rijndael function

i'm working at rijndael decryption, writing inverse function and get stack at InvMixColumns();

So, ref to wiki = http://en.wikipedia.org/wiki/Rijndael_mix_columns -- algorythm for MixColumns (there's also info about inverse MixColumns);

Here my MixColumns():

protected static function MixColumns($s, $Nb) {
    $Nb = 4;
    for ($c=0; $c<4; $c++) {
        $a = array(4);  // 'a' is a copy of the current column from 's'
        $b = array(4);  // 'b' is a•{02} in GF(2^8)
        for ($i=0; $i<4; $i++) {
            $a[$i] = $s[$i][$c];
            $b[$i] = $s[$i][$c]&0x80 ? $s[$i][$c]<<1 ^ 0x011b : $s[$i][$c]<<1;
            //However, this multiplication is done over GF(2^8). This means that the bytes being 
            //multiplied are treated as polynomials rather than numbers. Thus, a byte "muliplied" 
            //by 3 is that byte XORed with that byte shifted one bit left.

            //If the result has more than 8 bits (128 = 0x80), the extra bits are not simply discarded: instead, 
            //they're cancelled out by XORing the binary 9-bit string 100011011 (0x11b) with the result 
            //(shifted right if necessary). This string stands for the generating polynomial of the 
            //particular version of GF(2^8) used; a similar technique is used in cyclic redundancy checks.
        }
        // b[n] = a•{02} in GF(2^8);
        // a[n] ^ b[n] = a•{03} in GF(2^8);
        $s[0][$c] = $b[0] ^ $b[1] ^ $a[1] ^ $a[2] ^ $a[3]; // 2 * a0 + 3 * a1 + a2 + a3
        $s[1][$c] = $a[0] ^ $b[1] ^ $b[2] ^ $a[2] ^ $a[3]; // a0 * 2 * a1 + 3 * a2 + a3
        $s[2][$c] = $a[0] ^ $a[1] ^ $b[2] ^ $b[3] ^ $a[3]; // a0 + a1 + 2 * a2 + 3 * a3
        $s[3][$c] = $b[0] ^ $a[0] ^ $a[1] ^ $a[2] ^ $b[3]; // 3 * a0 + a1 + a2 + 2 * a3
    }
    return $s;
}

I need to find inverseMixColumns();

protected static function InvMixColumns($s) {
            //a test...
    /*
        r0 = 14a0 + 9a3 + 13a2 + 11a1
        r1 = 14a1 + 9a0 + 13a3 + 11a2
        r2 = 14a2 + 9a1 + 13a0 + 11a3
        r3 = 14a3 + 9a2 + 13a1 + 11a0
    */
            //$multiplyOf_ -- defined precalculated arrays from wikipedia;
    $t = array();
        $a = array(219, 19, 83, 69); 
        $t[0] = self::$multiplyOf14[$a[0]] ^ self::$multiplyOf9[$a[开发者_运维技巧3]] ^ self::$multiplyOf13[$a[2]] ^ self::$multiplyOf11[$a[1]];
        $t[1] = self::$multiplyOf14[$a[1]] ^ self::$multiplyOf9[$a[0]] ^ self::$multiplyOf13[$a[3]] ^ self::$multiplyOf11[$a[2]];
        $t[2] = self::$multiplyOf14[$a[2]] ^ self::$multiplyOf9[$a[1]] ^ self::$multiplyOf13[$a[0]] ^ self::$multiplyOf11[$a[3]];
        $t[3] = self::$multiplyOf14[$a[3]] ^ self::$multiplyOf9[$a[2]] ^ self::$multiplyOf13[$a[1]] ^ self::$multiplyOf11[$a[0]];
    echo "<br /> t = ";self::array_show($t); 
    //works!
    return $t;
}
//one of $multiplyOf__
 protected static $multiplyOf14 = array(
    0x00,0x0e,0x1c,0x12,0x38,0x36,0x24,0x2a,0x70,0x7e,0x6c,0x62,0x48,0x46,0x54,0x5a,
0xe0,0xee,0xfc,0xf2,0xd8,0xd6,0xc4,0xca,0x90,0x9e,0x8c,0x82,0xa8,0xa6,0xb4,0xba,
0xdb,0xd5,0xc7,0xc9,0xe3,0xed,0xff,0xf1,0xab,0xa5,0xb7,0xb9,0x93,0x9d,0x8f,0x81,
0x3b,0x35,0x27,0x29,0x03,0x0d,0x1f,0x11,0x4b,0x45,0x57,0x59,0x73,0x7d,0x6f,0x61,
0xad,0xa3,0xb1,0xbf,0x95,0x9b,0x89,0x87,0xdd,0xd3,0xc1,0xcf,0xe5,0xeb,0xf9,0xf7,
0x4d,0x43,0x51,0x5f,0x75,0x7b,0x69,0x67,0x3d,0x33,0x21,0x2f,0x05,0x0b,0x19,0x17,
0x76,0x78,0x6a,0x64,0x4e,0x40,0x52,0x5c,0x06,0x08,0x1a,0x14,0x3e,0x30,0x22,0x2c,
0x96,0x98,0x8a,0x84,0xae,0xa0,0xb2,0xbc,0xe6,0xe8,0xfa,0xf4,0xde,0xd0,0xc2,0xcc,
0x41,0x4f,0x5d,0x53,0x79,0x77,0x65,0x6b,0x31,0x3f,0x2d,0x23,0x09,0x07,0x15,0x1b,
0xa1,0xaf,0xbd,0xb3,0x99,0x97,0x85,0x8b,0xd1,0xdf,0xcd,0xc3,0xe9,0xe7,0xf5,0xfb,
0x9a,0x94,0x86,0x88,0xa2,0xac,0xbe,0xb0,0xea,0xe4,0xf6,0xf8,0xd2,0xdc,0xce,0xc0,
0x7a,0x74,0x66,0x68,0x42,0x4c,0x5e,0x50,0x0a,0x04,0x16,0x18,0x32,0x3c,0x2e,0x20,
0xec,0xe2,0xf0,0xfe,0xd4,0xda,0xc8,0xc6,0x9c,0x92,0x80,0x8e,0xa4,0xaa,0xb8,0xb6,
0x0c,0x02,0x10,0x1e,0x34,0x3a,0x28,0x26,0x7c,0x72,0x60,0x6e,0x44,0x4a,0x58,0x56,
0x37,0x39,0x2b,0x25,0x0f,0x01,0x13,0x1d,0x47,0x49,0x5b,0x55,0x7f,0x71,0x63,0x6d,
0xd7,0xd9,0xcb,0xc5,0xef,0xe1,0xf3,0xfd,0xa7,0xa9,0xbb,0xb5,0x9f,0x91,0x83,0x8d
    );

For InverseMixColumns(), as seen on the wikipedia page, you have:

r0 = 14a0 + 9a3 + 13a2 + 11a1
r1 = 14a1 + 9a0 + 13a3 + 11a2
r2 = 14a2 + 9a1 + 13a0 + 11a3
r3 = 14a3 + 9a2 + 13a1 + 11a0

Addition is just the XOR-operator ^.

For multiplication by 9, 11, 13 and 14, you either define a multiplication function or different lookup tables for multiplication by each of these numbers. You can find the tables on the wikipedia page.

As for the function, just use the fact that x * y = log( exp(x) + exp(y) ) and lookup tables for logarithm and exponentiation of the same base.