Verba volant, scripta manent.
I. Core Principles of Cryptography
This section focuses on the central ideas, definitions, and proof techniques that constitute the study of cryptography.
A. Foundational Concepts
An introduction to the core ideas and goals of cryptography.
What is Security ?
Perfect Secrecy
Definition of Cipher
B. The Adversarial Framework
Defining security through the lens of potential attacks.
Attack Games in Cryptography
C. The Mathematics of Provable Security
The tools for rigorously proving cryptographic security.
Distinguishing in a Probabilistic World
Part I
Part II
Part III
Part IV
Bias and Advantage
Why is Advantage An Absolute Value ?
Advantage Calculation
D. Proofs & Security Notions
Putting the theoretical framework into practice by examining specific security definitions.
An Overview of Proof Techniques in Cryptography
Exploring the Relationship Between Security Definitions:
Security Proof : Semantic Security implies Message Recovery Security
Does security against message recovery imply semantic security?
II. Mathematical Foundations (Primers)
This section provides the necessary mathematical background. These primers cover the formalisms required to understand the proofs and definitions in the main cryptography section.
A. Discrete Mathematics & Logic
Probability Primer
Counting Primer
Set Theory Primer
Logic Primer – Part 1
Formula and Free Variables
Equality
B. Number Theory
A self-contained, axiomatic study of numbers, from foundational principles to essential algorithms.