Complexity of lattice problems

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Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices (2006, background): “For general lattices, the best known reduction loses a √ n factor [17]; furthermore, that reduction performs manipulations on its input lattice that can destroy the cyclicity property.”
On lattices, learning with errors, random linear codes, and cryptography (2005, background): “¢(f(X);f(Y )) • ¢(X;Y ); see, e.g., [ 15 ]. In particular, this implies that the acceptance probability of any algorithm on inputs from X difiers from its acceptance probability on inputs from Y by at most”
Predicting Lattice Reduction (2008, background): “We refer to [29,23] for a bibliography on lattices.”