Essential Concepts in Modern Cybersecurity
1. Proving Euler’s Theorem: Example (a=3, n=10)
Euler’s Theorem Statement:
If the greatest common divisor gcd(a, n) = 1, then the following congruence holds:a^φ(n) ≡ 1 (mod n)
Step 1: Check GCD Condition
gcd(3, 10) = 1 ✅ (Condition met)
Step 2: Compute Euler’s Totient Function φ(10)
Prime factorization of 10: 10 = 2 × 5
Using the multiplicative property of φ:φ(10) = φ(2) × φ(5) = (2-1) × (5-1) = 1 × 4 = 4
Step 3: Substitute into the Theorem
We need to verify: 3^φ(10) = 3^4
Step 4: Compute
Read MoreUnderstanding Hacker Ethics and Cryptography Techniques
Hacker: Someone who seeks to understand how systems work and finds ways to make them do things they weren’t originally designed to do. Security depends on maintenance and verification, not trust.
Social Engineering: Manipulating people into revealing confidential info (pretexting, phishing, smishing, etc).
Encryption: Converts plaintext to ciphertext.
Decryption: Restores plaintext using a key.
Cipher: Algorithm pair for encryption and decryption.
Key: Secret value that controls the cipher. DES (56
Read MoreUnderstanding IoT Security Concepts and Terminology
Lectures 1–3
IoT (Internet of Things) – interconnected physical devices exchanging data.
MMU (Malfunction Management Unit) – hardware failsafe.
Invariant – rule defining safe system states.
NTCIP – network protocol for traffic signal controllers.
DoS / DDoS – denial of service (resource flooding).
Replay Attack – reuse of old valid data packets.
Eavesdropping – intercepting communication.
Injection Attack – unauthorized commands/data inserted.
Tampering – altering transmitted or stored
Read MoreCryptography and Network Security Fundamentals
Cryptanalysis: Principles and Attacks
Definition
Cryptanalysis is the process of studying and breaking encryption to recover plaintext or the secret key without knowing the key.
Purpose
The purpose of cryptanalysis is to find weaknesses in a cryptographic algorithm, recover hidden plaintext or keys, check how strong the encryption is, and determine how easily an attacker can exploit the system.
Working Process
- Attacker collects ciphertext.
- Makes guesses or analyzes patterns in the encryption.
- Tries decrypting
Fundamentals of Computer Security and Cryptography
Computer Security refers to the protection of computer systems and networks from theft, damage, unauthorized access, misuse, or disruption of services. It ensures confidentiality, integrity, and availability of data.
The need for security arises because of increasing cyber threats, sensitive data storage (e.G., financial records, medical data), online transactions, and dependence on cloud services. Without security, systems are vulnerable to data breaches, identity theft, and financial losses.
Security
Data Encryption Standard (DES) and Core Cipher Concepts
Data Encryption Standard (DES) Algorithm Explained
The Data Encryption Standard (DES) is a symmetric-key block cipher developed in the 1970s by IBM and adopted by the US government. It encrypts data in 64-bit blocks using a 56-bit key.
How DES Works
- Initial Permutation (IP): The 64-bit plaintext goes through an initial permutation, which shuffles the bits according to a fixed table.
- Divide into Halves: The permuted text is split into two 32-bit halves: Left (L0) and Right (R0).
- 16 Rounds of Feistel Operations: