Condensed Galois field computing system
First Claim
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1. A condensed Galois field computing system comprising:
- a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and
a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder for combining said folded partial result and the terms less than power n in the product to obtain Galois field transform of power n of said product, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the computing system used for error correction and/or encryption.
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Abstract
A condensed Galois field computing system including a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and a Galois field linear transformer circuit for applying an irreducible polynomial of power n to the product including a partial result generator responsive to terms of power n and greater in the product for providing a folded partial result and a Galois field adder for condensing the folded partial result and the terms less than power n in the product to obtain Galois field transformer of power n of the product.
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13 Claims
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1. A condensed Galois field computing system comprising:
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a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder for combining said folded partial result and the terms less than power n in the product to obtain Galois field transform of power n of said product, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the computing system used for error correction and/or encryption. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A condensed Galois field multiplier system comprising:
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a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder for combining said folded partial results and the terms less than power n in the product to perform a Galois field multiply operation, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the multiplier system used for error correction and/or encryption.
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12. A condensed Galois field multiply-accumulate system comprising:
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a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder for combining said folded partial results, the terms less than power n in the product and the output of the Galois field adder fed back to perform a Galois field multiply-accumulate operation, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the multiply-accumulate system used for error correction and/or encryption.
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13. A condensed Galois field multiplier-adder system comprising:
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a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder whose output is fed back to said multiplier circuit with one of said first and second polynomials and the other of said polynomials is a third input to said Galois field adder along with said folded partial results and the terms less than power n in the product to perform a Galois field multiply-add operation, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the multiplier-adder system used for error correction and/or encryption.
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Specification