// 有限域GF(28)弱對偶基乘法器
// 本原多項式: p(x) = x^8 + x^4 + x^3 + x^2 + 1 
// 多項式基: 	{1, a^1, a^2, a^3, a^4, a^5, a^6, a^7}
// 弱對偶基:	{1+a^2, a^1, 1, a^7, a^6, a^5, a^4, a^3+a^7}
`define M	8
module ff_mul(din1, din2, dout, dual_base);
	//parameter	CONST = 8'h3b;

	input  [`M-1:0]	din1, din2;		// din2需要轉換到弱對偶基
	output [`M-1:0]	dout;
	output [2*`M-2:0] dual_base;
	reg    [`M-1:0]	dout;

	reg	[2*`M-2:0]	dual_base;
	reg [`M-1:0]	temp;
	always @(din1 or din2)begin: Block1
	 integer i;
		  // 多項式基到對偶基坐標變換
		  dual_base[0] = din2[0] ^ din2[2];
		  dual_base[1] = din2[1];
		  dual_base[2] = din2[0];
		  dual_base[3] = din2[7];
		  dual_base[4] = din2[6];
		  dual_base[5] = din2[5];
		  dual_base[6] = din2[4];
		  dual_base[7] = din2[3] ^ din2[7];
		
		  // 對偶基擴展
		  for(i=0; i<`M-1; i=i+1) begin
				dual_base[`M+i] = dual_base[0+i] ^ dual_base[2+i] ^ 
										dual_base[3+i] ^ dual_base[4+i];
		  end
		
		  // 多項式基與對偶基相乘
		  for(i=0; i<`M; i=i+1) begin
		    temp[i]=(((dual_base[i+0]&din1[0])^ (dual_base[i+1]&din1[1])) 
					^((dual_base[i+2]&din1[2]) ^(dual_base[i+3]&din1[3])))
					^(((dual_base[i+4]&din1[4])^(dual_base[i+5]&din1[5]))
					^((dual_base[i+6]&din1[6]) ^ (dual_base[i+7]&din1[7])));
		  end
		
		  // 將乘法結果從對偶基變換到多項式基
		  dout[0] = temp[2];												
		dout[1] = temp[1];
		  dout[2] = temp[0] ^ temp[2];
		  dout[3] = temp[3] ^ temp[7];
		  dout[4] = temp[6];
		  dout[5] = temp[5];
		  dout[6] = temp[4];
		  dout[7] = temp[3];												
end
endmodule