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A Galois field and multiplier technology, applied in the field of small Galois field multiplier engines, can solve problems such as complex situations
Inactive Publication Date: 2006-01-04
ANALOG DEVICES INC
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The situation is further complicated by the fact that each error field check, encryption requires a Galois field multiplication on a different Galois field requiring a different lookup table
Recent improvements in Galois field multiplier systems or engines provide faster operations and reduced memory requirements, but still require faster, more power efficient and smaller designs
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[0036] Besides the preferred embodiment or preferred embodiments disclosed below, the invention is capable of other embodiments and of being practiced or carried out in different ways. It is therefore to be understood that the invention is not limited in application to the details of construction and the arrangement of component parts set forth in the following description or illustrated in the drawings.
[0037] A Galois Field GF(n) is a set of elements over which binary operations can be performed. Addition and multiplication must satisfy commutative, associative and distributive laws. A field with a finite number of elements is a finite field. An example of a binary field is the set {0, 1}, denoted by GF(2) under modulo 2 addition and modulo 2 multiplication. The modulo-2 addition and multiplication operations are defined by the table shown in the figure below. The first row and column indicate the inputs to the Galois field adder and multiplier. For example, 1+1=0 and ...
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Abstract
A compact Galois field parallel multiplier engine includes a multiplier circuit for multiplying together two polynomials with coefficients over a Galois field to obtain their product; a Galois field linear transformer circuit has a multiply input from the multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; first and second polynomial inputs; the Galois field linear transformer circuit may include a plurality of cells configured in a matrix section and a unity matrix section wherein the unity matrix section cells represent the prediction of the remainder when the output of the multiplier circuit is a polynomial with a power less than the power of the irreducible polynomial.
Description
technical field [0001] The present invention relates to a compact Calois field multiplier engine, and more particularly to a multiplier engine that can multiply, multiply-accumulate, and multiply-accumulate over a Galois field. [0002] This application claims priority from the following applications: U.S. Patent Application Serial No. 10 / 395,620 (AD-337J), filed March 24, 2003, entitled "Small Galois Field Multiplier," Stein et al., October 2002 U.S. Provisional Application Serial No. 60 / 417,384 (AD-337J) filed on the 9th entitled "Galois Field Multiplier" and U.S. Provisional Application Serial No. 60 / 417,384 (AD-337J) filed on Nov. 30, 2001 by Stein et al. and entitled "GF2-ALU" 60 / 334,662 (AD-239J), Ser. No. 60 / 334,662 (AD-239J), filed Nov. 20, 2001, entitled "Parallel Galois Field Multiplier," Stein et al., filed Dec. 18, 2001 Serial No. 60 / 341,635 (AD-299J) entitled "Galois Field Multiply-Add (MPA) Using GF2-ALU," Stein et al., filed December 18, 2001, entitled "Program...
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