Method and apparatus to perform squaring operation in finite...

Details Method and apparatus to perform squaring operation in finite... Method and apparatus to perform squaring operation in finite...

2004-06-16

2009-06-02

Bullock, Jr., Lewis A (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

C708S490000

Reexamination Certificate

active

07543012

ABSTRACT:
A method and apparatus to square an element A when a defining polynomial of a finite field GF(2n) is expressed asf⁡(x)=xn+∑i=1t⁢⁢xki+1,and the element A contained in the finite field is expressed as A=(a0,a1,a2, . . . ,an−1)∈GF(2n). The method determines coefficients mi, Iij, V0, Vij, and V such that the coefficient misatisfies a predetermined condition with respect to kiwhen 1≦i≦t is a natural number, Iijdepends on n, ki, and j when 2≦j≦mi, V0and Vijof n bits, respectively, depend on n, Iij, and ki, and obtains the coefficient V with respect to miaccording to the following formulaVi=⁢Vi⁢⁢2⊕Vi⁢⁢3⊕…⊕VimiV=⁢V0⊕∑mi≠0⁢⁢Videtermines a coefficient siaccording to kiand n and cyclically shifts the coefficient V by si; performing an XOR operation on the cyclically shifted coefficient V and the element A; and rewires a result of the XOR operation in a predetermined order and outputs results of the squaring.

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