Schedule
Elliptic curve cryptopgraphy
- Nov 18
- Elliptic curves Notes
- Pre-reading Section 6.1
- Nov 20
- Elliptic curves over finite fields Notes
- Pre-reading Section 6.2
RSA and questions in computational number theory
- Oct 11
- Roots modulo a product of two primes Notes
- Pre-reading Section 3.1
- Oct 14
- RSA public key cryptosystem Notes
- Pre-reading Section 3.2
- Oct 16
- Finding large primes Notes
- Pre-reading Section 3.4
- Oct 21
- Miller-Rabin primality test Notes
- Pre-reading Sections 3.4
- Oct 23
- Lots of primes (probably) Notes
- Pre-reading Sections 3.4.1, 3.4.2
- Oct 25
- Pollard’s $p-1$ factorization Notes
- Pre-reading Section 3.5
- Oct 28
- Factorizations using differences of squares Notes
- Pre-reading Section 3.6
- Oct 30
- Smooth numbers and the quadratic sieve Notes
- Pre-reading Sections 3.7.2
- Nov 1
- More on the quadratic sieve Notes
- Pre-reading Section 3.7.1
- Nov 4
- The number field sieve Notes
- Pre-reading Section 3.7.3
- Nov 6
- The index calculus method Notes
- Pre-reading Section 3.8
- Nov 8
- Quadratic residues Notes
- Pre-reading Section 3.9
- Nov 11
- Quadratic reciprocity Notes
- Pre-reading Section 3.9
Past topics
Mathematical preliminaries
- Aug 30
- Division algorithm Notes
- Pre-reading Section 1.2
- Sep 2
- Labor Day
- Sep 3
- HW 1 due
- Sep 4
- Euclidean algorithm Notes
- Pre-reading Section 1.2
- Sep 6
- Modular arithmetic Notes
- Pre-reading Section 1.3
- Sep 9
- Prime factorizations and finite fields Notes
- Pre-reading Section 1.4
- Sep 11
- Powers and primitive roots in finite fields Notes
- Pre-reading Section 1.5
- HW 2 due
- Sep 13
- The discrete logarithm problem Notes
- Pre-reading Section 2.2
Welcome and Orientation
- Aug 21
- Introducing the course and ourselves
Historical cryptography and cryptanalysis
- Aug 23
- Substitution and transposition ciphers Notes
- Pre-reading Section 1.1
- HW 0 due
- Aug 26
- Frequency analysis Notes
- Pre-reading Section 1.1.1
- Aug 28
- Evolution of cryptography
- Pre-reading Section 1.6
Diffie-Hellman key exchange and ElGamal public key cryptosystem
- Sep 16
- Symmetric and asymmetric ciphers Notes
- Pre-reading Section 1.7
- Sep 18
- Diffie-Hellman key exchange Notes
- Pre-reading Sections 2.1 2.3
- Sep 20
- Elgamal public key cryptosystem Notes
- Pre-reading Section 2.4
- Sep 23
- Shanks Babystep-Giantstep algorithm Notes
- Pre-reading Section 2.7
- Sep 25
- Chinese remainder theorem Notes
- Pre-reading Section 2.8
- Sep 27
- Hurricane Helene
- Oct 1
- Hurricane recovery day
- Oct 3
- More on Chinese remainder theorem Notes
- Pre-reading Section 2.8
- Oct 5
- Pohlig-Hellman algorithm Notes
- Pre-reading Section 2.9
- Oct 7
- Polynomial rings and the Euclidean algorithm Notes
- Pre-reading Section 2.10
- Oct 9
- Irreducible polynomials and new finite fields Notes
- Pre-reading Section 2.10