Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2006-09-26
2006-09-26
Ngo, Chuong D. (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
07113968
ABSTRACT:
A method and apparatus for performing Galois field multiplication with reduced redundancy. Generally, multiplication by a Galois field multiplier involves the multiplication of two polynomials modulo another polynomial. The Galois field multiplier has two Galois Field elements in a field of GF(2n) that correspond to the binary polynomials A[X] and B[X]:in-line-formulae description="In-line Formulae" end="lead"?A[X]=an-1Xn-1+an-2Xn-2+an-3Xn-3+ . . . a1X+a0,in-line-formulae description="In-line Formulae" end="tail"?in-line-formulae description="In-line Formulae" end="lead"?B[X]=bn-1Xn-1+bn-2Xn-2+bn-3Xn-3+ . . . b1X+b0,in-line-formulae description="In-line Formulae" end="tail"?where n corresponds to a number of terms in a Galois extension field of the Galois multiplier, and n-1 is an order of the polynomial A[X]. Premultiplier logic translates the binary polynomial A[X] into a binary vector cr, where r is the number of terms of the vector. The premultiplier logic is configured to modulo-2 add together various coefficients of the a0through an-1, coefficients to produce various terms c0through cr-1of the crbinary vector. Binary multiplication and addition logic then operates on the c0through cr-1coefficients and the b0through bn-1coefficients to produce d0through dncoefficients of a binary polynomial D[X]. The coefficients d0through dnare the output of the Galois field multiplier. Utilization of the premultiplier logic component reduces the amount of binary multiplication and addition logic needed to produce the coefficients d0through dnof the binary polynomial D[X].
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Ireland Howard H.
Nichols Jeffrey T.
Bernard Christopher L.
Brown Tyler S.
CIENA Corporation
Dougherty & Clements
Ngo Chuong D.
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