This course will give you a solid understanding of the concepts of modern cryptography systems, starting from a clear review of underlying mathematics, through analytical tools that will allow you to evaluate cryptographic solutions, to giving you a platform for truly understanding today’s most advanced cryptographic systems.
The 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.
This course is self-paced and pre-recorded
18 CPE Credits
You will learn:
- a variety of ways to break, and to measure/evaluate the security of cryptographic primitives;
- the mathematics behind cryptography;
- the security design principles;
- the internal structure and important properties of major cryptosystems;
- the major computational problems in cryptography (symmetric and public key);
- step by step analysis of mathematical/algebraic/statistical attacks;
You will need:
Just a computer equipped with Windows, Linux or Mac with access to the Internet.
No specialized software 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 algorithms.
The course provides support materials if you need to refresh your grasp on mathematical concepts present in the course.
All topics are explained and illustrated step-by-step by the instructor.
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.
Part 1: Algebra and number theory:
- Basic notions
- Solving ax + bx = d
- The Chinese Remainder Theorem
- Modular Exponentiation
- Fermat and Euler
- Primitive roots
- Inverting matrices mod n
- Square roots mod n
- Finite fields
All topics in this part of the course are strengthened with accompanying exercises.
Part 2: Classical cryptosystems
- Shift Ciphers
- Affine Ciphers
- Vigenère Cipher
- Substitution Ciphers
- Block Ciphers
- Challenges and exercises: classical cryptosystems in practice.
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.
- Hash Functions
- Digital Signatures
- Huffman codes
- Public Key Infrastructure
- Challenges and exercises: analysis and attacks on digital signatures.
MODULE 3: Cryptographic Algorithms
This module will present the main cryptographic algorithms and the attacks against them.
- Data Encryption Standard
- The Advanced Encryption Standard: Rijndael
- Challenges and exercises: analyze and attack algorithms.
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.
- Elliptic Curve Cryptosystems
- SSL/TLS Cryptography
- Impossible Differentials
- Challenges and exercises: advanced concepts in modern cryptography.
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