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This course features an introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of number theory applied in cryptographic system, public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements. The purpose of the course is to be more practical than theoretical, and it will be enriched with practical exercises, leaving most of the theory at the student’s disposal for further study.


Early bird discount for the first 10 seats!


This course is self-paced and pre-recorded

18 CPE Credits

Course release date: February 23rd 2018


You will learn:

You will learn the major topics in cryptanalysis, showing a variety of ways to break, and to measure/evaluate the security of cryptographic primitives. You will understand the maths, the security design principles, the internal structure and important properties of major cryptosystems, as well as the major computational hard problems in cryptography (symmetric and public key). Step by step analysis of mathematical/algebraic/statistical attacks, methods and algorithms in cryptanalysis.


You will need:

Just a computer equiped with Windows, Linux or Mac with access to the Internet.

No special application is required for this course.


Before you join you should be familiar with:

It is required that the students have knowledge of the fundamentals of number theory, algebra, probability and statistics, as well as a strong background in security communication algorihtms.


SYLLABUS


MODULE 1: Algebra and Number Theory & Classical Cryptosystems

This module will give the main math concepts that are widely used in the study of the cryptosystems and some classical cryptosystems.

Covered topics: 

1.1 Basic notions

1.2 Solving ax + bx = d + exercises

1.3 Congruences + exercises

1.4 The Chinese Remainder Theorem + exercises

1.5 Modular Exponentiation + exercises

1.6 Fermat and Euler + exercises

1.7 Primitive roots + exercises

1.8 Inverting matrices mod n + exercises

1.9 Square roots mod n + exercises

1.10 Finite fields + exercises

1.11 Challenging and fixing exercises 

1.12 Shift Ciphers + exercises

1.13 Affine Ciphers + exercises

1.14 Vigenère Cipher + exercises

1.15 Substitution Ciphers + exercises

1.16 Block Ciphers + exercises

Module 1 exercises:

Exercises will be given during the course, which make the course more practical than theoretical. At the end of the module, challenging exercises will be given to the students that will prepare them for the final exam.


MODULE 2: Cryptographic Techniques and Digital Signatures

This module will present the signature schemes and some techniques used in digital signatures. We also discuss the birthday attacks on signature schemes.

Covered topics: 

2.1 Hash Functions

2.1.1 Construction of Hash Functions

2.1.2 Data Integrity and Message Authentication

2.1.3 Birthday attacks

2.1.4 Multicolisions

2.1.5 Exercises

2.2 Digital Signatures

2.2.1 El Gamal Signature

2.2.2 Hashing and Signing

2.2.3 Birthday attacks on signatures

2.2.4 Exercises

2.3 Entropy

2.4 Huffman codes

2.4.1 Diffie–Hellman Key Exchange

2.5 Public Key Infrastructure

Module 2 exercises:

Exercises will be given during the course, which make the course more practical than theoretical. At the end of the module, challenging exercises will be given to the students that will prepare them for the final exam.


MODULE 3: Cryptographic Algorithms

This module will present the main cryptographic algorithms and the attacks against them.

Covered topics:

3.1 Data Encryption Standard

3.1.1 Description of DES

3.1.2 Differential Cryptanalysis

3.1.3 Breaking DES

3.1.4 Meet-In-The-Middle Attacks

3.1.5 Exercises

3.2 RSA

3.2.1 Attacks on RSA

3.2.2 The RSA Challenge

3.2.3 The Public Key Concept

3.2.4 Exercises

3.3 The Advanced Encryption Standard: Rijndael

3.3.1 The layers

3.3.2 Decryption

3.3.3 Exercises

Module 3 exercises:

Exercises will be given during the course, which make the course more practical than theoretical. At the end of the module, challenging exercises will be given to the students that will prepare them for the final exam.


MODULE 4: Cryptographic Techniques

This module will give some theorems so that the student can move forward in the more complex cryptosystems such as Elliptic Curve.

Covered topics: 

4.1 Theorems

4.2 Elliptic Curve Cryptosystems

4.2.1 Definition of Elliptic Curves

4.2.2 Elliptic Curves mod p

4.2.3 Exercises

4.2.4 Factoring with Elliptic Curves

4.3 SSL/TLS Cryptography

4.4 Impossible Differentials

4.4.1 Attacks using Impossible Differential

4.4.2 Exercises

Module 4 exercises:

Exercises will be given during the course, which make the course more practical than theoretical. At the end of the module, challenging exercises will be given to the students that will prepare them for the final exam.


Your instructor: Washington Almeida

Washington is a member of the International Information Systems Forensics Association (IISFA – Italy). He holds academic degrees in Electrical Engineering and Information Technology, with University Extension in Management Development Programme by Fundação Dom Cabral, and Specialist in Law and Information Technology by the Polytechnic School of USP – Poli/USP, with more than 25 years of experience and familiar with digital forensic procedures that comprises digital forensics investigations phases as collection, examination, analysis and reporting. His excellent technical background has been acquired through consistent support in cases involving the social media environment, instant messaging, droppers, ransomware, copyright infringements, e-mail systems, HR systems, databases, data theft, bank fraud, computer hacking, Internet applications, among others. He is a cyber security professional who also works with sophisticated systems invasion testing, helping companies to improve the security of their assets. In the assistance of the Justice, he is qualified by the “Tribunal de Justiça de São Paulo” and “Tribunal Regional do Trabalho da 2ª Região” acting as digital forensics expert appointed by the judge. He also acts as Consultant in Digital Security and Digital Forensic Expert.

Instructor curriculum: http://www.washingtonalmeida.com.br/curriculum.html

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