Description
Finding a short non zero vector in an Euclidean lattice is a well-studied problem which has proven useful to construct many cryptographic primitives. The current best asymptotic algorithm to find a relatively short vector in an arbitrary lattice is the BKZ algorithm. This algorithm recovers a vector which is at most $2^{n^{\alpha}}$ times larger than the shortest non zero vector in time $2^{n^{1-\alpha}}$ for any $\alpha$ between 0 and 1.<br/> In order to gain in efficiency, it is sometimes interesting to use structured lattices instead of general lattices. An example of such structured lattices are ideal lattices. One may then wonder whether, on the security front, it is easier to find short vectors in a structured lattice or not. Until 2016, there was no known algorithm which would perform better on ideal lattices than the BKZ algorithm (either classically or quantumly). In 2016 and 2017, Cramer-Ducas-Peikert-Regev and Cramer-Ducas-Wesolowski proposed a quantum algorithm that finds a $2^{\sqrt n}$ approximation of the shortest non zero vector in polynomial time. However, the BKZ algorithm remained the best algorithm in the classical setting or for approximation factor smaller than $2^{\sqrt n}$ in the quantum setting.<br/> In this talk, I will present an algorithm that extends the one of Cramer et al. and improves upon the BKZ algorithm for ideal lattices, both quantumly and classically. This algorithm is heuristic and non uniform (i.e., it requires an exponential time pre-processing).<br/> lien: http://desktop.visio.renater.fr/scopia?ID=723420***3028&autojoin
Next sessions
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptography
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Asymmetric primitive
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Mode and protocol
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York