# Schedule

## RSA and questions in computational number theory

- Oct 11
- Roots modulo a product of two primes
*Notes* - Pre-reading Section 3.1

- Roots modulo a product of two primes
- Oct 14
- RSA public key cryptosystem
*Notes* - Pre-reading Section 3.2

- RSA public key cryptosystem
- Oct 16
- Finding large primes
*Notes* - Pre-reading Section 3.4

- Finding large primes
- Oct 21
- Miller-Rabin primality test
*Notes* - Pre-reading Sections 3.4

- Miller-Rabin primality test
- Oct 23
- Lots of primes (probably)
*Notes* - Pre-reading Sections 3.4.1, 3.4.2

- Lots of primes (probably)
- Oct 25
- Pollard’s $p-1$ factorization
*Notes* - Pre-reading Section 3.5

- Pollard’s $p-1$ factorization
- Oct 28
- Factorizations using differences of squares
*Notes* - Pre-reading Section 3.6

- Factorizations using differences of squares
- Oct 30
- Smooth numbers and the quadratic sieve
*Notes* - Pre-reading Sections 3.7.2

- Smooth numbers and the quadratic sieve
- Nov 1
- More on the quadratic sieve
- Pre-reading Section 3.7.1

- Nov 4
- The number field sieve
- Pre-reading Section 3.7.3

- Nov 6
- The index calculus method
- Pre-reading Section 3.8

- Nov 8
- Quadratic residues
- Pre-reading Section 3.9

## Past topics

## Mathematical preliminaries

- Aug 30
- Division algorithm
*Notes* - Pre-reading Section 1.2

- Division algorithm
- Sep 2
- Labor Day
- Sep 3
**HW 1 due**- Sep 4
- Euclidean algorithm
*Notes* - Pre-reading Section 1.2

- Euclidean algorithm
- Sep 6
- Modular arithmetic
*Notes* - Pre-reading Section 1.3

- Modular arithmetic
- Sep 9
- Prime factorizations and finite fields
*Notes* - Pre-reading Section 1.4

- Prime factorizations and finite fields
- Sep 11
- Powers and primitive roots in finite fields
*Notes* - Pre-reading Section 1.5

- Powers and primitive roots in finite fields
**HW 2 due**- Sep 13
- The discrete logarithm problem
*Notes* - Pre-reading Section 2.2

- The discrete logarithm problem

## 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

- Substitution and transposition ciphers
**HW 0 due**- Aug 26
- Frequency analysis
*Notes* - Pre-reading Section 1.1.1

- Frequency analysis
- 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

- Symmetric and asymmetric ciphers
- Sep 18
- Diffie-Hellman key exchange
*Notes* - Pre-reading Sections 2.1 2.3

- Diffie-Hellman key exchange
- Sep 20
- Elgamal public key cryptosystem
*Notes* - Pre-reading Section 2.4

- Elgamal public key cryptosystem
- Sep 23
- Shanks Babystep-Giantstep algorithm
*Notes* - Pre-reading Section 2.7

- Shanks Babystep-Giantstep algorithm
- Sep 25
- Chinese remainder theorem
*Notes* - Pre-reading Section 2.8

- Chinese remainder theorem
- Sep 27
- Hurricane Helene
- Oct 1
- Hurricane recovery day
- Oct 3
- More on Chinese remainder theorem
*Notes* - Pre-reading Section 2.8

- More on Chinese remainder theorem
- Oct 5
- Pohlig-Hellman algorithm
*Notes* - Pre-reading Section 2.9

- Pohlig-Hellman algorithm
- Oct 7
- Polynomial rings and the Euclidean algorithm
*Notes* - Pre-reading Section 2.10

- Polynomial rings and the Euclidean algorithm
- Oct 9
- Irreducible polynomials and new finite fields
*Notes* - Pre-reading Section 2.10

- Irreducible polynomials and new finite fields

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