1- Help me with an example of Data Encryption Standard Decryption and Key generation

2- An avalanche effect is also desirable for the key: A one-bit change in a key should result in a dramatically different ciphertext if the plaintext is unchanged.

1. Assume an encryption with a given key. Now assume the key bit at position 1 (prior to PC 1) is being flipped. Which S-boxes in which rounds are affected by the bit flip during DES encryption?

2. Which S-boxes in which DES rounds are affected by this bit flip during DES decryption?

3- DES has a somewhat surprising property related to bitwise complements of its inputs and outputs. We investigate the property in this problem.

We denote the bitwise complement of a number A (that is, all bits are flipped) by A. Let denote bitwise XOR. We want to show that if

then

y = DESk(x)

y = DESk (x). (3.2)

This states that if we complement the plaintext and the key, then the ciphertext output will also be the complement of the original ciphertext. Your task is to prove this property.

Try to prove this property using the following steps:

1. Show that for any bit strings A, B of equal length, A B = A B

and

A B = (AB).

(These two operations are needed for some of the following steps.)

2. Show that PC 1(k) = (PC 1(k)).

3. Show that LSi(Ci1) = (LSi(Ci1)).

4. Using the two results from above, show that if ki are the keys generated from k,

then ki are the keys generated from k, where i = 1,2,...,16.

5. Show that IP(x) = (IP(x)).

6. Show that E(Ri) = (E(Ri)).

7. Using all previous results, show that if Ri1,Li1,ki generate Ri, then Ri1,Li1,ki

generate Ri.

8. Show that Eq. (3.2) is true.