Cryptography (Основы теории информации и криптографии)

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.

  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.

Welcome to the course, and enjoy your learning!

Weekly activities include:

·   watching videolectures;

·   answering ungraded quiz questions to make sure that the student understands the lecture material;

·   reading additional materials;

·   completing weekly graded quizzes which contribute to the final grade. 

Also, the students have to pass the final test at the end of the course to evaluate their overall knowledge of the course material.

Useful links:

• International Association for Cryptologic Research

• Cryptology ePrint Archive

• ArXiv.org Cryptography and Security

• Cryptography: Boolean functions and related problems

Resources in Russian: 

1. Городилова А.А., Токарева Н.Н., Шушуев Г.И. Криптография и криптоанализ: сборник задач. Учебное пособие. М-во образования и науки РФ, Новосиб гос. ун-т, Мех.-мат. фак., Каф. теорет. кибернетики. Новосибирск, 2014. – 325 с. – 147 экземпляров. 

2. Городилова А.А., Токарева Н.Н., Шушуев Г.И. Криптография и криптоанализ: сборник задач. Учебное пособие. М-во образования и науки РФ, Новосиб гос. ун-т, Мех.-мат. фак., Каф. теорет. кибернетики. Новосибирск, 2014. – 325 с. – электронный ресурс. Режим доступа: http://e-lib.nsu.ru/dsweb/Get/Resource-708/page001.pdf 3.

3. Соловьева Ф.И. Введение в теорию кодирования. Учебное пособие. М-во образования и науки Рос. Федерации, Новосиб. гос. ун-т, Мех.-мат. фак. 2-е изд., доп. и перераб. Новосибирск, 2011. – 123 с. – 69 экземпляров. 

4. Токарева Н.Н. Симметричная криптография: краткий курс. Учебное пособие. М-во образования и науки РФ, Новосиб гос. ун-т, Мех.-мат. фак., Каф. теорет. кибернетики. Новосибирск, 2012. – 234 с. – 43 экземпляра. 

5. Токарева Н.Н. Симметричная криптография: краткий курс. Учебное пособие. М-во образования и науки РФ, Новосиб гос. ун-т, Мех.-мат. фак., Каф. теорет. кибернетики. Новосибирск, 2012. – 234 с. – электронный ресурс. Режим доступа: http://elib.nsu.ru/dsweb/Get/Resource-1222/page001.pdf.

Module 1. The history of cryptorgaphy: an introduction

What is the course about?

• The beginning of the Russian cryptography

• Soviet and modern Russian cryptography

• From cryptanalysis to cryptographic Boolean functions

Module 2. Cryptographic Boolean functions

• Cryptographic Boolean functions: main properties

• Boolean functions in cryptographic ciphers

Module 3. Bent functions

• 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

Module 4. Bent functions: generalizations and applications

• Bent sum decomposition problem

• Generalizations of bent functions

• Cryptographic generalizations

Module 5. 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 6. Foundations of quantum key distribution

• Introduction to quantum information technology

• Mathematical foundations of quantum informatics

Module 7. QKD protocols

• Description of Quantum Key Distribution (QKD) protocol BB84

• Intercept and resend attack on BB84 protocol

• Description of QKD protocols B92 and E91

Module 8. Quantum key distribution: further implications

• Basics of PNS attack

• Key distillation

• Examples of using

The students who completed the course successfully, will acquire the following knowledge and skills:

• Knows the key events in the history of cryptography.

• Understands the main properties of Boolean functions and their applications in cryptography.

• Knows how the resistance of a cipher depends on cryptographic properties of a Boolean function.

• Knows the main methods in cryptography.

• Can apply the cryptography tools to solving theoretical and practical problems.

OPK-1. Is able to apply the fundamental knowledge gained in the field of mathematical and (or) natural sciences and use them in professional activities; in terms of the following learning outcomes:
OPK-1.1. Has fundamental knowledge in the field of mathematical and (or) natural sciences:
Knows the main sections of information theory and cryptography;
OPK-1.2. Is able to use fundamental knowledge in the field of mathematical and (or) natural sciences in professional activities:
He is able to apply the apparatus of information theory and cryptography to solve theoretical and practical problems;
OPK-1.3. Has the skills to choose methods for solving professional tasks based on theoretical knowledge
It is able to analyze methods of compression, storage, noise-resistant encoding and encryption of information.
OPK-4. Is able to solve the tasks of professional activity using existing information and communication technologies and taking into account the basic requirements of information security; in terms of the following learning outcomes:
OPK-4.1. Familiar with the basic information and communication technologies, resources, software tools necessary for the implementation of professional activities:
Knows the basic methods of compression, storage, noise-resistant encoding and encryption of information.
OPK-4.2. Is able to use information and communication technologies, resources, software tools in professional activities:
Is able to apply methods of compression, storage, noise-resistant coding and encryption of information to solve practical problems.