Cryptography: Boolean functions and related problems

The course invites you to learn more about cryptography; you will learn some important math which stands behind the ciphers, and defines how resistant the particular cipher will be to different types of attacks
36 lessons with assignments
Free schedule
Learning via chatbot
Certificate of completion
Sign up for the course for free. Learning will start in autumn 2022
Choose a messenger in which it will be convenient for you to study or leave your email so you don't miss the news
available soon
About the course
The key topics covered in the course:
  • how cryptography developed in Russia and in the Soviet Union, including the facts which used to be top secret until very recent times
  • Boolean functions and S-boxes, and how the resistance of a cipher depends on cryptographic properties of a Boolean function
  • methods of cryptanalysis
  • some special and most intriguing types of cryptographic Boolean functions: bent functions and APN-functions (Almost Perfect Nonlinear Functions)
  • AI and ML for cryptography

Who is the course for

  • University students at Math or IT departments
  • Junior cryptography specialists

Course difficulty level: advanced. Background in math is required

What will you learn

  • History of cryptography
  • Methods of cryptanalysis
  • Some special and most intriguing types of cryptographic Boolean functions
AUTHORS
Tokareva Natalia

PhD, Assistant professor

Department of mechanics and mathematics
Gorodilova Anastasia
PhD, Senior lecturer
Department of mechanics and mathematics
Kutsenko Alexander

Researcher. Department of mechanics and mathematics

Pintus George
Researcher. Department of mechanics and mathematics

Course program
Module 1. Introduction
  • What is the course about?
  • The beginning of the Russian cryptography
  • Soviet and modern Russian cryptography
  • From cryptanalysis to cryptographic Boolean functions
  • Cryptographic Boolean functions: main properties
  • Boolean functions in cryptographic ciphers
Module 2. S-Boxes and artificial intelligence
  • Boolean functions
  • S-boxes
  • Boolean functions and heuristics
  • S-boxes and heuristics
  • Artificial intelligence in cryptology
  • Machine learning and side-channel attack
Module 3. Bent functions generalizations and applications
  • Introduction and history
  • Algebraic normal form of a bent function
  • Bent rectangles and simple constructions of bent functions
  • Automorphisms of the set of bent functions
  • Bent functions in small number of variables
  • Bent sum decomposition problem
  • Generalizations of bent functions
  • Cryptographic generalizations
Module 4. Almost Perfect Nonlinear functions
  • Introduction. Differential uniformity
  • Basic properties of APN functions
  • EA- and CCZ-equivalence
  • Monomial APN functions
  • Polynomial APN functions
  • APN permutations
  • Differential equivalence of APN functions
Module 5. Foundations of quantum key distribution
  • Introduction to quantum information technology
  • Mathematical foundations of quantum informatics
  • Description of Quantum Key Distribution (QKD) protocol BB84
  • Intercept and resend attack on BB84 protocol
  • Description of QKD protocols B92 and E91
  • Basics of PNS attack
  • Key distillation
  • Examples of using
Modern visual language
All lessons are shot in a modern studio, and graphics were created by designers
36 lessons
This is enough to cover the topic. Each lesson is made in the format of a longread with video lectures, text and graphic materials and links
Vivid and constructive speech
The author speaks simply and clearly, using catchy examples
Free schedule
There are no deadlines or due dates for homework assignments. Materials are available immediately, you can start learning through the chatbot at any time and return to the course when you have time
Support
Directly through the chatbot where you learn, you can request the help of technical support, which will promptly answer you.
Certificate
To get a certificate, you need to complete the assignments for the lessons
Cryptography: Boolean functions and related problems
The course invites you to learn more about cryptography; you'll learn some important math which stands behind the ciphers, and defines how resistant the particular cipher will be to different types of attacks.

What will you get

  • 36 lessons with assignments in a chatbot
  • Author’s presentation: simple, clear and with interest in the subject
  • Free schedule: no deadlines and due dates for assignments
  • All materials are available immediately, you can start learning at a convenient time
  • Professional video and modern graphics
  • Quick contact with technical support
  • Certificate of Completion

What will you learn

  • History of cryptography
  • Methods of cryptanalysis
  • Some special and most intriguing types of cryptographic Boolean functions
Sign up for the course for free. Learning will start in summer 2022
Choose a messenger in which it will be convenient for you to study or leave your email so you don't miss the news
available soon