Description
The GGH Graded Encoding Scheme (of Garg, Gentry and Halevi), based on ideal lattices, is the first plausible approximation to a cryptographic multilinear map. Unfortunately, using the security analysis the authors provided, the scheme requires very large parameters to provide security for its underlying encoding re-randomization process. Our main contributions are to formalize, simplify and improve the efficiency and the security analysis of the re-randomization process in the GGH construction. We apply these results in a new construction that we call GGHLite. In particular, we first lower the size of a standard deviation parameter of the re-randomization process from exponential to polynomial in the security parameter. This first improvement is obtained via a finer security analysis of the drowning step of re-randomization, in which we apply the Rényi divergence instead of the conventional statistical distance as a measure of distance between distributions. Our second improvement is to reduce the number of randomizers needed from Omega(n log n) to 2, where n is the dimension of the underlying ideal lattices. These two contributions allow us to decrease the bit size of the public parameters from O(lambda^5 log lambda) for the GGH scheme to O(lambda log^2 lambda)$ in GGHLite, with respect to the security parameter lambda for a constant multilinearity parameter.
Next sessions
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Random lattices that are modules over the ring of integers
Speaker : Nihar Gargava - Institut de Mathématiques d'Orsay
We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideal or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattice as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Speaker : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…] -
Yoyo tricks with a BEANIE
Speaker : Xavier Bonnetain - Inria
TBD-
Cryptography
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Symmetrical primitive
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