RSA (cryptosystem)

Pre-modern cryptography

Pseudorandom Generator (PRG)

Pseudorandom Permutation (PRP)

Message integrity

Commitment schemes

Message authentication code (MAC)

Definitions in cryptography

Computational assumptions

Block cipher

Number-theoretic constructions of symmetric primitives

Trapdoor permutations

Randomized encryption

Constructing PRGs

Modes of operation

Authenticated encryption

Relationships between symmetric primitives

Digital signature

Information-theoretic security

Chosen Plaintext Attacks (CPA)

Constructing block ciphers

Identification protocols

Diffie-Hellman key exchange

Chosen Ciphertext Attacks (CCA) security

Public-key cryptography

Stream ciphers

Pseudorandom Function (PRF)

Attacks on block ciphers

Collision-resistant hashing

COS 433 - Cryptography Princeton University Fall 2020 An introductory course into modern cryptography, grounded in rigorous mathematical definitions. Covers topics such as secret key and public key encryption, pseudorandom generators, and zero-knowledge proofs. Requires a basic understanding of probability theory and complexity theory, and entails some programming for course projects.  Cryptography is an ancient practice dating back almost 4000 years. However, cryptography practiced today is very different than the cryptography used as recently as a few decades ago. For one, traditional cryptography was mostly synonymous with encryption: translating data into secret codes. Today, however, cryptography extends far beyond basic codes to encompass concepts such as authentication and integrity, and can be used to solve seemingly impossible tasks such as public key encryption (exchanging secret messages without ever having met in person to share a secret key) and zero knowledge proofs (proving theorems without revealing the proof).

Another new feature in modern cryptography is its foundations. Until recently, cryptography was largely an art form based on intuition and ad hoc tweaks to block vulnerabilities. Modern crytpography is instead more of a science, characterized by rigorous mathematical definitions and theorems that guide the design of new systems.

This course is an introduction to modern cryptography, focusing on the theoretical foundations, with some attention to practical considerations. We will cover a variety of topics, including secret key and public key encryption, authentication, commitments, pseudorandom generators, and zero knowledge proofs.  Basic probability theory. Basic complexity theory (as in COS340) recommended. The course projects will involve programming, but no specific programming language is required. 

COS 433 - Cryptography

Computer Security and Cryptography

Proofs

Modular arithmetic

Countability

Conditional probability

Random variable

Continuous Probability

Poisson distribution

Fermat’s Little Theorem

Secret Sharing

Counting

Combinations of Events

Total Expectation

Central Limit Theorem

Stable Matching

Expectation

Propositional calculus (Propositional logic)

Graphs

Chinese Remainder Theorem

Error Correcting Codes

Discrete Probability

Bayes' theorem

Variance

Concentration Inequalities

Induction

Euclid

Polynomials

Computability

Independence (probability theory)

Distributions

Joint and Conditional PMFs

Gaussian Distribution

CS 70: Discrete Mathematics and Probability Theory UC Berkeley Fall 2022 CS 70 presents key ideas from discrete mathematics and probability theory with emphasis on their application in Electrical Engineering and Computer Sciences. It addresses a variety of topics such as logic, induction, modular arithmetic, and probability. Sophomore mathematical maturity and programming experience equivalent to an Advanced Placement Computer Science A exam are prerequisites. Logic, infinity, and induction; applications include undecidability and stable marriage problem. Modular arithmetic and GCDs; applications include primality testing and cryptography. Polynomials; examples include error correcting codes and interpolation. Probability including sample spaces, independence, random variables, law of large numbers; examples include load balancing, existence arguments, Bayesian inference. The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in Electrical Engineering and Computer Sciences. The course aims to present these ideas "in action"; each one will be geared towards a specific significant application. Thus, students will see the purpose of the techniques at the same time as learning about them. Sophomore mathematical maturity, and programming experience equivalent to that gained with a score of 3 or above on the Advanced Placement Computer Science A exam. There is no textbook for this class. Instead, there is a set of comprehensive lecture notes posted on [the front page](https://www.eecs70.org/) for each lecture. Make sure you revisit the notes after every lecture. Each note may be covered in one or more lectures.

Distinguished Alum Megan says, “When I took the course, I studied the notes until I was able to comfortably reproduce all of the proofs.

CS 70: Discrete Mathematics and Probability Theory

Mathematical Foundations

The Pigeon Hole Principle

Statement (logic)

Proof by contradiction

Truth table

Conjunctive normal form (CNF)

Disjunctive normal form (DNF)

First-order logic

Quantifier (logic)

Set theory

Relation (mathematics)

Binary relation

Bijection, injection and surjection

Mathematical induction

Number theory

Binomial theorem

Probability theory

Graph theory

Tree (graph theory)

Random walk on graphs

CSCI 0220 Discrete Structures and Probability Brown University Spring 2023 CSCI 0220 provides a foundation in discrete math and probability theory. Key topics include logic, set theory, number theory, combinatorics, graph theory, and probability. No prior math background assumed. Aims to develop problem solving, communication, and collaboration skills. Introduces new concepts and ways of thinking to enable analyzing problems arising in computer science. Beginner-friendly introduction to core mathematical concepts underlying many aspects of CS. I don't know about you, but we're feeling 22! This class gives you the tools to explore interesting questions and convince yourself and others of their answers. You'll be introduced to new worlds of ideas and ways of thinking. We'll learn about Set Theory, Logic, Number Theory, Combinatorics, Graph Theory, and Probability. If these topics sound unfamiliar, not to fear: you're in exactly the right place! This course assumes no prior experience with these topics.  CS can feel like a very applied field. Why learn math?

