Abstract: A method for decoding an encrypted electromagnetic signal W encoded by a first computer with public key N_0=r×s, where N_0, r and s are integers. There is the step of obtaining the electromagnetic signal W from a telecommunications network, or a data network or an Internet or a first non-transient memory. There is the step of storing the electromagnetic signal W in a second non-transient memory. There is the step of decoding with a second computer in communication with the second non-transient memory the electromagnetic signal W in the second non-transient memory by factoring the public key N_0 in at most a time O(log^6 N_0). A non-transitory readable storage medium which includes a computer program stored on the storage medium for decoding an encrypted electromagnetic signal W.

Abstract: This patent describes a method, apparatus and computer program which factor a large integer N0 in a time of the order of p2·logp4 N0, where p denotes a prime.

Abstract: A redundant controller engine (RCE) of a system includes a first, second and at least a third redundant processing unit (RPU). The RCE includes an arbitrator in communication with the first, second and third RPUs which sends a message for a corresponding time requiring a decision to the first, second and third RPUs, and receives the decisions made by the first, second and third RPUs. The arbitrator accepts a first two matching decisions for the corresponding time received from the first, second and third RPUs, and sending the matching decision for the corresponding time to the system. The arbitrator has a first message processing unit (MPU) and a second MPU. The first MPU sends the message for the corresponding time to and receives the decisions for the corresponding time from the first, second and third RPUs. A method for processing data from a system. An apparatus for conferencing.

Abstract: A network over which a medium is transferred. The network includes S core rings. Each core ring can be modeled as a set of nodes interconnected by links, where S is greater than or equal to 4 and is an integer, each said core ring having at least N nodes, where N is greater than or equal to 4 and is an integer. Each node/link is configurable in terms of directing the medium from a given source toward a given destination, and where each of the core rings is directly connected by means of k spanning links, where k is greater than or equal to 2, so as to comprise a spanning ring to at least a second and a third of the other core rings. The combinations of core rings spanned by each core ring is such that there is a path comprised of links and nodes from each node on any core ring to any other node on any other core ring. A method for transferring a medium.

Abstract: A network over which a medium is transferred. The network includes S core rings. Each core ring can be modeled as a set of nodes interconnected by links, where S is greater than or equal to 4 and is an integer, each said core ring having at least N nodes, where N is greater than or equal to 4 and is an integer. Each node/link is configurable in terms of directing the medium from a given source toward a given destination, and where each of the core rings is directly connected by means of k spanning links, where k is greater than or equal to 2, so as to comprise a spanning ring to at least a second and a third of the other core rings. The combinations of core rings spanned by each core ring is such that there is a path comprised of links and nodes from each node on any core ring to any other node on any other core ring. A method for transferring a medium.