# Math 75 Mathematics of Cryptography

Textbooks:

Other resources:

• [HPS] Jeffrey Hoffstein, Jill Pipher, and Joseph Silverman
An Introduction to Mathematical Cryptography, Second edition
Springer.
Some free excerpts (also see Amazon)

Weekly problem sets will be due at the start of lecture on Friday of the week they are due. Reading responses will be due on the Monday after the week the reading is assigned.

## Weekly Syllabus and Homework

Updated June 1, 2020.

 Week Date Topics Reading Homework 1 Mon 30 Mar Introduction. Read S Ch. 1 Wed 01 Apr Shift and substitution ciphers. RS 1.1-3.4 HPS 1.1, 1.3 Fri 03 Apr Modular arithmetic. Euclidean algorithm. RS 4.1-4.6 HPS 1.2, 1.4 2 Mon 06 Apr Affine cipher. RS None HPS 1.7.4 Read S Ch. 2 Problem Set #1 Wed 08 Apr VigenĂ¨re cipher. RS 5.1-5.4 HPS 5.2 Fri 10 Apr No class. 3 Mon 13 Apr VigenĂ¨re cipher. RS 5.4-5.6 HPS 4.1, 4.3, 4.4 Read S Ch. 3-4 Problem Set #2 Wed 15 Apr Hill cipher. Block ciphers. RS 6.1-6.3 HPS None Fri 17 Jan Enigma RS None HPS 1.6 4 Mon 20 Apr Enigma, continued. RS HPS 1.6 Read S Ch. 5 Problem Set #3 Wed 22 Apr Feistel ciphers, SDES. RS HPS 8.12 Fri 24 Apr SDES, DES. Rijndael (AES). RS None HPS 2.10 5 Mon 27 Apr Finite fields. Read S Ch. 6 Enigma simulator Problem Set #4 Wed 29 Apr Public key cryptography. RSA. RS 11.1-11.5 HPS 2.1, 3.2, 3.4 Fri 01 May Primality testing. RS 12.1-12.2 HPS 3.3 6 Mon 04 May Pollard rho RS 12.3 HPS 5.5 Problem Set #5 Wed 06 May Smooth numbers. RS 12.4 HPS 3.7 Fri 08 May Quadratic sieve RS 12.5 HPS 3.6 7 Mon 11 May Discrete log. RS 10.2 HPS 1.5, 2.2, 2.3 Read S Ch. 7 Problem Set #6 Wed 13 May Diffie-Hellman. Baby step-giant step. RS 10.1-10.5 HPS 2.6, 2.7, 5.4 Fri 15 May Pohlig-Hellman. RS 10.6 HPS 2.8-2.9 8 Mon 18 May ElGamel. RS 10.3 HPS 4.1-4.3 Problem Set #7 Wed 20 May Elliptic curves. RS 14.1-14.4 HPS 6.1-6.2 Fri 22 May Elliptic curves. Lenstra's factorization method. RS 15.2-15.3 HPS 3.5, 6.3-6.6 9 Mon 25 May No class: Memorial Day. Read S Ch. 8 Wed 27 May Elliptic curve discrete logarithms. RS 14.6-14.8 HPS 3.5, 6.3-6.6 Fri 29 May SSL/TLS. Live demos of key exchange protocols in the wild. RS HPS 10 Mon 01 Jun Homomorphic encryption. RS 12.2 HPS 8.9 Wed 20 May Zero-knowledge proofs. Authentication schemes. RS 16 HPS 8.3