# Course page for Math 4440/5440, Fall 2017

## Daily Schedule, Readings, and Homeworks

Date Section and Topic Read before class Homework
August 28 Organization and introduction Section 1.1 HW 1 due Sept 6
August 30 Cryptosystems and applications Section 1.2 Start of HW 1, click here
Sept 1 Shift and affine ciphers Sections 2.1, 2.2 HW 1 (cont.) p55, 1-6 (grad students also do 7)
Sept 6 Vigenere Codes Section 2.3 HW 2 due Sept 13
Sept 8 Block ciphers, ASCII, one-time pads Sections 2.7-2.9 p55, 10, 13, 14, 15, 17, 18 (grad students also do 11, and prove that a (square) matrix with integer entries is invertible module n if and only if its determinant is invertible mod n.)
Sept 11 Divisors, primes, and GCDs Section 3.1 HW 3: Due Sept 20
Sept 13 Back substitution, unique factorization Section 3.2 p 104, 1, 3, 4, 5, 6, 7, 8 (grad students prove there are infinitely-many primes congruent to 5 mod 6.)
September 15 Infinitude of primes, integers mod n Section 3.3
September 18 Division mod n, CRT Section 3.4 HW 4 due Sept 27
September 20 Modular exponentiation: Fermat and Euler Sections 3.5, 3.6 105, 10, 13, 15, 16, 17, 20, 21, 26 (grad students, also 22, 39)
September 22 Phi function, Primitive roots Sections 3.7-3.9
September 25 Inverting matrices mod n, Square roots mod n, Quadratic Residues Sect 3.10 Exam 1, Sept. 29
September 27 Review for Exam I Sect 1.1-1.2, 2.1-2.4, 2.7-2.9, 3.1-3.8
September 29 Exam I Have a good weekend
October 2 RSA Sect 6.1 HW 5 due Oct 11
October 4 Attacks on RSA Sect 6.2 p. 192, 1, 2 a, 5, 6, 7, 9, 10, 15. Grad students do 23.
October 6 Primality testing: Miller-Rabin Sect 6.3
October 9 Primality testing: Solovay-Strassen Sect 6.3 HW 6 due October 18
October 11 Factoring Sect 6.4 HW #6: p 192, 12, 13, 28. Use the Miller-Rabin test to show that 49 is composite. Use the Solovay-Strassen test to show 49 is composite. Use Pollard method to factor 49.
October 13 Discrete logarithms, Diffie-hellman key exchange Sect 7.1, 7.4
October 16 Pohlig-Hellman Sect 7.2
October 18 ElGamal Cryptosystem Sect 7.5
October 20 RSA digital signatures Sect 9.1 HW 7 due Oct 25: p 252, 1, 2, 4, 6, Grad students do 8
October 23 ElGamal digital signatures Sect 9.2
October 25 Intro to Probability Sect 15.1 HW 8 due Nov 1: p 343, 1, 2, 3, 4, Grad students due 6a
October 27 Randon variables, entropy Sect 15.2
October 30 Joint and condition entropy: information Sections 15.2
November 1 Answer questions about test Sections 3.10, 6.1-6.4, 7.1 , 7.2, 7.4, 7.5, 9.1, 9.2, 15.1, 15.2
November 3 Exam 2 Have a good weekend!
November 6 Prefect security of the 1-time pad
November 8 Introduction to coding Sect 18.1
November 10 Hamming metric, rate, Shannon's coding theorem Sect 18.2 HW 9 due Nov 15: Test corrections plus p 445, 1, 2, 5, 7, 15.
November 13 Bounds on codes Sect 18.3
November 15 Gilbert-Varshamov bound; intro to finite fields Sect 18.3, 3.11 HW 10 due Dec. 1: p 110, 33, 34; p. 446, 3, 6, 8. For the grad students: for which primes p is x^2+x+1 irreducible mod p?
November 17 Construction of finite fields Sect 3.11 Have a good break!
November 27 Intro to Linear Codes 18.4
November 29 Generating Matrices and Check Matrices 18.4
December 1 Dual Codes and Syndromes 18.4 HW 11 due Dec 6: Chpt 18; 4, 9, 10, Grad students 16.
December 4 Cosets, Hamming codes 18.5
December 6 Cyclic Codes 18.7 Take home final due 4pm on Dec 18
December 8 Cyclic codes, BCH bound 18.7, p. 433
December 11 Reed-Soloman codes 18.9
December 13 McEliece Cryptosystem 18.10