Principles of Cryptography

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.

Axiomatic Foundations

Number Theory Primer : An Axiomatic Study Of Numbers
Peano’s Axioms for Natural Number
Proving Properties of Natural Numbers Using Proof by Induction
Well-Ordering Principle

Properties of Integers

The Division Algorithm
The Greatest Common Divisor
The Euclidean Algorithm
The Diophantine Equation ax + by = c