The patent badge is an abbreviated version of the USPTO patent document. The patent badge does contain a link to the full patent document.
The patent badge is an abbreviated version of the USPTO patent document. The patent badge covers the following: Patent number, Date patent was issued, Date patent was filed, Title of the patent, Applicant, Inventor, Assignee, Attorney firm, Primary examiner, Assistant examiner, CPCs, and Abstract. The patent badge does contain a link to the full patent document (in Adobe Acrobat format, aka pdf). To download or print any patent click here.
Patent No.:
Date of Patent:
Aug. 17, 2004
Filed:
Feb. 28, 2001
Lih-Jyh Weng, Shrewsbury, MA (US);
Dana Hall, Hopkinton, MA (US);
Christine Imrich, Cambridge, MA (US);
Maxtor Corporation, Longmont, CO (US);
Abstract
A system determines the multiplicative inverse of A∈GF(2 ) by representing A using a selected basis in which basis elements are squares of one another, and performing various operations that involve raising A to powers of 2 as cyclic rotations of A. The system also performs multiplication operations over GF(2 ) or subfields thereof by calculating the coefficients of the product of two elements A and B that are represented using the selected basis as combinations of the coefficients of cyclically rotated versions of A and B. The system further utilizes a relatively small look-up table that contains the multiplicative inverses of selected elements of a subfield of GF(2 ). The system may then cyclically rotate the multiplicative inverse values read from the table to produce the multiplicative inverses of the remaining elements of the subfield. Thereafter, as applicable, the system further manipulates the multiplicative inverse of the subfield element, to produce the multiplicative inverse of the desired element of GF(2 ). Using the selected basis, elements of GF(2 ) that are elements of the subfields have m lowest-order coefficients that are duplicates of the m highest order coefficients. Each element in the look-up table can thus be represented using only m bits, and the table can be entered with m bits.