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