmanuel Thomé et Pierrick Gaudry Rachelle Heim Boissier Épiphane Nouetowa Dung Bui Plus d'infos sur https://seminaire-c2.inria.fr/ -
Attacking the Supersingular Isogeny Problem: From the Delfs–Galbraith algorithm to oriented graphs
Orateur : Arthur Herlédan Le Merdy - COSIC, KU Leuven
The threat of quantum computers motivates the introduction of new hard problems for cryptography.One promising candidate is the Isogeny problem: given two elliptic curves, compute a “nice’’ map between them, called an isogeny.In this talk, we study classical attacks on this problem, specialised to supersingular elliptic curves, on which the security of current isogeny-based cryptography relies. In[…]-
Cryptography
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