In this course, it is aimed to provide the necessary mathematical infrastructure for institutions that want to improve their mathematical infrastructure in the field of Cryptography.

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1. Introduction to Number Theory

2. Introduction to Group Theory

3. Introduction to Ring and Field Theory

4. Introduction to Polynomials and Polynomial Rings

5. Finite Fields

6. Boolean Function

7. Algebraic Normal Form

8. Generating Functions

In this course, it is planned to strengthen the knowledge of people in cryptography by giving information about the development of cryptosystems and the importance of their building blocks.

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1. Encryption by Substitution

a) Caesar's Algorithm and Basic Concepts

b) Shift Cipher

c) Affine Cipher

d) General Substitution Cipher

e) Play-Fair

f) Hill Cipher

2. Basic Methods of Cryptanalysis

a) Brute Force Attack

b) Frequency Analysis

c) Plaintext/Ciphertext Attack

3. Design Criteria for Encryption by Substitution

4. Transposition Cipher

5. Vigenere Cipher

6. Cryptanalysis of Vigenere Cipher

In this course, it is planned to provide information on the creation and evaluation of stream ciphers which are used in the infrastructure of many cryptographic systems today.

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1. What are Stream Ciphers?

2. Finite State Machines

3. Generating Functions

4. Golomb's Postulates

5. LFSRs

6. Linear Complexity

7. Berlekamp Massey Algorithm

8. Stream Cipher Systems Based on LFSR

9. Correlation Attack

10. Modern Stream Ciphers

In this course, it is aimed to provide education on Block Cipher, which is a part of symmetric encryption systems in the field of Cryptography.

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1. The Basics

2. DES and Its Features (2DES, 3DES)

3. AES and Its Features

4. Basic Building Blocks and Algebraic Properties (Equilibrium, Algebraic Order,
Correlation Immunity, Nonlinearity, Differential Uniformity, DDT-LAT, SAC and PC)

5. Other Block Cipher Systems

6. Block Cipher Modes: ECB, CBC, CFB, OFB, CTR, etc.

In this course, it is planned to cover the details of cryptanalysis methods, which play an important role in the creation of cryptosystems and the evaluation of their security.

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1.Differential Cryptanalysis

2. Linear Cryptanalysis

3. Impossible Differential Cryptanalysis and Differential-Linear Cryptanalysis

4. Meet-in-the-Middle Attack

5. Algebraic Attacks (Interpolation)

6. Square Attack for AES

In this course, it is planned to give detailed information about asymmetric cryptosystems which are used in many cryptographic systems to provide key and data transfer

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1. RSA Cryptosystem and Its Attacks

a. Modular Arithmetic

b. Generating Prime Number

c. RSA Cryptosystem

d. Attacks on the RSA Cryptosystem

2. Discrete Logarithm Problem and Cryptosystems

a. Discrete Logarithm Problem

b. DH key Exchange

c. El-Gamal Encryption

d. DSA Signing

e. Safe Parameter Selection and Attacks

3. Edwards Curve Digital Signature Algorithm and Its Attacks

a. Elliptic Curve Forms

b. Signing

c. Safe Curve Selection

d. Attacks On The Elliptic Curve Cryptosystem

4. Public Key Cryptosystems

a. Certificates

b. Authorities (Registration Authority, Certificate Authority, Root Certification Authority)

c. Principles

d. Public Key Infrastructure Architectures

e. Application Examples

In this course, it is planned to include the details of the analysis methods that play an important role in the construction of symmetric-key cryptosystems and the evaluation of their security.

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1. Stream Cipher Cryptanalysis Methods

2.Cryptanalysis Attack Types

a.General Attacks

b.Analysis of Stream Cipher based on LFSR

c.A5/1 Cryptanalysis

3.Cryptographic Protocols

4.Diffie Hellman Key Exchange

a.Types of Attacks on Protocols

b.Key Management / Distribution

c.Authentication

5.Authentication (Entity Authentication)

a.Some Commonly Used Protocols

6.Hash Functions and Their Expected Security Features

a.Construction of Hash Function

b.Message Authentication Code - MAC

In this course, it is planned to give detailed information about blockchain systems, which have started to take a place in today's systems and which many containing academic studies are about.

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1.Blockchain Fundamentals

2. Bitcoin Mechanics

3. Wallets, Mining and Pools

4. Smart Contracts - Ethereum, Neo, et al

5. Blockchain Security – Multi, Delegatable, Hierarchical signatures

6. Consensus Algorithms - PoW, PoS, Voting, Federated et al.

7. Blockchain Scaling - Segregated Witness, Lightning, Sidechains, Sharding

8. Real World Applications – HyperLedger, Tendermint, et al.

9. Future of Blockchain - Anonymity, Comptutational integrity, et al.

In this course, Quantum secure cryptographic algorithms that will take an important place in information security after the standardization process and the problems they are based on will be explained.

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1) Quantum Computers and Post-Quantum Cryptography

2) Lattice-Based Cryptography

a) Lattices

b) Lattice Reduction Algorithms

c) Difficult Lattice Problems

d) Ajtai's Short Integer Solution Problem (SIS) and Family of One Way Functions

e) Learning With Error Problem (LWE)

f) Ring - Learning With Error Problem (RLWE)

g) Module - Learning With Error Problem (MLWE)

3) LWE Based Algorithm: FRODO

4) RLWE Based Algorithm: NEW HOPE

5) MLWE Based Algorithm: KYBER

6) NTRU

7) Hash - Based Signature Schemes

a) Hash-Based One-Time Signature Schemes

b) Lamport–Diffie One-Time Signature Scheme

c) Winternitz One-Time Signature Scheme

d) Merkle Signature Scheme

e) Hash-Based Algorithm: PICNIC