Similar to Problem 3.5 in the textbook: 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. To check the avalanche property of DES we change the 32-bit of the input R0 (to the f-function) from all zeros to a single "1" followed by 31 zeros, i.e., in Hex 80 00 00 00.

This 32-bit word goes through an expansion to 48 bits before being added to the 48-bit round key that we will assume to be all zeroes.

1. How many S-boxes get different inputs compared to the case when an all-zero 32-bit R0 input is provided?

2. How many S-Boxes' output bits will change compared to the case when R0 is all zero?

3. How many bits in the 64-bit word (L1,R1) will change compared to the case when R0 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.