MIT 6.875 (Fall 2021)
Foundations of Cryptography
Foundations of Cryptography
Course Description
The field of cryptography gives us a technical language to define important realworld problems such as security, privacy and integrity, a mathematical toolkit to construct mechanisms such as encryption, digital signatures, zeroknowledge proofs, homomorphic encryption and secure multiparty computation, and a complexitytheoretic framework to prove security using reductions that together help us enforce the rules of the road in digital interactions.The last few years have witnessed dramatic developments in the foundations of cryptography, as well as its applications to realworld privacy and security problems. For example, cryptography is abuzz with solutions to longstanding open problems such as fully homomorphic encryption and software obfuscation that use an abundance of data for public good without compromising security.
The course will explore the rich theory of cryptography all the way from the basics to the recent developments.
Prerequisites: This is an introductory, but fastpaced, graduate course, intended for beginning graduate students and upper level undergraduates in CS and Math. We will assume fluency in algorithms (equivalent to 6.046), complexity theory (equivalent to 6.045) and discrete probability (equivalent to 6.042). Mathematical maturity and an ease with writing mathematical proofs will be assumed starting from the first lecture.
Course Information
INSTRUCTOR 
Vinod Vaikuntanathan Email: vinodv at csail dot mit dot edu 
LOCATION AND TIME  Monday and Wednesday 1:002:30pm in 4237 
TAs 
Lali Devadas Email: lali at mit dot edu Office hours: Monday 56pm in 24310, Tuesday 1011am in 34304 Sacha ServanSchreiber Email: 3s at mit dot edu Office hours: Tuesday 67pm in 24310, Friday 121pm in 24310 Aparna Gupte Email: agupte at mit dot edu Office hours: Wednesday 121pm in 26314 
RECITATIONS 
Probability review: Friday September 10 121pm in 24310
[Probability theory handout] Complexity and reductions review: Friday September 17 121pm in 24310 [Complexity theory handout] Number theory review: Friday October 1 121pm in 24310 [Number theory handout] 
RESOURCES 
The main references will be the course materials including lecture notes, slides and/or videos.
We will also post relevant papers after every lecture.
Here are a few supplementary references for the entire course material.
Lecture notes Textbooks

PIAZZA  We will use Piazza for class communication. Our class Piazza is here. Please ask your questions there, so that other students can see the questions and answers. 
ASSIGNMENTS AND GRADING 
Grading will be based on the problem sets (95%) and class participation (5%).
There will be 6 problem sets and your top 5 scores will count towards your grade. You have a total of 10 late days to use across the 6 psets (max of 5 late days for any single pset). You can use these late days however you like; we will use the timestamp of your Gradescope submission to calculate the number of late days.
Submitting psets:
Released psets: 
COLLABORATION POLICY  Collaboration is permitted and encouraged in smallgroups of at most three. You are free to collaborate in discussing answers, but you must write up solutions on your own, and specify in your submission the names of any collaborators. Do not copy any text from your collaborators; the writeup must be entirely your work. Additionally, you may make use of published material, provided that you acknowledge all sources used. Of course, scavenging for solutions from prior years is forbidden. 
Schedule (tentative and subject to change)
Lecture  Topic 
Module 1.  
Lecture 1 (Wed Sep 8) HW #1 out 
Resources: Lecture video and slides. Topics covered:
Recommended reading:

Lecture 2 (Mon Sep 13) 
Resources: Lecture video and slides. Topics covered:
Recommended reading:

Lecture 3 (Wed Sep 15) 
Resources: Lecture video and slides. Topics covered:
Recommended reading:

Lecture 4 (Mon Sep 20) 
Resources: Lecture video and slides. Topics covered:
Recommended reading:
Advanced reading:

Lecture 5 (Wed Sep 22) HW #2 out 
Resources: Lecture video and slides and lecture notes. Topics covered:
Advanced reading:

HW #1 due Fri Sep 24  Module 2. 
Lecture 6 (Mon Sep 27) 
Resources: Lecture video and lecture notes. Topics covered:
Advanced reading (same as last time):

Lecture 7 (Wed Sep 29) 
Resources: Lecture video and slides. Topics covered:

Module 3.  
Lecture 8 (Mon Oct 4) 
Resources: Lecture video and slides. Topics covered:

Lecture 9 (Wed Oct 6) HW #2 due, HW #3 out 
Resources: Lecture video and slides. Topics covered:
Advanced reading:

No lecture (Mon Oct 11) Indigenous Peoples' Day 

Lecture 10 (Wed Oct 13) 
Resources: Lecture video and slides. Topics covered:

Lecture 11 (Mon Oct 18) 
Resources: Lecture video and slides. Topics covered:
Advanced reading:

Lecture 12 (Wed Oct 20) 
Resources: Lecture video and slides. Topics covered:

Module 4.  
Lecture 13 (Mon Oct 25) 
Resources: Lecture video and slides. Topics covered:

Lecture 14 (Wed Oct 27) HW #3 due, HW #4 out 
Resources: Lecture video and slides. 
Lecture 15 (Mon Nov 1) 
Resources: Lecture video and slides. Recommended reading:
Advanced reading:

Lecture 16 (Wed Nov 3) 
Resources: Lecture video and slides. Recommended reading:

Lecture 17 (Mon Nov 8) 
Resources: Lecture video and slides and lecture notes. Recommended reading:

Module 5.  
Lecture 18 (Wed Nov 10) HW #4 due, HW #5 out 
Resources: Lecture video and slides and lecture notes. Advanced reading: 
Lecture 19 (Mon Nov 15) 
Resources: Lecture video and slides and lecture notes. Advanced reading:

Lecture 20 (Wed Nov 17) 
Resources: Lecture video and slides. 
Module 6.  
Lecture 21 (Mon Nov 22) HW #5 due, HW #6 out 
Resources: Lecture video and slides. Topics covered:
Recommended reading:

Lecture 22 (Mon Nov 29) 
Resources: Lecture video and slides. Recommended reading:
Advanced reading: 
Lecture 23 (Wed Dec 1) 
Resources: Lecture video and slides. Recommended reading:

Lecture 24 (Mon Dec 6) HW #6 due 

Lecture 25 (Wed Dec 8) 