Abstract: Disclosed are methods and systems for encrypting numeric messages using Geometric Algebra on at least one source device and then storing and sorting the encrypted messages on an intermediary system without decrypting the encrypted numeric messages on the intermediary system and/or on a sort request device requesting the sort. Both the intermediary and sort request devices/systems do not need to have knowledge of the encryption security keys. A sort result (sorted group of cryptotext multivectors) may be sent to a destination device. The sorted encrypted data may be decrypted and kept in sorted order on the destination device. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data with one or more other multivectors that carry encryption keys. Decrypt operations decrypt encrypted data by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.

Abstract: Disclosed are methods and systems for encrypting numeric messages using Geometric Algebra on at least one source device and then storing and searching the encrypted messages on an intermediary system without decrypting the encrypted numeric messages on the intermediary system and/or on a search request device requesting the search. Both the intermediary and search request devices/systems do not need to have knowledge of the encryption security keys. A search result (FOUND/NOT-FOUND) may be sent to a destination device. The FOUND encrypted data, as well as other encrypted data linked to the FOUND encrypted data, may be sent to a destination device and decrypted. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data with one or more other multivectors that carry encryption keys. Decrypt operations decrypt encrypted data by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.

Abstract: Disclosed are methods and systems for encrypting a numeric message using Geometric Algebra on a source computing device, performing scalar-vector multiplication on the encrypted numeric message and an unencrypted scalar data value to get an encrypted scalar multiplicative result without decrypting the encrypted numeric message on an intermediary computing system that does not have knowledge of the encryption security keys, and decrypting using Geometric Algebra the encrypted scalar multiplicative result on a destination computing device such that the decrypted result is equal to multiplication of the unencrypted numeric message and the scalar data value. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data of the numeric data message with one or more other multivectors that carry encryption keys.

Abstract: A method is provided for navigating a vehicle. Waypoint exclusion zones are efined as circles whose centers are known-position waypoints. The vehicle is steered along a path that is tangential to the "current" waypoint exclusion zone. This path that is maintained until a relative bearing between the vehicle and a center of the current waypoint exclusion zone is at least 90.degree. if the path is left of the center of the current waypoint exclusion zone, and at most -90.degree. if the path is right of the center of the current waypoint exclusion zone. When either of these conditions is met, the vehicle is located along the circle of the current waypoint exclusion zone. The vehicle is then advanced along the circle of the current waypoint exclusion zone until a heading of the vehicle matches a heading of a path that: is tangential to the "next" waypoint exclusion zone.

Abstract: The method of the present invention minimizes the time required to display portion of a time sampled data file. A plurality of compressed data files are generated based on the time sampled data file. Each of the compressed data files is defined by a corresponding unique compression ratio such that each compressed data file contains fewer data points than the original time sampled data file. Each compressed data file characterizes the original time sampled data file. The compressed data files are stored in a data storage device for subsequent retrieval. A resolution factor is defined for each of the compressed data files. One of the compressed data files is then selected based on the resolution factor and the portion of the time sampled data file requested for display. The selected compressed data file is transferred from the data storage device to the display device.