The RSA Encryption Algorithm - How Does It Actually Work + Step-by-Step Example.

By the end of this video, you’ll have a solid understanding of how RSA works, from key generation to encryption and decryption, with a practical example of how Alice can send a secure message to Bob using RSA encryption. With engaging animations and clear explanations, we make learning RSA easy and fun!

1. Introduction: Alice and Bob's Communication Without Encryption:
We start by simulating a basic communication between Alice and Bob, where they send messages without any encryption. Through animated characters, you'll see how easily a hacker (Eve) can intercept and read messages when no encryption is applied.

2. Numerical Representation of Text:
Ever wondered how computers convert strings into numbers? We’ll show you how letters and words can be represented as integers in binary and ASCII. For example, how the string "HELLO" can be transformed into a number.

3. Modular Arithmetic: The Core of RSA:
Next, we introduce modular arithmetic, one of the key concepts in RSA encryption. We’ll explain the modulus operator with easy-to-understand animations:

How it works .
Understanding terms like modulus and remainder through visual examples.

4. Euler’s Totient Function (Φ(N)) and Euler’s Theorem:
In this section, we cover Euler's Totient Function, explaining its role in RSA:
What Φ(N) represents for an integer N.
We’ll walk through Euler’s Theorem with visual illustrations to make the mathematical concepts more intuitive.

5. The Prime Factorization Problem in RSA:
The security of RSA is based on the difficulty of prime factorization. We’ll visualize Why factoring the product of two large prime numbers (as in RSA) is computationally hard and how this underpins the security of the RSA algorithm.

6. RSA Encryption Algorithm: Step-by-Step Explanation
Now, we move into the heart of the video:
Public and Private Key Generation: We explain how to generate large prime numbers, compute N = p × q, and find e and d (public and private exponents).
Encryption Process: Watch as Alice uses Bob’s public key to encrypt her message.
Decryption Process: See how Bob uses his private key to decrypt Alice’s message, recovering the original plaintext.

7. RSA Example: Alice Sends “HELLO” to Bob
In the final part, we demonstrate an actual communication using the RSA encryption algorithm with the message "HELLO":
Step 1: Alice converts "HELLO" into an integer.
Step 2: Alice encrypts the numbers with Bob’s public key.
Step 3: Bob decrypts the numbers with his private key and retrieves the original message.

💬 Let us know in the comments if you found this video helpful or if you have any questions! Don’t forget to like and subscribe for more videos.

[sander_bouwhuis]

You lost me at 4:25 where you choose e and compute d from e.
1. You picked a number e which is co-prime with Φ(N). Should that number be as big as possible, or maybe somewhere close to half Φ(N)?
2. I don't understand how to get d from e. I understand I could do d = k * (Φ(N)+1)/e very easily. But, you don't explain where all of a sudden the variable k comes from.