Boots – shoes – and leggings
Patent
1987-06-26
1990-12-04
Malzahn, David H.
Boots, shoes, and leggings
G06F 752
Patent
active
049758675
ABSTRACT:
The invention is an apparatus and/or method which enables one to divide two elements, A and B, of GF(2.sup.2M), that is, perform the operation B/A, by finding the multiplicative inverse of the divisor A, and then multiplying the inverse by the numerator, B. The multiplicative inverse, A.sup.-1, of A is found by computing a conversion factor, D, and then multiplying A by D to convert it to an element C, where C is also an element of a smaller Galois Field, GF(2.sup.M), which is a subfield of GF(2.sup.2M). Specifically, C is equal to A.sup.2.spsp.M.sbsp.+1), or A.sup.2.spsp.M *A, in the field GF(2.sup.2M). Next, the multiplicative inverse, C.sup.-1, of C in GF(2.sup.M) is found by appropriately entering a stored look-up table containing the 2.sup.M elements of GF(2.sup.M).
The multiplicative inverse, C.sup.-1, of C is thereafter converted, by multiplying it by the conversion factor D calculated above, to the element of GF(2.sup.2M) which is the multiplicative inverse, A.sup.-1, of the original divisor, A. The multiplicative inverse, A.sup.-1, of A is then multiplied by B to calculate the quotient, B/A.
REFERENCES:
patent: 4473887 (1984-09-01), Odaka
patent: 4567568 (1986-01-01), Inagawa et al.
patent: 4574361 (1986-03-01), Inagawa et al.
patent: 4800515 (1989-01-01), Hori et al.
Wang et al., "VLSI Architectures for Computing Multiplications and Inverses in GF (2.sup.m)", IEEE Trans. on Computers, vol. C-34, No. 8, 1985, pp. 709-717.
Digital Equipment Corporation
Malzahn David H.
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