Cryptography Distinguisher/ LFSRs

Use LFSR in this assignment. LFSR refered as Max. Define A(s) as follows: The seed s is a starting state for Max. This is a truly random 4-bit value. Produce A(s) by letting Max generate 64 bits of output. Thus l=64 and n=4 in this case. SHOW that A is not a PRNG by exhibiting a Z which distinguishes A from the true uniform distribution on 64-bit strings. Some property that the outputs of A have that true random 64-bit strings are very unlikely to have. Start by coding up Max and producing some sample data. Can you see a pattern in Max's outputs that true random strings shouldn't have? This is the basis for how your Z will work. Once you have designed your Z, you should implement it and see how well it works. 1. The code for Tom 2. The code for Z 3. A mathematical argument that quantifies how likely Z is to give the correct output 4. Empirical data that shows that D is correct with something close to this frequency. Remember that Z must succeed more than 50% of the time to be a real distinguisher. C++ only, or C, basic and willing to add comments to explain!