S2011: MAT4930 7554 Number Thy & Cryptography MWF6 LIT219 (SW)

  Office: 402 Little Hall (Top floor, NE corner)   392-0281 x270.
[If I am not in the office then it is best to EMAIL me; I rarely pick-up
phone messages.  If urgent then telephone to the secretaries at
392-0281.x221 and they can contact me at home.

  Office hours:      http://www.math.ufl.edu/~squash/info.jksched.html
  My OHs will v*a*r*y during the semester, so please check the webpage.
Currently, OHs are:   Mon.: 7th, 8th.  Wed.: 7th.

  PREREQUISITE:  General NT knowledge: Modular-arithmetic, Euler-phi fnc,
Chinese Rem. Thm., basic prime numbers.  Also assumes basic calculus, and
proof techniques [e.g, mathematical induction] from Sets&Logic (MHF3202)
or Numbers&Polynomials (MAS3300).  Assumes knowledge of the math-Greek alphabet.
/Helpful/, but not required: A Linear Algebra course.

Course pages: http://www.math.ufl.edu/~squash/teaching.html
              http://www.math.ufl.edu/~squash/course.numt2.2011g.html

ARCHIVE: >> Please keep our archive private to our class. <<
  /Read/ the Archive at		(ANNOUNCED IN CLASS)
  To /post/ to our class (and me), email to
				(ANNOUNCED IN CLASS)

TEXT: For a few weeks we will use the free, online
  "A Computational Introduction to Number Theory and Algebra"
by Victor Shoup.  [It is a pdf file.]  I will choose the main textbook
later, and you can order it online.


EXAMS: In addition to "pop" quizzes, there will be a prereq exam
on >>Friday, 07Jan<<, counting 7%-9% if course-grade.  An extra-long
practice prereq is on our webpage.

  There be 2 or 3 take-home exams (done in teams), with an in-class
component (done individually). Instead of a final exam, there is an
Individual-project, due >>11AM, Friday, 22Apr2011<<

  The project, and the take-home exams, must be carefully typed.

  My course has a SUBSTANTIAL class-participation grade, and attendance is REQUIRED.

  HOMEWORK: I'll ask that you post your homework to the Archive, so that
we can get intelligent comments from many minds.

  I will email-out grade estimates on Thur, 07Apr, or before.
The withdraw-date is Fri., 08Apr.

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CLASS-PHOTO DAY: Wednesday, 12Jan.  Look sharp!  Please bring name-card
with (optional but useful) your telephone number.

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Letters-of-recommendation: I generally ask that students have had
/two/ courses with me before asking for a LOR.  See
    http://www.math.ufl.edu/~squash/teaching.html#namelor
for important details.

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Potential topics: Our webpage has a list; here is a partial list:

  Huffman codes.  Huffman's theorem on Minimum Expected Coding-Length codes.

  Diffie-Hellman Cryptosystem.  Shank's Baby-step Giant-step method for
trying to break the Diffie-Hellman protocol.

  RSA Cryptosystem.

  Miller-Rabin algorithm.  Also, polytime testing whether N is a prime-power.

  Pollard's p-1 and rho factorization algorithms.

  Smith Normal Form of a matrix to solve a system
        of linear Diophantine equations.

Review:  Euclidean Algorithm (the Lightning Bolt alg).  Also over the
Gaussian Integers.  Proving unique factorization in the Gaussian Integers.
  Using Lightning Bolt to write certain primes as sums-of-two-squares.
  Euler phi function, Fermat's Little Thm.
  The Chinese Remainder Thm and a brief introduction to Rings and Ring-isomorphism.
  The Legendre and Jacobi symbols.
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