Thursday, October 28, 2010

Oct 29 2010 Section 7.2

  This discusses the discrete log problem and shows how difficult a discrete log equation is to solve and shows a few algorithms for solving them.  The DES and AES algorithms were easier to read because they were diagrammed, I think that drawing out the steps is pretty critical to having them sink in.
  The three algorithms that were mentioned were Pohlig-Hellman, Baby Step-Giant Step and Index Calculus.
  Baby Step-Giant Step seems to be the easiest to understand.  You find a^j=ba^(-nk) with 0<j,k < n and that gives you j+nk  is the answer.  This is only effective for problems with p is less than 10^20.  Not as effective as the Index Calculus, which the book says is effective up to p is less than 10^200.
  I don't understand the P-H.
  I see lots of problems with the primes that are 3 mod 4.  First they have problems with factoring, then they have problems with the discrete log.  I bet they are related to the Collatz conjecture.  And all those other hard problems that haven't been solved yet.
How is it that 4 comes into both factoring and discrete logs?
Come to think of it, 4 is really important in the Collatz conjecture too.  Maybe I should look into that.

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