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The Short Integer Solution (SIS) problem is an average case problem that is used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Ajtai [ 1 ] who presented a family of one-way functions based on the SIS problem.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
The subject is only allowed to access an object if the security level of the subject is greater than or equal to that of the object. Mathematically, the security level access may also be expressed in terms of the lattice (a partial order set) where each object and subject have a greatest lower bound (meet) and least upper bound (join) of access ...
Many lattice-based cryptographic schemes are known to be secure assuming the worst-case hardness of certain lattice problems. [ 3 ] [ 6 ] [ 7 ] I.e., if there exists an algorithm that can efficiently break the cryptographic scheme with non-negligible probability, then there exists an efficient algorithm that solves a certain lattice problem on ...
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...
5 lattice is the union of two A 5 lattices: ∪ . The A 3 5 is the union of three A 5 lattices: ∪ ∪ . The A * 5 lattice (also called A 6 5) is the union of six A 5 lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-simplex. ∪ ∪ ∪ ...
If one ignores the geometry and merely considers the problem an algebraic one of Diophantine inequalities, then there one could increase the exponents appearing in the problem from squares to cubes, or higher. The dot planimeter is physical device for estimating the area of shapes based on the same principle. It consists of a square grid of ...
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.