| US 7,539,719 B2 | ||
| Method and apparatus for performing multiplication in finite field GF(2n) | ||
| Weon-il Jin, Suwon-si (Korea, Republic of); Mi-suk Huh, Suwon-si (Korea, Republic of); Kyung-hee Lee, Yongin-si (Korea, Republic of); and Bum-jin Im, Suwon-si (Korea, Republic of) | ||
| Assigned to Samsung Electronics Co., Ltd., Suwon-si (Korea, Republic of) | ||
| Filed on Oct. 18, 2004, as Appl. No. 10/965,907. | ||
| Claims priority of application No. 2003-72140 (KR), filed on Oct. 16, 2003. | ||
| Prior Publication US 2005/0086278 A1, Apr. 21, 2005 | ||
| Int. Cl. G06F 7/00 (2006.01) | ||
| U.S. Cl. 708—492 [708/490] | 8 Claims |
| 1. A method of performing multiplication through d-bit parallel processing using a serial multiplier by obtaining C=(c0, . . . , cn−1) of a product of two elements A and B of a finite field GF(2n) when a defining polynomial f(x) of degree n in the finite field GF(2n) is defined by
f(x)=xn+h(x)=xn+(fn−1xn−1+ . . . +f1x+f0), fi∈{0,1} ,
where fn−1= . . . =fn−d+1=0, d≧2, d is an integer, α is a root of the defining polynomial, A and B of the finite field are expressed as
A=α0+α1α+α2α2+ . . . +αn−1αn−1=(α0,α1,α2, . . . ,αn−1),
B=b0+b1α+b2α2+ . . . +bn−1αn−1=(b0,b1,b2, . . . ,bn−1)
with respect to the root α, and C of the product of A and B can be rewritten as C=A×B mod f(α), the method comprising:
permuting the last d coefficients (an−1, . . . , an−d) of a multiplier, which is A, with predetermined variables (sn−1, . . . , sn−d);
operating C:=C⊕(bi+jA) for (i+j)th coefficient of a multiplicand, which is B, to update coefficients of C, where i and j are integers, and
A:=(sn−1−j,α0, . . . ,αn−2)⊕(0,sn−1−jf1, . . . ,sn−1−jfn−d,0, . . . ,0)
repeatedly for j=0 to (d−1) to update coefficients of A, where ⊕ represents an XOR operation and represents an AND operation;
and
repeatedly performing the permuting and operating by increasing i from 0 to (n−1) by d to obtain a final product C.
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