Sunday, December 11, 2016

Doing my homework


Nigel Smart's book, a good start if you have some history in groups,rings and fields. Think of groups rings and fields as machines that generate different sets of integers using modulo arithmetic.  These machines use only a small, finite subset of all the integer modulo possibilities.  So abstract algebra is a study on the mechanics of these machines as in: do they cycle through the same set of modulo integers?  can they multiply? divide? How big are the finite set? Are there any subsets in the set? Can the machine go backwards?

So, in crypto, if  I  know some way to talk using a systematic subset of all modulo arithmetic, then I can send the message and my receiver has the code to identify the subset I am using.  The hacker has no code, and must work backwards from the complete set of integer operation, trying to narrow down the search.

Anyway, I like the book because I can bounce around and a lot of it is my second time around. His appendix is great, he essentially builds up the complete context of 'counting stuff' from scratch, 'a small set of different things'

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