Abstract: The present invention proposes a continuous multi-parameter version of Diffie-Hellman protocol based on matrices over topological monoids. In its turn, based on this continuous protocol, a method for public establishment and distribution of keys for encryption systems is implemented. An embodiment of the method, while providing a high security level, is several orders of magnitude faster than the existing key establishment systems. The present invention is a further development of the method of the geometric key establishment first proposed in U.S. patent application Ser. No. 10/708,197 by A. Berenstein and L. Chernyak.

Abstract: A method for processing a document in a set of documents is disclosed comprising the steps of generating a topological search query comprising a set of search terms having a defined interrelationship between at least two of the terms, and generating a non-linear representation for at least one document in the set based on the topological search query, the nonlinear representation representing a measure of at least proximity of the search terms within the document.

Abstract: The present invention proposes a continuous multi-parameter version of Diffie-Hellman protocol based on topological groups. In its turn, based on this continuous protocol, a method for public establishment and distribution of keys for encryption systems is implemented. An embodiment of the method, while providing an extremely high security level, is several orders of magnitude faster than the existing key establishment systems.

Abstract: A method of communicating information between users of a communication system includes the following steps of: generating a module V over a ring R; generating an outer component P of encryption key that includes sequence (p1, p2, . . . , pk) where each member pj of the sequence belongs to the set {1, 2, . . . , m} (the length k of the sequence is arbitrary and thus repetitions are allowed in the sequence); generating an inner component Q of encryption key that includes elements v1,v2, . . . , Vm of V and automorphisms g1, g2, . . . , gm of V; generating the encryption key K=(P; Q), where P is the outer component and Q is the inner component; generating an encryption automorphism Te of V based on the encryption key K, where Te includes a composition of certain automorphisms T1, T2, . . .