Compound galois field engine and galois field divider and square root engine and method

Abstract

A Galois field divider engine and method inputs a 1 and a first Galois field element to a Galois field reciprocal generator to obtain an output, multiplies in a Galois field reciprocal generator a first Galois field element by a first element of the Galois field reciprocal generator for predicting the modulo remainder of the square of the polynomial product of an irreducible polynomial m−2 times where m is the degree of the Galois field to obtain the reciprocal of the first Galois field element, and multiplying in the Galois field reciprocal engine the reciprocal of the first Galois field element by a second Galois field element for predicting the modulo remainder of the polynomial product for an irreducible polynomial to obtain the quotient of the two Galois field elements in m cycles; in a broader sense the invention includes a compound Galois field engine for performing a succession of Galois field linear transforms on a succession of polynomial inputs to obtain an ultimate output where each input except the first is the output of the previous Galois field linear transform; Galois field square root is achieved by inputting a Galois field element to a Galois field square root generator to obtain an output which is squared in the Galois field square root generator to predict the modulo remainder of the square of the polynomial product of an irreducible polynomial m−1 times where m is the degree of the Galois field to obtain the square root of the Galois field to obtain the square root of the Galois field element in (m−1) cycles.

1 . A Galois field square root method comprising: 
 inputting a Galois field element to a Galois field square root generator to obtain an output; and    squaring in the Galois field square root generator the output of the Galois field square root generator for predicting the modulo remainder of the square of the polynomial product of an irreducible polynomial m−1 times where m is the degree of the Galois field to obtain the square root of the Galois field element in (m−1) cycles.    
     
     
         2 . A Galois field square root engine comprising: 
 a Galois field square root generator;    an input circuit for inputting a Galois field element to the Galois field square root generator to obtain the square root of the Galois field elements in one cycle.    
     
     
         3 . The Galois field square root engine of  claim 2  in which said Galois field square root engine includes a Galois field multiplier, and a program circuit for programming said Galois field multiplier to perform a compound square operation of m−1 times in one cycle.