- Problem solving
- Communication
- Collaboration

A key result of this class: you’ll have a vocabulary for discussing certain kinds of
problems that appear in many different contexts, and a toolbox of general approaches
for solving them.

A vital point of computer science (academic, industry, hobbyist): *communication*. Our expectations from you

- No mathematical background is assumed. We’re not doing calculus, statistics, ...
- Approach things with an open mind.
- Try to communicate clearly and concisely.
- Respect your classmates and TAs: we’re in this together.
- Let us know how you’re doing! [Mathematics for Computer Science — Lehman, Leighton, Meyer](https://cs22.io/static/files/Mathematics_for_Computer_Science.pdf)

Reading (and purchasing!) this textbook is not required, though many students in the past have found it helpful in reinforcing what's covered in lecture! 

CSCI 0220 Discrete Structures and Probability

Cryptography

One-time pad

Symmetric-key encryption

ElGamal public key encryption

DSA signature schemes

Secure Hash Algorithm (SHA)

Pseudorandom generator (PRG)

CBC-MAC

Password-based authentication

Zero-knowledge proof

Sigma protocol

Succinct Non-Interactive Arguments (SNARGs)

GMW: MPC for any function

Fully homomorphic encryption

Private information retrieval

Hardware security module (HSM)

Differential privacy

Shannon's Theorem

Collision-resistant hash functions

Hash-based Message Authentication Code (HMAC)

Pseudorandom function/permutation (PRF/PRP)

Secure shell protocol (SSH)

Two-factor authentication

Diffie-Hellman tuple

Non-interactive zero-knowledge (NIZK) proof

Secure multi-party computation (MPC)

Malicious security: GMW compiler

Somewhat homomorphic encryption over integers

Bootstrapping SWHE to FHE

Cryptography in blockchain

Privacy in machine learning

Computational security

Birthday attack

HKDF

Certificates

Secure authentication

Proof of knowledge

Fiat-Shamir heuristic

Garbled circuit

Cut-and-choose for garbled circuits

GSW: SWHE from LWE

Secure deployment of MPC applications

Random oracle model

Hash-and-Sign paradigm

Public key infrastructure (PKI)

Single Sign-On (SSO) authentication

Schnorr's identification protocol

Anonymous online voting

Oblivious transfer (OT)

Private set intersection

BFV: SWHE from RLWE

Secure hardware: secure enclaves (Intel SGX)

Blockchain

 CSCI 1515 Applied Cryptography Brown University Spring 2023 Applied Cryptography at Brown University offers a practical take on securing systems. By learning foundational cryptographic algorithms and advanced topics like zero-knowledge proofs and post-quantum cryptography, students gain both theoretical insights and hands-on experience in implementing cryptosystems using C++ and crypto libraries. Label: State-of-art concepts. ### Welcome to Applied Cryptography (CSCI 1515) at Brown!

This course teaches cryptography from a practical perspective and provides hands-on experience in building secure systems.

We first introduce foundational cryptographic algorithms including secret-key and public-key encryption schemes, message authentication codes, digital signatures, and hash functions, from which you will build secure communication and authentication systems.

More advanced topics that are covered include zero-knowledge proofs, secure multi-party computation, fully homomorphic encryption, post-quantum cryptography, and differential privacy. You will learn how these cryptographic techniques can be used to develop more advanced applications such as secure online anonymous voting, secure computation, and private information retrieval.

Besides the high-level design of these cryptosystems, you will also get hands-on experience implementing them using tools from the existing crypto libraries written in C++.    ## Textbooks

- [MOV] [Handbook of Applied Cryptography](https://cacr.uwaterloo.ca/hac/) by Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone
- [BS] [A Graduate Course in Applied Cryptography](http://toc.cryptobook.us/book.pdf) by Dan Boneh and Victor Shoup
- [KL] [Introduction to Cryptography](https://eclass.uniwa.gr/modules/document/file.php/CSCYB105/Reading%20Material/%5BJonathan_Katz%2C_Yehuda_Lindell%5D_Introduction_to_Mo%282nd%29.pdf) by Jonathan Katz and Yehuda Lindell
- [R] [The Joy of Cryptography](https://joyofcryptography.com/pdf/book.pdf) by Mike Rosulek

 CSCI 1515 Applied Cryptography

RSA (cryptosystem)

4 courses cover this concept

COS 433 - Cryptography

CS 70: Discrete Mathematics and Probability Theory

CSCI 0220 Discrete Structures and Probability

CSCI 1515 Applied Cryptography