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caesgalois-field

galois field multiplication for AES mix column block in c language

I am working on AES encryption program using c, while doing the galois field multiplication in mix column block,

ex. [https://crypto.stackexchange.com/questions/2402/how-to-solve-mixcolumns][1]

code

for galois field multiplication
    int galois_multiply( int a,int b){
        int flag,res;
        switch (a){
            case 1:
                return b;
                break;
            case 2: flag= b * 0x80;
                b= b << 1;      //left shift
                if (flag)
                    res= b ^ 0x1b;
                else
                    res= b ^0x00;
                printf("\nnumber  %d returned by galois_multiply function\n",res);
                return res;

            case 3: res= b ^ galois_multiply(2,b);
                printf("\nnumber  %d returned by galois_multiply function\n",res);
                return res;

            default:
                printf("Invalid number  %d passed to galois_multiply function\n",a);
                exit(EXIT_FAILURE);
        }
                         return 0;
    }

suppose for

  • d4×02 is d4<<1, exclusive-ored with 1b (because the high bit of d4 is set), correct ans is b3; whereas using this code I am getting 1b3
  • bf×03 is bf<<1 exclusive-ored with 1b (because the high bit of bf is set) and bf (because we're multiplying by 3), should give da; but using the code result is 1da

even though the above problem is solved by masking the msb, when used in mixcolumn in following code, the answer seems to be incorrect,its general matrix operation only where multiplication is replaced by galois multilication and addition by XOR operation

void mixColumn(unsigned char **state){
    int mc[4][4]={{2,3,1,1},{1,2,3,1},{1,1,2,3},{3,1,1,2}};
    int res[4][4]={{0}};
    int i,j,k;

    for(i=0;i<4;i++){
            for(j=0;j<4;j++){
                    res[i][j]=0;
                    for(k=0;k<4;k++)
                        res[i][j]= res[i][j] ^ galois_multiply(mc[i][k],state[k][j]);
                    state[i][j]=res[i][j];
            }
    }

}

can u locate any mistakes which might be causing the error...

Solution

  • finally caught the mistake i did in case 2, I have used

    flag= b * 0x80;

    but What I should have used is

    flag= b & 0x80;

    thinking in biary made me think both these are same operators, but at byte level the story is quite different, * will multiply the content by 80h whereas & will bitwise AND(multiply) the two operands, which is what I needed.