3.5. Remember that it is desirable for good block ciphers that a change in one i

Question

3.5. Remember that it is desirable for good block ciphers that a change in one input bit affects many output bits, a property that is called diffusion or the avalanche effect. We try now to get a feeling for the avalanche property of DES. We apply an input word that has a “1” at bit position 57 and all other bits as well as the key are zero. (Note that the input word has to run through the initial permutation.)

1. How many S-boxes get different inputs compared to the case when an all-zero plaintext is provided?

2. What is the minimum number of output bits of the S-boxes that will change according to the S-box design criteria?

3. What is the output after the first round?

4. How many output bit after the first round have actually changed compared to the case when the plaintext is all zero? (Observe that we only consider a single round here. There will be more and more output differences after every new round. Hence the term avalanche effect.)

Explanation / Answer

Solution:

• IP(x) maps bit 57 to position 33, which is position 1 in R0.

• E-Expansion box maps bit position 1 to positions 2 and 48.

• Input to S-Boxes:

S1 : 0 1 0 0 0 0 S2 =

S3 = ··· = S7 : 0 0 0 0 0 0

S8 : 0 0 0 0 0 1

Two S-Boxes get a different input.

P(S) = D058 5B9E (L1,R1) = 8000 0000 D058 5B9E

1. 2 S-Boxes, S1 and S8

2. According to design criteria, a minimum of 2 bits/bit. 2 · 2 = 4bits

3. See (1).

4. 6 bits have changed:

3 from S1

2 from S8

1 in the left half

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.