The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography

This survey illustrates and investigates the application of polynomial rings over finite fields to generate PRN codes for Global Navigation Satellite System (GNSS) satellites. In GNSS, satellites continually broadcast signals at two or more frequencies, including pseudo-random noise (PRN) codes. Each GNSS satellite has its own PRN code, and due to the unique mathematical properties of PRN codes, all satellites can communicate at the same frequency without interfering with another one. Although PRN code appears to be devoid of any discernible structure, it is composed of a deterministic series of pulses that will repeat itself after its period. The PRN code generator employs two shift registers known as Gold polynomials, and the suitable polynomial is decided by the number of satellites. The approach used in satellites is based on the usage of two primitive polynomials, with the output of the first polynomial being used as input for the second polynomial.