Abstract: The present invention provides a method and an apparatus for generating sequences of pseudo-random numbers. Seed random sequences are used to establish independent pseudo-random sub-processes. Those independent pseudo-random sub-processes are combined through a technique of successive interaction to create final pseudo-random sequences. One set of pseudo-random sub-processes is used to continually reorder a table of potential output values. The table can contain uniformly distributed values or may contain values distributed in a non-uniform manner. A second set of pseudo-random sub-processes is used to select a sequence of output values from the table. The invention creates final pseudo-random sequences of output values that can be equidistributed over large samples or final pseudo-random sequences of output values that have non-uniform distributions.

Abstract: Random numbers are used for a variety of purposes and play key roles in systems such as simulation studies, information processing, communication, and encryption. Truly random numbers are generally the result of processes that cannot be successfully repeated to generate the same sequence of results, and thus are unpredictable. Pseudo-random numbers, on the other hand, are easily replicated as the output of deterministic processes. Such a series of pseudo-random numbers will eventually repeat itself in perpetuity once it has exhausted its cycle length. The claimed invention introduces a new class of random numbers called idem-random numbers that have many of the essential characteristics of random numbers but which may be successfully replicated at different locations and at different times and which will never repeat themselves. The claimed invention uses the characteristics of prime and prime-like numbers to create endless sequences of idem-random numbers. Idem-random numbers are produced by a.

Abstract: The present invention provides a method and an apparatus for generating pseudo-random numbers with very long periods and very low predictability. A seed random sequence is extended into a much longer sequence by successive iterations of matrix operations. Matrices of candidate output values are multiplied by non-constant transition matrices and summed with non-constant offset matrices; the result is then processed through one or more modulus operations, including non-constant modulus operators, to generate the actual output values. The invention also includes the possibility of introducing non-invertible matrices into the operations. The invention creates final results that are equidistributed over large samples. Secondary pseudo-random and other processes determine the non-constant transition matrices, offset matrices, and modulus operators.

Abstract: A cryptographic system transmits a fully secure cryptographic message over a non-secure communication channel without prior exchange of cryptographic keys using a three-pass protocol. The transmitting agent initiating the communication embodies the message for the designated receiving agent in the composite output of two distinct transformations such that a generalized reversal of the combined transformations cannot be determined from that output. That output is transmitted as a first-pass over a non-secure channel to the receiving agent. The receiving agent generates a second composite output by transforming the received message such that a generalized reversal of this second combined transformation cannot be determined from that resulting output. That second output is transmitted as a second-pass over a non-secure channel to the initial transmitting agent.