For this homework, please submit two pseudo-code samples to answer question 1 and 2 below.
Review sections 4 and 5 in FIPS 197 (see Lab 1) to understand details about finite field arithmetic in AES:
Section 4: Focus on 4.1 and 4.2. 4.3 is less important to study (and more complicated), but it may help you understand section 5.
Section 5: See the high-level pseudo-code for the Cipher algorithm
in 5.1. The MixColumns function in 5.1.3 is important to
understand. Near the end of that section, it gives you the formulas
you need to implement the MixColumns function.
Submit pseudo-code for the MixColumns function in 5.1.3. Your
submission should demonstrate that you understand how to implement the
ideas in section 4. Study these sections and the lecture slides to be
able to distinguish between the abstract mathematical ideas (e.g.,
polynomial representation) and the implementation methodology (i.e.,
bit shifting, MOD, AND, XOR).
Hint: Start with a Mixcolumns(state) where the state is a 4×4
array of bytes. You can reference each byte with a state(x,y)
reference.
Submit psuedo-code for a finite field multiply function that takes two
bytes as input and produces a byte as output, the result of
multiplying a * b where * is the finite field multiply described in
section 4.2. Your code should use an xtime function that is described
in 4.2.1. Include your pseudo-code for xtime as part of your finite field multiply submission.
Hint: Assume a function uint8_t ffMultiply(uint8_t a, uint8_t b) where
the function returns a * b.
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