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 Let’s walk through a step-by-step encryption example with real numbers , keeping it simple so you see exactly what happens . Because modern algorithms like AES or RSA use huge numbers (hundreds or thousands of bits), I’ll show you a tiny toy example using RSA , with small numbers you can follow by hand . This will not be secure (too small), but it will demonstrate the principle perfectly. KEYS OF THE UNIVERSE - Awesome booklets on amazon 🎯 RSA Example (Small Numbers) Goal: Encrypt and decrypt the number M = 7 🛠️ STEP 1: Key Generation ✅ Choose two prime numbers: p = 3 q = 11 ✅ Compute n = p × q: n = 3 × 11 = 33 This number n will be part of your public key and private key . ✅ Compute Euler’s totient: ϕ ( n ) = ( p − 1 ) ( q − 1 ) = ( 3 − 1 ) ( 11 − 1 ) = 2 × 10 = 20 phi(n) = (p-1)(q-1) = (3-1)(11-1) = 2 × 10 = 20 ✅ Choose public exponent e: e must be coprime with 20. Let’s pick e = 3. Public Key = (e, n) = (3, 33) ✅ Compute private expon...

  POLYNOMIAL OF DEGREE 5 KEYS OF THE UNIVERSE - Awesome booklets on amazon let’s do a very simple example of a Reed–Solomon code , in clear terms. Reed–Solomon codes can look scary because they use finite field arithmetic , but the concept is quite intuitive: You treat your data as a set of numbers and fit a polynomial through them. Then you send extra points on the curve so the receiver can reconstruct the polynomial, even if some points are missing or wrong. We’ll keep it super basic. 🎯 Tiny Example ✅ Scenario Message to send: 3 numbers Goal: Be able to recover if 1 of them gets corrupted. ✅ Step 1: Data as polynomial coefficients Suppose your 3 data symbols are: [5, 3, 2] You can treat them as coefficients of a polynomial: P ( x ) = 5 + 3 x + 2 x 2 P(x) = 5 + 3x + 2x^2 This is a degree-2 polynomial (because there are 3 coefficients). ✅ Step 2: Evaluate the polynomial at known points Pick 5 points (more than needed) to create redundancy. Let’s pick ...

  KEYS OF THE UNIVERSE - Awesome booklets on Amazon 🎯 What Is Error Correction? When you send or store data (text, audio, video), sometimes errors creep in : Noise in a communication line (like static on a phone call). Scratches on a CD. Weak Wi-Fi signal. Error correction means: Detecting if something got corrupted. Fixing it, if possible, without asking for the data again . 🌱 Basic Idea When you send data, you also send extra information (redundant bits) that help the receiver: Check whether the data was received correctly. Reconstruct any missing or flipped bits. 🛠️ Two Main Concepts Error Detection You can only tell that something is wrong. Example: parity bits, checksums. Error Correction You can figure out what was wrong and fix it. Example: Hamming codes, Reed-Solomon codes. ✏️ How Does It Work? (Analogy) Imagine sending a short message on paper: HELLO To protect it, you add: A parity bit : “I have...

  KEYS OF THE UNIVERSE - Awesome booklets on Amazon 🎯 What Does “Text Compression” Mean? Text compression means reducing the number of bits needed to store or transmit text , without losing the information (or with acceptable loss in some cases). Imagine you have a book with 1 million characters . Instead of storing each character in a fixed 8 bits (1 byte), you can find patterns to represent the same content with fewer bits. 🌱 Two Main Types of Text Compression Lossless Compression No information is lost. You can always reconstruct the exact original text . Used for text files, code, documents. Examples: ZIP, GZIP, PNG for images. Lossy Compression (rare for plain text) Some information is discarded. Not typically used for text because even a small change may change meaning. More common in audio/video compression. ⚙️ How Does Lossless Text Compression Work? There are many methods, but the main idea is finding redundancy —repeated patter...

 🎨 How a Picture is Compressed (JPEG) – Simply Explained Imagine you have a big photo and you want to make the file size smaller. JPEG compression does this in smart steps : ✨ Step 1: Separate Brightness and Color Your eyes care much more about brightness than precise color. So, the image is split into: Brightness layer (Y) Color layers (Cb and Cr) 👉 Why? Because we can * reduce color detail without you noticing much. ✨ Step 2: Reduce Color Detail The color layers are shrunk in resolution (less pixels). For example, 4 pixels of color can be replaced by 1 average color. This alone saves a lot of data. ✨ Step 3: Break Into Small Blocks The picture is cut into small 8×8 pixel squares. Think of cutting a photo into little tiles. ✨ Step 4: Turn Pixels Into Frequencies Each 8×8 block is converted into frequencies using math called DCT (Discrete Cosine Transform). This shows: Big changes (like edges) Small changes (t...

 🎵 What does “compressing music” mean? Compression means reducing the file size of an audio recording so it takes up less space (for example, turning a 50 MB song into a 5 MB MP3). This is different from dynamic range compression , which adjusts loudness. Here, you’re asking about data compression (making files smaller). 🎯 How is music compressed? (Digital audio compression) Most audio compression works by removing information that your ears don’t easily notice , using psychoacoustics—the science of how humans perceive sound. 🔑 Main Steps in Music Compression: 1️⃣ Splitting into frequency bands The sound is broken down into lots of frequency slices (like a prism splitting light into colors). This is called a transform , usually the Modified Discrete Cosine Transform (MDCT) . 2️⃣ Psychoacoustic model finds what can be discarded Your ear can’t hear quiet sounds that are masked by loud sounds nearby in frequency (called masking ). Example: a loud drum hit ...