Cryptography (CY 4770)

This is the webpage for the Northeastern University course Cryptography (CY 4770) in Spring, 2021.

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Course Description

This course serves as an introduction to modern cryptography. The aim of this course is to teach the basic principles and concepts of modern cryptography, focusing on cryptographic problems from the real world (such as encryption, message authentication, and digital signatures) and their solutions. We will present definitions of security of every such problem and will prove the security of the constructions we see according to these definitions. If time permits we will cover at the end of the course advanced topics such as zero-knowledge proofs and secure multi-party computation. We will follow the textbook Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell, but all required material will be covered in class.

Pre-requisites:The main pre-requisite is mathematical maturity and comfort with understanding/writing proofs. Familiarity with basic probability and discrete math is assumed (e.g., of conditional probability, modular arithmetic, and the big O notation). Prior knowledge on number theory is not assumed, but may be useful - we will cover the required background in class.

Grading: The final grade will be based on:

Each assignment will include a breakdown of how it will be graded. Some assignments may include extra credit components that can boost your grade above the maximum score.

Lateness and Collaboration Policy:

Schedule (subject to change)

Lecture Topics Covered Relevant Reading
(based on KL, 2nd edition)
Problem Set Quiz
L1 (Jan 21) Introduction, encryption problem, perfect secrecy Chapters 1, 2.1
L2 (Jan 25)One-time pad, Shannon's Theorem, computational security, PRGChapters 2.2-3, 3.1-3PS1, due Feb 8
L3 (Jan 28)More on PRG, OWF, encrypting multiple messages, CPA securityChapters 7.1.1, 7.4.2, 3.4Quiz 1, due Feb 1
L4 (Feb 1)PRF, CPA-secure encryption from PRFChapter 3.5
L5 (Feb 4)PRF from PRG, PRP, block ciphersChapter 3.5Quiz 2, due Feb 8
L6 (Feb 8)Modes of operationChapter 3.6PS2, due Feb 22
L7 (Feb 11)CCA security, padding-oracle attacksChapter 3.7Quiz 3, due Feb 15
No lecture (Feb 15)Presidents' Day
L8 (Feb 18)MACsChapter 4Quiz 4, due Feb 24
L9 (Feb 22)Hash functionsChapters 5.1, 5.2, 5.4PS3, due Mar 8
L10 (Feb 25)Hash functions continued, basic number theoryChapters 5.5, 8.1.1Quiz 5, due Mar 3
L11 (Mar 1)Modular arithmetic, basic group theoryChapters 8.1.2, 8.1.3, B.1
L12 (Mar 4)Basic group theory, the factoring assumptionChapters 8.1.4, 8.2.1, 8.2.3, 8.4.1Quiz 6, due Mar 10
L13 (Mar 8)The RSA assumption, CRT, cyclic groupsChapters 8.1.5, 8.2, 8.3.1PS4, due Mar 22
L14 (Mar 11)DL, CDH, DDHChapters 8.3, 8.4.2, 9.2.1, 9.2.2Quiz 7, due Mar 17
L15 (Mar 15)Key Agreement, the Diffie-Hellman protocolChapter 10
L16 (Mar 18)El Gamal encryptionChapters 11.1, 11.2, 11.4.1Quiz 8, due Mar 24
L17 (Mar 22)KEM, Textbook RSAChapters 11.3, 11.4.2, 11.4.3, 11.5.1PS5, due Apr 5
L18 (Mar 25)Padded RSAChapters 11.5.2, 11.5.4Quiz 9, due Mar 31
L19 (Mar 29)RSA-based KEM (CPA/CCA)Chapter 11.5.5
L20 (Apr 1)Digital signatures, RSA-FDHChapters 12.1, 12.2, 12.3, 12.4Quiz 10, due Apr 7
L21 (Apr 5)Schnorr's signaturesChapter 12.5.1PS6, due Apr 19
L22 (Apr 8)(EC)DSA, Lamport's signatures, certificates, TLSChapters 12.5.2, 12.6, 12.7, 12.8Quiz 11, due Apr 14
No lecture (Apr 12)
L23 (Apr 15)Signcryption, pairings, 3-party KA, BLS, IBE, Boneh-Franklin
L24 (Apr 19)MPC, oblivious transfer, garbled circuits, Yao's protocol


We will follow the textbook Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell. There is no need to purchase the book as we will cover all relevant material in class. Note that there are 3 editions to this book, but we will cover basic material that is clearly presented in all 3 editions, so prior editions will also be very useful.

Other useful resources include:

Tentative Syllabus

The following is an ambitious list of topics to be covered. Depending on time, some of the topics may be omitted.