[SOLVED] Homework 5 – csci 181

1. (15 points) As mentioned in the lecture, in a hash function the word diffusion refers
to how the change of a single bit in input can affect many different bits in the output.
Consider a single application of θ step.
(a) If we change the bit in ain[1][4][63] which bits exactly are affected in aout? Remember that affected does not necessarily mean the bit changed, it means that
there is the potential for change.
(b) How many unique bits will be affected if you apply the θ step for a second round?
(Note that we are assuming that we are only applying θ and not any of the other
functions.) Show which bits are affected.
2. (10 points) Find RC[3] in the iota step. Write RC[3] in hex similar to RC[0] and RC[1]
that is provided in the lecture. Show your work by checking the constant term of x
t
similar to the approach in the lecture.
3. (10 points) [Programming assignment] Implement the function ρ from a 3-dimensional
array ain[0 . . . 4][0 . . . 4][0 . . . 63] to a 3-dimensional array aout[0 . . . 4][0 . . . 4][0 . . . 63].
Note that the rho matrix is:
rhomatrix=[0,36,3,41,18;1,44,10,45,2;62,6,43,15,61;28,55,25,21,56;27,20,39,8,14]
To check your work, apply your function to the input file provided to you, the output
aout[4][3][9 . . . 18] should be 0110011001.
Apply ρ to the input file provided. In your homework writeup, list the ten bits
aout[3][1][15 . . . 24].
4. (10 points) [Programming assignment] Implement the function π from a 3-dimensional
array ain[0 . . . 4][0 . . . 4][0 . . . 63] to a 3-dimensional array aout[0 . . . 4][0 . . . 4][0 . . . 63].
To check your work, apply your function to the input file provided and the output
aout[4][3][9 . . . 18] should be 0110110001. Apply π to the input file provided. In your
homework writeup, list the ten bits aout[3][1][15 . . . 24].
5. (10 points) [Programming assignment] Implement the function χ from a 3-dimensional
array ain[0 . . . 4][0 . . . 4][0 . . . 63] to a 3-dimensional array aout[0 . . . 4][0 . . . 4][0 . . . 63].
To check your work, apply your function to the input file provided (sha3in.txt) and the
output aout[4][3][9 . . . 18] should be 0110100001. Apply χ to the input file provided. In
your homework writeup, write down the ten bits aout[3][1][15 . . . 24].