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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MIKE: An efficient and compact NIKE Based on a Commutative Monoidal Action
Speaker : 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
Speaker : Anmoal Porwal - Technical University of Munich
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Cryptography
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Asymmetric primitive
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