CSc 48000: Cryptography

Instructor: Prof. Nelly Fazio
Lectures: Tu/Th, 2:00–3:15pm, Shepard Hall 275
Office hours: T/Th, 12:30–1:30pm or by appointment, SH-279
Email: nfazio AT ccny DOT cuny DOT edu [Put CSc480 in Subject line]

List of Topics

Introduction
- Classical vs. modern cryptography.
- Information-theoretic security: Shannon's definition of perfect secrecy.
- Limitation of the information theoretic approach.
Computational Hardness and One-Wayness
- One-way functions. One-way permutations. Trapdoor permutations. Concrete examples: integer multiplication and modular exponentiation.
- \epsilon-universal, universal one-way, and collision resistant hash functions.
- The hash-the-MAC paradigm.
Computationally Secure Symmetric Cryptography
- Definition of secure symmetric encryption: IND, CPA, CCA.
- Block-ciphers and mode of operations.
- Message authentication codes.
- Hash-then-authenticate paradigm.
Managing Shared Keys
- The key distribution problem
- Merkle Puzzles
- Diffie-Hellman Key Exchange
Computationally Secure Asymmetric Cryptography
- Definition of secure asymmetric encryption: IND, CPA, CCA.
- Efficient constructions (ElGamal, RSA and Rabin's schemes) and padding schemes (OAEP+).
Digital Signatures
- Definition of secure digital signatures.
- Lamport's one-time signature scheme.
- The hash-then-sign paradigm.
- Rabin and RSA signature schemes. Padding Schemes (PSS, PSSR).
- Schnorr signature scheme.
- Signature schemes for multiple messages: chain-based and tree-based constructions.
Additional Topics (as times permits)
- A taste of more advanced topics (identification schemes, commitment schemes, secret sharing, anonymity, cryptocurrencies, ...)

Recommended Textbook

Introduction to Modern Cryptography
by Jonathan Katz and Yehuda Lindell. Chapman & Hall/CRC Press.

Probability Theory Background. Katz-Lindell, Appendix A
Number Theory Background. Katz-Lindell, Appendix B

A Computational Introduction to Number Theory and Algebra, 2nd Edition
by Victor Shoup. Cambridge University Press. 2008.

Weekly Schedule (tentative)

Lecture	Date	Topic
1	Jan 25	Introduction to Cryptography. Information-Theoretic Setting.
2	Jan 30	Introduction to the Computational Setting.
3	Feb 1	Brush-up on Number Theory.
4	Feb 6	Hash Functions. Applications: Fingerprinting.
5	Feb 8	Commitment Schemes.
6	Feb 13	Snow Day: Review of security definitions for symmetric encryption schemes.
7	Feb 15	Review of Number Theory concepts. Examples.
8	Feb 20	Symmetric Encryption: Block ciphers and Modes of Operation.
	Feb 22	No class! Monday schedule.
9	Feb 27	Data Integrity: Message Authentication Protocols.
10	Feb 29	The key distribution problem. Merkle puzzles. Diffie-Hellman Key Exchange.
11	Mar 5	Asymmetric Encryption Schemes. ElGamal encryption scheme. RSA encryption and padding schemes (OAEP,OAEP+)
12	Mar 7	Digital Signatures. Lamport's one-time signature scheme. RSA signature scheme. Schnorr signature scheme. Signature schemes for multiple messages: "chain-based" signatures and "tree-based" signatures
13	Mar 12	Review
14	Mar 14	Midterm Exam.
	?	Final Exam, 2:00—3:15pm, Shepard Hall 275

Cryptography

CSc 48000–Spring 2024

Course Description

List of Topics

Recommended Textbook

Grading

CUNY Academic Integrity Policy

Weekly Schedule (tentative)