Quasi-complete ideal lattices

Analogizing Hutton's quasi-uniformities for complete lattices and extending Shi's quasi-uniformities to closed set lattices

This paper gives analogies of Hutton’s quasi-uniformities for complete lattices and extensions of Shi’s pointwise quasi-uniformities to closed set lattices.CLGOH denotes the category of all complete lattices with generalized order homomorphisms asmorphisms and CSL the category of all closed set lattices.HQUnif and SPQUnif denote the categories of Hutton quasi-uniform spaces on complete lattices...

Ideal Lattices of Lattices

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

Density of Ideal Lattices

The security of many efficient cryptographic constructions, e.g. collision-resistant hash functions, digital signatures, identification schemes, and more recently public-key encryption has been proven assuming the hardness of worst-case computational problems in ideal lattices. These lattices correspond to ideals in the ring Z[ζ], where ζ is some fixed algebraic integer. Under the assumption th...

Ideal Lattices and NTRU

Identifying Ideal Lattices

Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant ha...