Abstract: An homomorphic encryption technique enables one to carry on operations on encrypted messages without decrypting them, these encrypted messages being associated to unencrypted messages that belong to a discrete set consisting of pi distinct elements, with pi being an odd number, the elements of the discrete set being such that twice the difference between any two of these elements is not an integer number, said discrete set being for instance the discrete torus Tpi={?(pi?1)/2, ?(pi?1)/2+1, . . . , (pi?1)/2?1, (pi?1)/2}/pi. In particular, a specific bootstrapping procedure form such encrypted messages is disclosed. The disclosed technology concerns also an homomorphic encryption technique for carrying on operations on encrypted messages associated to unencrypted messages that belong Zp, p being equal to the product of r integer numbers pi, i=1 . . . r that are pairwise coprime. The disclosed technology concerns also associated electronic devices and systems implementing such techniques.

Abstract: The present invention is a process of organization of a relational data base, aimed to be used in a computer system containing at least a processor and some memory, characterized in that it includes the steps consisting in: Elaborate a hierarchical expansion table; Create the thesaurus of each of the columns; For each of the words of the thesaurus, create the radix tree of the set of line indexes at which the aforementioned word appears; For each of the primary keys, store the sequence of these values and a permutation on this set of values in order to find back a given value.

Abstract: A method of computing shortest paths in a weighted graph having vertices and an adjacency matrix with memory resources and a processor including (a) selecting integer weights; (b) carrying out a series of incrementations, an incrementation including finding a set of vertices to which one may arrive from a given set of vertices; (c) carrying out a series of decrementations, a decrementation including finding a set of vertices from which one may go to arrive to a given set of vertices; (d) causing the incrementations and decrementations to be carried out in any order; (e) transforming vectors of increments/decrements in paths, the paths making up a set E1 of the shortest paths in term of number of arcs or using a given number of arcs, Na; (f) selecting n-uple of paths C of lowest cost among set of paths E1; (g) calculating Nb=Na+1; (h) computing iteratively, while Nb?W(C) the following steps: i.

Abstract: The present invention is a process of organization of a relational data base, aimed to be used in a computer system containing at least a processor and some memory, characterized in that it includes the steps consisting in: Elaborate a hierarchical expansion table; Create the thesaurus of each of the columns; For each of the words of the thesaurus, create the radix tree of the set of line indexes at which the aforementioned word appears; For each of the primary keys, store the sequence of these values and a permutation on this set of values in order to find back a given value.

Abstract: A method of computing shortest paths in a weighted graph having vertices and an adjacency matrix with memory resources and a processor including (a) selecting integer weights; (b) carrying out a series of incrementations, an incrementation including finding a set of vertices to which one may arrive from a given set of vertices; (c) carrying out a series of decrementations, a decrementation including finding a set of vertices from which one may go to arrive to a given set of vertices; (d) causing the incrementations and decrementations to be carried out in any order; (e) transforming vectors of increments/decrements in paths, the paths making up a set E1 of the shortest paths in term of number of arcs or using a given number of arcs, Na; (f) selecting n-uple of paths C of lowest cost among set of paths E1; (g) calculating Nb=Na+1; (h) computing iteratively, while Nb≦W(C) the following steps: i.