Universal galois field multiplier
First Claim
1. A universal Galois field multiplier, comprising:
- a first operation unit including first AND-gates for ANDing a corresponding bit value of a multiplicand and a most significant bit value of a multiplier; and
a plurality of second operation units connected to the first operation unit or a preceding operation unit for logically operating upon a bit value of a multiplicand and the second most significant bit to a least significant bit, respectively, of the multiplier in accordance with coefficient values of a generating polynomial which defines a Galois field, said second operation unit including;
second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier;
first XOR-gates each for XORing a corresponding leftwardly rotated output value of the second AND-gates and a corresponding output value of the preceding operation unit;
third AND-gates each for ANDing the corresponding coefficient value of the generating polynomial and a most significant bit value among the output values of the preceding operation unit; and
second XOR-gates for XORing output values of the third AND-gates and the first XOR-gates, wherein the second XOR-gates become effective in accordance with outputs of the third AND-gates.
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Abstract
A universal Galois field multiplier which is adaptable to any form of polynomial having a predetermined n-order when it is controlled by a coefficient of polynomial which defines a Galois field, which includes second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier; first XOR-gates each for XORing a corresponding leftwardly rotated output value of the second AND-gates and a corresponding output value of the preceding operation unit; third AND-gates each for ANDing the corresponding coefficient value of the generating polynomial and a most significant bit value among the output values of the preceding operation unit; and second XOR-gates for XORing output values of the third AND-gates and the first XOR-gates, wherein the second XOR-gates become effective in accordance with outputs of the third AND-gates.
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Citations
16 Claims
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1. A universal Galois field multiplier, comprising:
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a first operation unit including first AND-gates for ANDing a corresponding bit value of a multiplicand and a most significant bit value of a multiplier; and a plurality of second operation units connected to the first operation unit or a preceding operation unit for logically operating upon a bit value of a multiplicand and the second most significant bit to a least significant bit, respectively, of the multiplier in accordance with coefficient values of a generating polynomial which defines a Galois field, said second operation unit including; second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier; first XOR-gates each for XORing a corresponding leftwardly rotated output value of the second AND-gates and a corresponding output value of the preceding operation unit; third AND-gates each for ANDing the corresponding coefficient value of the generating polynomial and a most significant bit value among the output values of the preceding operation unit; and second XOR-gates for XORing output values of the third AND-gates and the first XOR-gates, wherein the second XOR-gates become effective in accordance with outputs of the third AND-gates. - View Dependent Claims (2, 3)
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4. A universal Galois field multiplier, comprising:
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a first operation unit including first AND-gates for ANDing a corresponding bit value of a multiplicand and a most significant bit value of a multiplier; and a plurality of second operation units connected to the first operation unit or a preceding operation unit for logically operating upon a bit value of a multiplicand and the second most significant bit to a least significant bit, respectively, of the multiplier in accordance with coefficient values of a generating polynomial which defines a Galois field, said second operation unit including; second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier; a first XOR-gate for XORing an output value of a second AND-gate among the second AND-gates and an output value of a preceding operation unit which is leftwardly rotated; third AND-gates for ANDing a coefficient value of the generating polynomial, and a most significant bit value among output values of the predetermined operation unit; and second XOR-gates each for XORing a corresponding output value of the third AND-gates, a corresponding output value of the second AND-gates, and a corresponding output value of a preceding operation unit which is leftwardly rotated. - View Dependent Claims (5, 6)
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7. A universal Galois field multiplier, comprising:
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a first operation unit including first AND-gates for ANDing a corresponding bit value of a multiplicand and a most significant bit value of a multiplier; and a plurality of second operation units connected to the first operation unit or a preceding operation unit for logically operating upon a bit value of a multiplicand and the second most significant bit to a least significant bit, respectively, of the multiplier in accordance with coefficient values of a generating polynomial which defines a Galois field, said second operation unit including; second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier; first XOR-gates each for XORing a corresponding leftwardly rotated output value of the second AND-gates and a corresponding output value of the preceding operation unit; third AND-gates for ANDing a corresponding coefficient value of a generating polynomial and a most significant bit value among output values of a preceding operation unit when at least one term among opposing terms of generating polynomials which define a Galois field has a coefficient value of one (1); and second XOR-gates for XORing output values of the third AND-gates and the first XOR-gates, wherein the second XOR-gates become effective in accordance with outputs of the third AND-gates. - View Dependent Claims (8, 9, 10)
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11. A reconfigurable Galois field multiplier comprising:
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zeroith to nth power means for using at least one logical gate to represent a zeroith to nth power of a variable, X, respectively, in a first polynomial f1 (X)=1+k1 X+k2 X2 +k3 X3 + . . . kn-1 Xn-1 +Xn, where n is an integer and n>
1, where kj is an integer equal to one or zero, and where j is an integer and j=1, 2, . . . (n-1); andfirst to (n-1)th coefficient means for selectively setting said coefficients k1, k2, k3, . . . kn-1 at a value of either one or zero to selectively nullify an effect of said first to (n-1)th power means so as to achieve multiplication according to a second polynomial having the same or fewer terms than said polynomial f1 (X). - View Dependent Claims (12, 13, 14, 15, 16)
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Specification