System and method for determining the cube root of an element of

Details System and method for determining the cube root of an element of System and method for determining the cube root of an element of

1995-12-28

1998-06-02

Elmore, Reba I.

Boots, shoes, and leggings

G06F 700, G06F 1500

Patent

active

057611025

ABSTRACT:
A system for determining a cubic root of an element .alpha..sup.3k of a Galois Field GF(2.sup.2m) raises the element .alpha..sup.3k to the 2.sup.m +1 power if m is even or to the 2.sup.m -1 power if m is odd. Next the system uses a small look-up table to determine the cube root of .alpha..sup.3k(2.spsp.m.sup..+-.1). The system then multiplies this cube root .alpha..sup.k(2.spsp.m.sup..+-.1) by .alpha..sup.3k raised to the ##EQU1## power, to produce ..alpha..sup.k(2.spsp.m.sup.+1)..alpha..sup.k(2.spsp.m.sup.-1) =.alpha..sup.k(2.spsp.m+1.sup.). The system then raises the result to the ##EQU2## power, to produce the cube root .alpha..sup.k. Since not all elements of GF(2.sup.2m) have cube roots within the field, the system tests the result by multiplying it by itself twice, to determine if the product is .alpha..sup.3k.

REFERENCES:
patent: 4866716 (1989-09-01), Weng
patent: 5001715 (1991-03-01), Weng
patent: 5107503 (1992-04-01), Riggle et al.

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