Approximate lattices
نویسندگان
چکیده
منابع مشابه
Approximate common divisors via lattices
We analyze the multivariate generalization of Howgrave-Graham’s algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size Nβ , this improves the size of the error tolerated from Nβ 2 to Nβ (m+1)/m , under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the rec...
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Password-based authenticated key exchange (PAKE) enables two users with shared low-entropy passwords to establish cryptographically strong session keys over insecure networks. At Asiacrypt 2009, Katz and Vaikuntanathan showed a generic three-round PAKE based on any CCA-secure PKE with associated approximate smooth projective hashing (ASPH), which helps to obtain the first PAKE from lattices. In...
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Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the...
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We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2018
ISSN: 0012-7094
DOI: 10.1215/00127094-2018-0028