S2014: MAT4930 7554  Number Thy & Cryptography MWF6 LIT221

<STRONG>Office:</STRONG> 402 Little Hall (Top floor, NE corner, "Maximize x, y and z.")
Telephone: <EM>352-294-2314</EM>.    If I am not in the office then it is best to
EMAIL me at the <STRONG>squash@ufl.edu</STRONG> eddress.  
  If urgent then telephone to the Math Office  and they can contact me at home.

OFFICE HOURS: Currently Mondays and Wednesdays 8th period [15:00-15:50].
I am also available for APPOINTMENT, especially on Mon. or Wedn., 9th [16:05-16:55].
  My OHs will >>VARY<< during the semester; I will announce changes. 

ARCHIVE: You and I will post/read Solutions to problems, at our Class Archive.
I will email, to each student individually, how to read our Archive, and
how to post to the Archive.

  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&amp;Logic (MHF3202) or Numbers&amp;Polynomials
(MAS3300).  /Helpful/, but not required: Knowledge of the math-Greek alphabet.  A
Linear Algebra course.

  There be 2 take-home exams (done in teams), with an in-class component (done
individually); the score is approx. 250+140=290points for each exam.

  Instead of a final exam, there is an Individual-project, due 11:30AM, due Friday,
25Apr2014.    The project, and the take-home exams, must be carefully typed.

  There will be a number of pop-quizzes, each counting 30points.  You get 5points
for free, simply for attempting the pop-quiz, as this encourages folks to be in 
class :)

  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 give a CP (class participation) grade each
month, approx. 45points, based on Posting, Speaking in class, Speaking with me
outside of class, and helping your classmates, e.g, lending notes, working at the
blackboard with other students.

<STRONG>GRADES:</STRONG> During the week before the withdraw date, <EM>Friday, 11Apr2014</EM>, 
I give you a <STRONG><EM>written estimate</EM></STRONG> of your course letter-grade.


________________________________________________________________
CLASS-PHOTO DAY: Wednesday, 15Jan2014.  Look sharp!  Please
bring name-card with (optional but useful) your telephone number.

  Letters-of-recommendation (LORs): I base LOR substantially on how a student
"thinks on his feet".  I require have had /two/ courses with me before asking
for a LOR.  See my Teaching Page for important details.

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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