Methods and Apparatus in Alternate Finite Field Based Coders and Decoders

Abstract

Methods and apparatus for coding and decoding n-state symbols with n≧2 and n>2 and n>3 and n>4 are provided with at least one implementation of a switching function based on an addition and a multiplication over an alternate finite field GF(n) wherein a zero element in not 0. Encoders and decoders implementing a single n-state truth table of an addition over an alternate finite field modified in accordance with at least one inverter defined by a multiplication over the alternate finite field are also provided. Coders include scramblers, Feedback Shift Register (FSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders, CRC coders and hash function generators. Systems applying encoders and decoders also are provided.

Dependencies are inferred from the claim text.