Method and apparatus for generating encryption stream ciphers

Abstract

A method and apparatus for generating encryption stream ciphers. The recurrence relation is designed to operate over finite fields larger than GF(2) and is maximal length. An output equation generates the output based on a plurality of elements in the shift register used to implement the recurrence relation. The recurrence relation and the output equation are selected to have distinct pair distances such that, as the shift register shifts, no particular pair of elements of the shift register are used twice in either the recurrence relation or the output equation.

I claim:  
     
         1 . A method for generating a non-linear output stream from a linear feedback shift register (LFSR), comprising: 
 shifting a plurality of bits through the LFSR, wherein the LFSR is structured in accordance with a recurrence relation;    performing modular multiplications upon the plurality of bits, wherein the modular multiplications are implemented through pre-computed look-up tables, wherein the pre-computed look-up tables are computed using an irreducible polynomial; and    performing a non-linear operation on a selected portion of the shifted plurality of bits, wherein the selected portion is selected so that the pairwise distances between elements in the selected portion are distinct values.    
     
     
         2 . The method of  claim 1 , wherein the non-linear operation is defined as V n =(S n +S n+5 )×(S n+2 +S n+12 ), where the non-linear operation is defined over GF(2 8 ).  
     
     
         3 . The method of  claim 1 , wherein the non-linear operation is a stuttering operation.  
     
     
         4 . The method of  claim 1 , further comprising the step of initializing the LFSR before shifting the plurality of bits, wherein initializing the LFSR comprises: 
 adding a byte of a secret key to an element in the LFSR; and    adding a byte of a secondary key to the LFSR for each frame of data that passes through the LFSR.