| 摘要 |
The invention provides improved techniques for multiplication of signals represented in a normal basis of a finite field. An illustrative embodiment includes a first rotator which receives a first input signal representative of a first normal basis field element (a0 a1 . . . am-1), and a second rotator which receives a second input signal representative of a second normal basis field element (b0 b1 . . . bm-1). A word multiplier receives output signals from the first and second rotators, corresponding to rotated representations of the first and second elements, respectively, and processes the rotated representations w bits at a time to generate an output signal representative of a product of the first and second elements, where w is a word length associated with the word multiplier. The rotated representation of the first element may be given by A[i]=(ai ai+1 . . . ai+w-1), the rotated representation of the second element may be given by B[i]=(bi bi+1 . . . bi+w-1), and the product may be given by c=(C[0], C[w], C[2w], . . . , C[m-w]), where C[i]=(ci Ci+1 . . . ci +w-1), m is the degree of the finite field, w is the word length, and i=0, 1, . . . m-1. The invention is particularly well suited for implementation in software, and can provide performance advantages for both general normal basis and optimal normal basis.
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