MAT5123
Catalog entry
MAT 5123. Introduction to Cryptography. (30) 3 Credit Hours.
Prerequisite: MAT 4213. Congruences and residue class rings, Fermat’s Little Theorem, the Euler phifunction, the Chinese Remainder Theorem, complexity, symmetrickey cryptosystems, cyclic groups, primitive roots, discrete logarithms, oneway functions, publickey cryptosystems, digital signatures, finite fields, and elliptic curves. Differential Tuition: $150. Course Fees: GS01 $90.
Textbook
J. Hoffstein, J. Pipher, J. H. Silverman, An Introduction to Mathematical Cryptography (2nd Ed.) Springer Undergraduate Mathematics Series, SpringerVerlag (2014). ISBN: 9781493917112.
Week  Sections  Topics  Student Learning Outcomes 

1 
1.2, 1.3 
Substitution ciphers and basic theory of divisibility. 

2 
1.4, 1.5. 
Modular arithmetic and finite fields. 

3 
1.7, 2.1–2.3. 
Public and privatekey cryptosystems. Cyclic groups. Discrete Logarithms. DiffieHellman key exchange. 

4 
2.4, 2.5. 2.6, 2.7. 
Elgamal publickey cryptosystem (EGPKC). Cyclic groups. Collision algorithms. 

5 
2.8, 2.9, 2.10 
Rudiments of ring theory. The Chinese Remainder Theorem. The PohligHellman Algorithm. 

6 
None 
Review. First midterm exam. 

7 
3.1, 3.2, 3.3. 
Modular groups of units. The RSA cryptosystem. Practical considerations of security in implementation. 

8 
3.4, 3.5. 
Primality testing and factorization attacks on RSA. 

9 
4.1, 4.2, 4.3 
Digital Signatures. 

10 
5.1, 5.3, 5.6, 5.7. 
Probability, entropy, information theory and complexity. 

11 
None 
Review. Second midterm exam.  
12 
6.1, 6.2., 6.3 
Elliptic curves and discrete logarithms. 

13 
6.4, 6.7 
EllipticCurve Cryptography (ECC). Elliptic curves in characteristic 2. 

14 
6.6 AtkinMorain's “ECs and Primality Proving” (Math. Comp. 61 (1993) 29–68. [1]) 
ECbased primality testing and factorization techniques. 

15 
None. 
Student Presentations. Wrapup and review. 