CSc 48000: Cryptography

Instructor: Prof. Nelly Fazio
Lectures: Tu/Th, 2:00–3:15pm, Shepard 20
Office hours: T/Th, 12:30–1:30pm or by appointment, NAC 8/201
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.

Bitcoin and Cryptocurrency Technologies
by Arvind Narayanan, Joseph Bonneau, Edward Felten, Andrew Miller, and Steven Goldfeder.

Weekly Schedule (tentative)

Lecture	Date	Topic
1	Aug 26	Introduction to Cryptography. Information-Theoretic Setting.
2	Aug 28	Introduction to the Computational Setting.
3	Sep 2	Brush-up on Number Theory.
4	Sep 4	Hash Functions. Applications: Fingerprinting.
5	Sep 9	Commitment Schemes.
6	Sep 11	One-Way Functions. One-Way Permutations. OWF Candidate: Integer Multiplication. OWP Candidate: Modular Exponentiation..
7	Sep 16	Computational-Secure Private-Key Encryption. Pseudorandomness. Pseudorandom generators.
8	Sep 18	Symmetric Encryption: Block ciphers and Modes of Operation.
9	Sep 25	Data Integrity: Message Authentication Protocols.
10	Sep 30	The key distribution problem. Merkle puzzles. Diffie-Hellman Key Exchange.
11	Oct 7	Asymmetric Encryption Schemes. ElGamal encryption scheme. RSA encryption and padding schemes (OAEP,OAEP+)
12	Oct 9	Digital Signatures. Lamport's one-time signature scheme. RSA signature scheme.
13	Oct 16	Schnorr signature scheme. Signature schemes for multiple messages: "chain-based" signatures and "tree-based" signatures.
14	Oct 21	Review
15	Oct 23	Midterm Exam.
16	Oct 28	Introduction to cryptocurrencies
17	Oct 30	Consensus layer, Merkle trees and proof-of-work
18	Nov 4	Byzantine generals problem
19	Nov 6	Sybil Attak, Mining and Nakamoto consensus
20	Nov 11	Bitcoin transactions and scripts
21	Nov 13	Wallets & SPV
22	Nov 18	Forks
23	Nov 20	-
24	Nov 25	Transactions fees
25	Dec 2	Proof-of-Stake. Blockchain CAP Theorem
26	Dec 4	Ethereum
27	Dec 9	Review
28	Dec 11	Final Exam, 2:00—3:15pm, Shepard 20

Cryptography

CSc 48000–Fall 2025

Course Description

List of Topics

Recommended Textbook

Grading

CUNY Academic Integrity Policy

Weekly Schedule (tentative)