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tth is a hash function similar in spirit to SHA that operates on letters instead of binary data. Given a message consisting of a sequence of letters, tth produces a hash value consisting of four letters. First, tth divides the message into blocks of 16 letters, ignoring spaces, punctuation, and capitalization. If the message length is not divisible by 16, it is padded out with nulls. A four-number running total is maintained that starts out with the value (0, 0, 0, 0); this is input to the compression function for processing the first block. The compression function consists of two rounds.

Round 1 Get the next block of text and arrange it as a row-wise 4 * 4 block of text and convert it to numbers (A = 0, B = 1, etc.). For example, for the block ABCDEFGHIJKLMNOP, we have

Then, add each column mod 26 and add the result to the running total, mod 26. In this example, the running total is (24, 2, 6, 10).

Round 2 Using the matrix from round 1, rotate the first row left by 1, second row left by 2, third row left by 3, and reverse the order of the fourth row.

In our example:

Now, add each column mod 26 and add the result to the running total.

The new running total is (5, 7, 9, 11). This running total is now the input into the first round of the compression function for the next block of text. After the final block is processed, convert the final running total to letters.

For example, if the message is ABCDEFGHIJKLMNOP, then the hash is FHJL.

a) Calculate the hash function for the 22-letter message Practice makes us perfect. Show all rounds!

b) To demonstrate the weakness of tth, find a message of length 32-letter to produce the same hash.

A B D 0 1 2 3 E F H 4 5 6 7 I J K L 8 9 10 11 M N o P 12 13 14 15 B D A 1 2 3 0 G H E F 6 7 4 5 L I J K 11 8 9 10 P o N M 15 14 13 12