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 May 16, 2022.
Week Date Topics Reading Homework
1 Mon 28 Mar Introduction. Read S Ch. 1
Wed 30 March Modular arithmetic. Shift and substitution ciphers. RS 1.1-3.4
HPS 1.1, 1.3
Fri 01 Apr Modular arithmetic. Euclidean algorithm. RS 4.1-4.6
HPS 1.2, 1.4
2 Mon 04 Apr Affine cipher. RS None
HPS 1.7.4 		Read S Ch. 2

Problem Set #1
Wed 06 Apr Big O notation. Base expansion. Vigenère cipher. RS 5.1-5.4
HPS 5.2
Fri 08 Apr Vigenère cipher, continued. Displacement coincidences. Kasiski test. Sage implementation. RS 5.4-5.6
HPS 4.1, 4.3, 4.4
3 Mon 11 Apr Hill cipher. Block ciphers. RS 6.1-6.3 Read S Ch. 3-4

Problem Set #2
Wed 13 Apr Enigma HPS 1.6
Thu 14 Apr X-hour class: Enigma, continued. HPS 1.6
Fri 15 Apr No class: Good Friday/Passover.
4 Mon 18 Apr Feistel ciphers, SDES. RS
HPS 8.12 		Read S Ch. 5

Problem Set #3
Wed 20 Apr SDES, DES. Rijndael (AES). RS None
HPS 2.10
Fri 22 Apr The history of DES (Dickie George).
5 Mon 25 Apr Finite fields. Read S Ch. 6

Enigma simulator

Problem Set #4
Wed 27 Apr Public key cryptography. RSA. RS 11.1-11.5
HPS 2.1, 3.2, 3.4
Fri 29 Apr Primality testing. RS 12.1-12.2
HPS 3.3
6 Mon 02 May Pollard rho RS 12.3
HPS 5.5 		Problem Set #5
Wed 04 May Smooth numbers. RS 12.4
HPS 3.7
Thu 05 May Quadratic sieve RS 12.5
HPS 3.6
Fri 06 May No class!.
7 Mon 09 May Discrete log. RS 10.2
HPS 1.5, 2.2, 2.3 		Read S Ch. 7

Problem Set #6
Wed 11 May Diffie-Hellman. Baby step-giant step. RS 10.1-10.5
HPS 2.6, 2.7, 5.4
Fri 13 May Pohlig-Hellman. RS 10.6
HPS 2.8-2.9
8 Mon 16 May ElGamel. Signature schemes. RS 10.3
HPS 4.1-4.3 		Problem Set #7
Wed 18 May Elliptic curves. RS 14.1-14.4
HPS 6.1-6.2
Fri 20 May Elliptic curves. Lenstra's factorization method. RS 15.2-15.3
HPS 3.5, 6.3-6.6
9 Mon 23 May Elliptic curve discrete logarithms. RS 14.6-14.8
HPS 3.5, 6.3-6.6 		Read S Ch. 8
Wed 25 May SSL/TLS. Live demos of key exchange protocols in the wild.
Fri 27 May Additional topic!
10 Mon 30 May No class: Memorial Day.
Wed 01 Jun Additional topic!


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