MD5 - shift function

Question

I try to understand MD5 algorithm. I found on the wikipedia a pseudocode. This is a fragment:

//Main loop:
for i from 0 to 63
    if 0 ≤ i ≤ 15 then
        F := (B and C) or ((not B) and D)
        g := i
    else if 16 ≤ i ≤ 31
        F := (D and B) or ((not D) and C)
        g := (5×i + 1) mod 16
    else if 32 ≤ i ≤ 47
        F := B xor C xor D
        g := (3×i + 5) mod 16
    else if 48 ≤ i ≤ 63
        F := C xor (B or (not D))
        g := (7×i) mod 16
    dTemp := D
    D := C
    C := B
    B := B + leftrotate((A + F + K[i] + M[g]), s[i])
    A := dTemp
end for

I almost understand it but I'm wondering what's stored in g variable?

Answer 1

Wikipedia states:

"The processing of a message block consists of four similar stages, termed rounds; each round is composed of 16 similar operations". From the pseudo code it can be seen that each round the parts of the message, denoted by M, are mixed in at a different time of the round.

The function to generate g - an index into the message block - will make sure that each part of the message is mixed in. 5, 3 and 7 are all primes and of course they don't have a common divisor with each other or 16. That means that, together with the initial offsets 1, 5 and 0 they make sure that the distribution is as dissimilar as possible.

The index i goes from 0 to 63, which is 4 x 16 - 1. This makes sure that all the parts of the message are mixed in once, at each of the rounds.

EDIT: I thought that the initial g = i could generate an index out of bounds, but that code is only executed for i in the range 0..15 so the % 16 can indeed be left out.

---

Below is an "unrolled" (meaning all the loops have been written out) implementation of the inner structure of MD5. Here you can see how g operates on the in array:

/* Basic MD5 step. Transform buf based on in.
 */
static void Transform (buf, in)
UINT4 *buf;
UINT4 *in;
{
  UINT4 a = buf[0], b = buf[1], c = buf[2], d = buf[3];

  /* Round 1 */
#define S11 7
#define S12 12
#define S13 17
#define S14 22
  FF ( a, b, c, d, in[ 0], S11, 3614090360); /* 1 */
  FF ( d, a, b, c, in[ 1], S12, 3905402710); /* 2 */
  FF ( c, d, a, b, in[ 2], S13,  606105819); /* 3 */
  FF ( b, c, d, a, in[ 3], S14, 3250441966); /* 4 */
  FF ( a, b, c, d, in[ 4], S11, 4118548399); /* 5 */
  FF ( d, a, b, c, in[ 5], S12, 1200080426); /* 6 */
  FF ( c, d, a, b, in[ 6], S13, 2821735955); /* 7 */
  FF ( b, c, d, a, in[ 7], S14, 4249261313); /* 8 */
  FF ( a, b, c, d, in[ 8], S11, 1770035416); /* 9 */
  FF ( d, a, b, c, in[ 9], S12, 2336552879); /* 10 */
  FF ( c, d, a, b, in[10], S13, 4294925233); /* 11 */
  FF ( b, c, d, a, in[11], S14, 2304563134); /* 12 */
  FF ( a, b, c, d, in[12], S11, 1804603682); /* 13 */
  FF ( d, a, b, c, in[13], S12, 4254626195); /* 14 */
  FF ( c, d, a, b, in[14], S13, 2792965006); /* 15 */
  FF ( b, c, d, a, in[15], S14, 1236535329); /* 16 */

