Modern CryptographyCSc 80010–Fall 2018 |
CUNY Graduate Center Computer Science Department |
Instructor:
Dr. Nelly Fazio
Lectures: Thursdays, 11:45am–1:45pm (Room 3310B)
Office hours: By appointment (Room 4439)
Email: nfazio AT gc DOT cuny DOT edu
[ Course Description | List of Topics | Textbook | Weekly Schedule ]
Lecture | Topic | Readings |
1 | Introduction. Classical vs. Modern Cryptography.
Brush-up on Probability Theory. Information-Theoretic Security. |
KL Ch. 1–2 KL Appendix A |
2 | More on Perfect Secrecy. From Information Theory to the Computational Approach. | KL Ch. 3.1 |
3 | Brush-up on Number Theory. | KL Appendix B KL Ch. 7.1, 7.2.1, 7.2.3-7.2.4, 7.3.1-7.3.3 |
4 | Computational-Secure Private-Key Encryption. Pseudorandomness. Pseudorandom generators. | KL Ch. 3.2–3.4.2 |
5 |
One-Way Functions. One-Way Permutations.
OWF Candidate: Integer Multiplication. OWP Candidate: Modular
Exponentiation. Quadratic Residue. Legendre Symbol. LSB. MSB. Hardcore Bits. Goldreich-Levin Theorem. |
KL 6.1, 6.2, 6.3.1, 7.4.1 |
6 | Next-Bit Unpredictability. Blum/Micali Construction. Pseudo Random
Generators. Computational Indistinguishability. Hybrid Argument. |
KL 6.4 |
7 | Blum-Micali construction. Efficient instantiation: Blum-Blum-Shub
construction. Pseudo-random functions (PRF). Goldreich-Goldwasser-Micali construction. Application of PRF. Pseudo-random permutations (PRP). Feistel Network. Luby-Rackoff construction. |
KL 3.6.1, 6.5 KL 3.6.2, 3.6.3, 6.6 |
8 |
Security for Multiple Encryptions. Security Against Chosen-Plaintext
Attacks (CPA). Security Against Chosen-Ciphertext Attacks (CCA). Block-ciphers and mode of operations. Integrity. Message Authentication Codes (MACs). ε-universal, universal one-way, and collision resistant hash functions. Merkle-Damgaard construction. Hash-then-MAC paradigm. |
KL 3.4.3, 3.5 3.6.2-3.6.4, 3.7 KL 4.1–4.6.4 |
9 | Diffie-Hellman Key Exchange. Asymmetric
Setting. Computationally-Secure Public-Key Encryption. Security Against Chosen-Plaintext Attacks (CPA). |
KL 9, 10.1–10.2 |
10 |
Security for Multiple Encryptions. Hybrid
Encryption. ElGamal. Security Against Chosen-Ciphertext Attacks (CCA). |
KL 10.2.2, 10.3, 10.5, 10.6 |
11 | Trapdoor Permutations and Hardcore
Predicates. Blum-Goldwasser Construction. Example of trapdoor permutations: RSA. OAEP. OAEP+ |
KL 10.4 10.7 |
12 | Digital Signatures. The Hash_then_Sign paradigm. One Time Signature Schemes. Lamport's Scheme. Rabin and RSA Schemes. Padding Schemes (PSSR). |
KL 12.1–12.5 |
13 | Schnorr signature scheme. Signature schemes for multiple messages:
"chain-based" signatures and "tree-based" signatures |
KL 12.6 |
14 | TBD | |
Final Report Presentations |
Copyright © Nelly Fazio