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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