  /* Round 2 */
#define S21 5
#define S22 9
#define S23 14
#define S24 20
  GG ( a, b, c, d, in[ 1], S21, 4129170786); /* 17 */
  GG ( d, a, b, c, in[ 6], S22, 3225465664); /* 18 */
  GG ( c, d, a, b, in[11], S23,  643717713); /* 19 */
  GG ( b, c, d, a, in[ 0], S24, 3921069994); /* 20 */
  GG ( a, b, c, d, in[ 5], S21, 3593408605); /* 21 */
  GG ( d, a, b, c, in[10], S22,   38016083); /* 22 */
  GG ( c, d, a, b, in[15], S23, 3634488961); /* 23 */
  GG ( b, c, d, a, in[ 4], S24, 3889429448); /* 24 */
  GG ( a, b, c, d, in[ 9], S21,  568446438); /* 25 */
  GG ( d, a, b, c, in[14], S22, 3275163606); /* 26 */
  GG ( c, d, a, b, in[ 3], S23, 4107603335); /* 27 */
  GG ( b, c, d, a, in[ 8], S24, 1163531501); /* 28 */
  GG ( a, b, c, d, in[13], S21, 2850285829); /* 29 */
  GG ( d, a, b, c, in[ 2], S22, 4243563512); /* 30 */
  GG ( c, d, a, b, in[ 7], S23, 1735328473); /* 31 */
  GG ( b, c, d, a, in[12], S24, 2368359562); /* 32 */

  /* Round 3 */
#define S31 4
#define S32 11
#define S33 16
#define S34 23
  HH ( a, b, c, d, in[ 5], S31, 4294588738); /* 33 */
  HH ( d, a, b, c, in[ 8], S32, 2272392833); /* 34 */
  HH ( c, d, a, b, in[11], S33, 1839030562); /* 35 */
  HH ( b, c, d, a, in[14], S34, 4259657740); /* 36 */
  HH ( a, b, c, d, in[ 1], S31, 2763975236); /* 37 */
  HH ( d, a, b, c, in[ 4], S32, 1272893353); /* 38 */
  HH ( c, d, a, b, in[ 7], S33, 4139469664); /* 39 */
  HH ( b, c, d, a, in[10], S34, 3200236656); /* 40 */
  HH ( a, b, c, d, in[13], S31,  681279174); /* 41 */
  HH ( d, a, b, c, in[ 0], S32, 3936430074); /* 42 */
  HH ( c, d, a, b, in[ 3], S33, 3572445317); /* 43 */
  HH ( b, c, d, a, in[ 6], S34,   76029189); /* 44 */
  HH ( a, b, c, d, in[ 9], S31, 3654602809); /* 45 */
  HH ( d, a, b, c, in[12], S32, 3873151461); /* 46 */
  HH ( c, d, a, b, in[15], S33,  530742520); /* 47 */
  HH ( b, c, d, a, in[ 2], S34, 3299628645); /* 48 */

  /* Round 4 */
#define S41 6
#define S42 10
#define S43 15
#define S44 21
  II ( a, b, c, d, in[ 0], S41, 4096336452); /* 49 */
  II ( d, a, b, c, in[ 7], S42, 1126891415); /* 50 */
  II ( c, d, a, b, in[14], S43, 2878612391); /* 51 */
  II ( b, c, d, a, in[ 5], S44, 4237533241); /* 52 */
  II ( a, b, c, d, in[12], S41, 1700485571); /* 53 */
  II ( d, a, b, c, in[ 3], S42, 2399980690); /* 54 */
  II ( c, d, a, b, in[10], S43, 4293915773); /* 55 */
  II ( b, c, d, a, in[ 1], S44, 2240044497); /* 56 */
  II ( a, b, c, d, in[ 8], S41, 1873313359); /* 57 */
  II ( d, a, b, c, in[15], S42, 4264355552); /* 58 */
  II ( c, d, a, b, in[ 6], S43, 2734768916); /* 59 */
  II ( b, c, d, a, in[13], S44, 1309151649); /* 60 */
  II ( a, b, c, d, in[ 4], S41, 4149444226); /* 61 */
  II ( d, a, b, c, in[11], S42, 3174756917); /* 62 */
  II ( c, d, a, b, in[ 2], S43,  718787259); /* 63 */
  II ( b, c, d, a, in[ 9], S44, 3951481745); /* 64 */

  buf[0] += a;
  buf[1] += b;
  buf[2] += c;
  buf[3] += d;
}