Vectorial topology

The vectorial λ-calculus

We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. ...

Normality of Vectorial Functions

The most important building blocks of symmetric cryptographic primitives such as the DES or the AES, are vectorial Boolean functions, also called S-boxes. In this paper, we extend the definition of normality for Boolean functions into several new affine invariant properties for vectorial Boolean functions. We compute the probability of occurrence of these properties and present practical algori...

Vectorial Pattern Databases

In this work, a new approach for creating Pattern Databases (PDBs) is suggested that induces non-consistent heuristic functions just by recognizing feasible (yet admissible) heuristic values. This approach serves to generalize even further the BPMX propagation rule, that will work now even in directed graphs. Experiments in different state spaces show a noticeable improvement over the Scalar Pa...

Vectorial fast correlation attacks

Vectorial Signatures for Pattern Recognition

Due to the variety of shapes and sizes that present both living organisms and static objects, the necessity to look for automated systems of identification, both in industry and scientific research has arisen. During the 1960s, the scientific community in the field of optics has used the Fourier transform and other types of mathematical transformations for pattern recognition, taking advantage ...