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.

Description

RELATED APPLICATIONS [0001] This application is a divisional application of U.S. patent application Ser. No. 10 / 440,330 filed May 16, 2003 which is hereby incorporated herein by reference and to which this application claims priority, and claims priority of U.S. Provisional application to Stein et al. entitled A COMPACT GALOIS FIELD MULTIPLIER, filed Oct. 9, 2002 (AD-337J), U.S. Provisional application Ser. No. 60 / 334,662, filed Nov. 30, 2001 to Stein et al., entitled GF2-ALU (AD-239J); U.S. Provisional application Ser. No. 60 / 334,510 filed Nov. 20, 2001 to Stein et al., entitled PARALLEL GALOIS FIELD MULTIPLIER (AD-240J); U.S. Provisional application Ser. No. 60 / 341,635, filed Dec. 18, 2001 to Stein et al., entitled GALOIS FIELD MULTIPLY ADD (MPA) USING GF2-ALU (AD-299J); U.S. Provisional application Ser. No. 60 / 341,737, filed Dec. 18, 2001, to Stein et al., entitled PROGRAMMABLE GF2-ALU LINEAR FEEDBACK SHIFT REGISTER—INCOMING DATA SELECTION (AD-300J). This application further clai...

AI Technical Summary

Benefits of technology

[0006] It is a further object of this invention to provide such an improved Galois field divider engine which can complete the search for the divisor reciprocal in m−1 iterations.

[0007] It is a further object of this invention to provide such an improved Galois field divider engine which can be easily reconfigured to accommodate different irreducible polynomial Galois fields of different degrees.

[0008] It is a further object of this invention to provide such an improved Galois field divider engine which can function to generate both the divisor reciprocal and multiply it by the dividend.

[0009] It is a further object of this invention to provide such an improved Galois field divider engine which requires less power and less area.

[0011] The invention results from the realization that such an improved Galois field division engine and method which is smaller, faster, and more efficient can be achieved with a Galois field reciprocal generator and an input selection circuit for initially inputting a 1 and a first Galois field element to the Galois field reciprocal generator to obtain an output, subsequently multiplying in the Galois field reciprocal generator a first Galois field element by the output 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 reminder of the polynomial product for an irreducible polynomial to obtain the quotient of the two Galois field elements in m cycles.

Problems solved by technology

One problem with this approach is that for each field of each irreducible polynomial there must be stored a separate table.

One problem with this approach is that for each Galois field of each irreducible polynomial for each degree a different pair of LFSRs is required.

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