1) Public and private key problem. I’m the sender, and based on p. 352, I’ve chosen N = 515, and C = 8. My P or public key value generated from this is “81”.

a. What would you have to do to figure out what “I” value or secret seed I had used?

b. You as the receiver chose a secret seed “J” of  “7”. What would the common public seed X(0) generated by you using your “J” and my ”P” have as a value? Would it be the same or different from my public seed X(0)?

c. What would that public seed X(0) be used for by both of us? If A = 187, B = 714, and N = 515, find the X(1) value for this public seed.

·  A primer on Shannon's theory is linked below at Bell labs. It has some flash tutorials on his work.

2) How many bits of information are required to represent "stuff"? If you know that tomorrow's lunch menu offers you 2 kinds of burgers, 9 vegetables, 5 drinks, 7 starches, and 4 deserts, how can information theory help you decide the smallest number of bits required to represent that efficiently?            

 a. Find the H or Shannon entropy limit for this data set.

3) What is the smallest number of bits required to encode for any “stuff”? 1 bit of course. This can be termed an “elementary system”- a system with one binary degree of freedom. How many elementary systems can you think of? Please list a few.

·  The holographic universe model takes Thermodynamic entropy and Shannon entropy and considers them to be conceptually equivalent. Please read the Scientific American article below from August 2003