Pseudorandom generator (PRG)

k-wise Independence

Error Correcting Codes

SL=L

Code concatenation

Expander Mixing Lemma

Existence of Seeded-Extractors

Next-Bit Unpredictability

Discrete Fourier Analysis

Cheeger's Inequality

Error reduction

Graph Theoretic View

Trevisan's Extractor

Combinatorics

Expander Graphs

Randomness Extractors

Small biased distributions

Random Walks on Expanders

Leftover Hash Lemma

Nisan-Wigderson Construction

Max-Cut

ε-Biased Distributions

Zig-Zag Product

Spectral Expansion

Samplers

Two-Source Extractor

CS 294-202 Pseudorandomness UC Berkeley Fall 2021 This course explores the role of randomness in computation and pseudorandomness, focusing on the applications in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. The course will also address the question of derandomization of small-space computation. Prerequisites are unspecified, but the course content suggests a high level of expertise. Randomized algorithms give a broad and rich algorithmic toolkit (e.g., sampling, Monte Carlo methods). Randomness is an essential resource in distributed computing, cryptography, and interactive proofs. In this course, we would explore the role of randomness in computation: Can we derandomize algorithms without changing their time or space complexity? Can we "purify" randomness from a weak source of randomness? 

Pseudo-randomness is the property of "appearing random" while having little or no randomness. Pseudo-randomness plays a significant role in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. In this course, we will see all these beautiful applications. In the second part of the course, we would focus on the question of derandomization of small-space computation, also known as the "**RL** versus **L**" question. It asks whether all problems that can be decided in randomized logarithmic space (RL) can also be decided in deterministic logarithmic space (L). We would cover recent approaches towards showing that RL = L.    Salil Vadhan -  [Pseudorandomness](https://www.google.com/url?q=https%3A%2F%2Fpeople.seas.harvard.edu%2F~salil%2Fpseudorandomness%2F&sa=D&sntz=1&usg=AOvVaw2jc9ipUift6CNRnbiOuSkb)

CS 294-202 Pseudorandomness

Theoretical Computer Science

Cryptography

One-time pad

Computational assumptions

Symmetric-key encryption

Public-key cryptography

ElGamal public key encryption

DSA signature schemes

RSA (cryptosystem)

Diffie-Hellman key exchange

Authenticated encryption

Secure Hash Algorithm (SHA)

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

Message integrity

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

Message authentication code (MAC)

Birthday attack

HKDF

Block cipher

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

Modes of operation

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

Computer Security and Cryptography