Monday, February 9, 2009

5.1

1. The most difficult thing for me was recognizing that the congruence classes for linear polynomials are unique for each unique l. p. and the corollary to that talked about what x^2+1 was related to.

2. Obviously, this has a lot to do with congruence classes for integers. I'm waiting for the big reveal when we see that all this information lets us send information securely via encryption or something very practical like that. Or maybe this is a course to prepare undergraduates for graduate work. What is a real world application of polynomial congruence classes?
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1 comment:

  1. Paul JenkinsFebruary 9, 2009 at 8:06 AM

    Polynomial congruence classes in Zp[x] let us construct finite fields of order p^n for any positive integer n. The AES encryption standard uses a finite field of order 2^8, constructed by looking at polynomials in Z2[x] modulo x^8 + x^4 + x^3 + x + 1.

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