| 摘要 |
PURPOSE:To obtain an arithmetic circuit for a finite field appropriate for LSI- implementation without using a ROM by successively squaring an optional element alpha<i> and successively squaring the squared result to find out alpha<(2m-2)i>. CONSTITUTION:In a 1st step, an input alpha<i> is inputted to a squaring circuit 2 through a switch 1 and its squared result alpha<2i> is outputted. From a 2nd step, the switch 1 passes the output of the circuit 2. Thereby, the alpha<2i> is inputted to the circuit 2. In the 2nd step, the output alpha<2i> of the circuit 2 is multiplied by the output '1' of a register 4 through a multipler 3 and the multiplied output alpha<2i> is inputted to the register 4. In a 8th step, after executing 3rd-7th steps, the output alpha<128i> of the circuit 2 is multiplied by the output alpha<126i> of the register 4 through the multiplier 3 and the multiplied result alpha<254i> is outputted. The result alpha<254i> is equal to the reverse element alpha<-1> of the input alpha<i>. Thus, the reverse element of an optional element alpha<i> of GF(2<8>) can be obtained from 8 steps.
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