Friday, October 19, 2012

6.4.1 and 6.4.2, due on October 22

1. (Difficult): I'm still not understanding why the Universal Exponent Factorization Method and the Exponent Factorization Method work.

Also, in the Miller-Rabin test do we find a nontrivial factor of n using gcd(b0-1,n) only or do we get a nontrivial factor of n for any gcd(bk-1,n)?

And, on page 185 it talks about finding squares of the form 2j(in)^2+j^2 but then the in its example the book used squares of the form j(in)^2+j^2. What happened to the 2 in 2j(in)^2?

Lastly, why does gcd(x-y,n) give a nontrivial factor (in the Basic Principle) again?

2.(Reflection): We could only factor up to 20 digits the year after my dad was born. Now we can do up to 200 digits. We really have come a long way recently in the world of computers. I love it!

How is the quadratic sieve improved from the method these sections teach?


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