Difference between revisions of "MAT5123"
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Revision as of 10:52, 24 March 2023
MAT 5123. Introduction to Cryptography. (3-0) 3 Credit Hours.
Prerequisite: MAT 4213. Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem, complexity, symmetric-key cryptosystems, cyclic groups, primitive roots, discrete logarithms, one-way functions, public-key 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, Springer-Verlag (2014). ISBN: 978-1-4939-1711-2.
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 private-key cryptosystems. Cyclic groups. Discrete Logarithms. Diffie-Hellman key exchange. |
|
4 |
2.4, 2.5. 2.6, 2.7. |
Elgamal public-key cryptosystem (EGPKC). Cyclic groups. Collision algorithms. |
|
5 |
2.8, 2.9, 2.10 |
Rudiments of ring theory. The Chinese Remainder Theorem. The Pohlig-Hellman 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 |
Elliptic-Curve Cryptography (ECC). Elliptic curves in characteristic 2. |
|
14 |
6.6 Atkin-Morain's “ECs and Primality Proving” (Math. Comp. 61 (1993) 29-68.) [1] |
EC-based primality testing and factorization techniques. |
|
15 |
None. |
Student Presentations. Wrap-up and review. |