MATH 341 / LGIC 220 online
Discrete Mathematics II
Professor Scedrov's Office Hours: Online Tuesdays 10:30 a.m. -
11:50 a.m. EDT and Fridays 7:30 p.m. - 9 p.m. EDT, or by appointment.
TA Office Hours: Mr.
will also hold office hours online by appointment.
- Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman:
"An Introduction to Mathematical Cryptography", Springer.
First edition may be purchased online. List of corrections is
Topics Covered So Far
Overview of Probability Theory: Probability Distribution, Random
Variable, Conditional Probability, Bayes Theorem, Expected Value.
Basic Concepts of Cryptology: Substitution Ciphers, Permutation Ciphers,
Vigenere Cipher, Rotor Machines, Attack Models.
Symmetric Ciphers, Block Ciphers, One-Time Pad, Information-Theoretic
Properties of One-Time Pad, Perfect Secrecy, Misuses of One-Time Pad,
Malleability. Stream Ciphers, Linear Feedback Shift Register, Golomb's
Randomness Postulates, Linear Complexity, Non-linear Filters, Knapsack
Introduction to Number Theory: Congruences, Chinese Remainder Theorem,
Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by
Repeated Squaring. Finite Fields. Splitting Fields. Quadratic Residues.
Legendre Symbol. Jacobi Symbol. Law of Quadratic Reciprocity.
Diffie-Hellman Key Exchange, Person-in-the Middle Attack. Discrete
Logarithm. RSA Public-Key Cryptosystem.
Topics Still To Be Covered
Attacks on RSA.
ElGamal Public-Key Cryptosystem.
Digital Signatures, Selective Forgery, Existential Forgery,
Signature Schemes Based on RSA, Signature Schemes Based on Discrete
Logarithm: ElGamal Signature Scheme.
Selected topics from modern cryptography and computer network security.
Take-Home Midterm #1 due in class Tuesday, February 18
This is the complete set of problems for Take-Home Midterm #1 due in class
on Tuesday, February 18, 2020.
- Exercise 1.1 on p. 47 of Hoffstein et al., 1st edition.
- Exercise 4.10b on p. 264 of Hoffstein et al., 1st edition.
- Exercise 4.11a on p. 264 of Hoffstein et al., 1st edition.
- Exercise 4.23 on pp. 268-269 of Hoffstein et al., 1st edition.
- Exercise 4.24ab on p. 269 of Hoffstein et al., 1st edition. Hint:
Use the previous problem, 4.23.
- Consider the LFSR given by the connection polynomial
1 + x + x2 + x3 + x6 +x7
and the initial content 1010101. Using the stream cipher, encrypt
the plaintext 111000111100011110001.
Take-Home Midterm #2 due in pdf by email on or before Thursday, April 2,
12 noon EDT
This is the complete set of problems for the Take-Home Midterm due as a pdf
file by email on or before Thursday, April 2, 2020, 12 noon EDT.
- Exercise 1.9ab on p. 49 of Hoffstein et al., 1st edition.
- Exercise 1.11 on p. 49 of Hoffstein et al., 1st edition.
- Exercise 1.12ac(i)(ii)de on p. 50 of Hoffstein et al., 1st edition.
No programming is required for the midterm.
- Exercise 1.15 on pp. 50-51 of Hoffstein et al., 1st edition.
- Exercise 1.23 on p. 52 of Hoffstein et al., 1st edition.
- Exercise 4.42 on p. 274-275 of Hoffstein et al., 1st edition.
- Exercise 4.43 on p. 275 of Hoffstein et al., 1st edition.
Please note: Also due with Midterm #2 is your choice of a topic of your
report for the final exam. This is only the choice of the topic; the report
itself will be due together with the final exam.