🗣️ The Whisper Game

Why Group Messaging is Hard

In 10 minutes: Understand why encrypting group chats is challenging
Prerequisite: Curiosity

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🎯 The Simple Story

Remember playing the "whisper game" as a kid?

Alice whispers a secret to Bob. Bob whispers it to Charlie. Charlie whispers it to David.

By the end, the secret is completely wrong

This is the exact problem with secure group messaging

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🧠 Mental Model

Hold this picture in your head:

The Whisper Game:

Alice → Bob → Charlie → David
     ↓       ↓        ↓
  Cat  Hat  Bat??

Each whisper goes through the next person.
Each person hears something different.
Each person has their own version

Problem: Can't agree on one secret

Think of encryption the same way:

Encrypted Group Chat (Naive):

Alice encrypts to Bob   → Bob gets his message
Alice encrypts to Charlie → Charlie gets his message
Alice encrypts to David → David gets his message
Bob encrypts to Alice   → Alice gets her message
Bob encrypts to Charlie → Charlie gets his message
...

Each person gets their own encrypted message version
Each encryption uses different keys
LOTS of work

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📊 See The Problem

Let's watch how this gets out of hand:

Look at all those arrows

For 4 people, that's 12 separate encrypted messages for ONE conversation

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🎮 Try It Yourself

Question 1: For a group of 5 people, how many separate encryptions does Alice need to send one message to everyone?

Show Answer

formula: n × (n-1)

For 5 people:

• Alice encrypts to Bob (1)
• Alice encrypts to Charlie (2)
• Alice encrypts to David (3)
• Alice encrypts to Eve (4)
• Bob encrypts to Alice (5)
• Bob encrypts to Charlie (6)
• Bob encrypts to David (7)
• Bob encrypts to Eve (8)
• Charlie encrypts to Alice (9)
• Charlie encrypts to Bob (10)
• Charlie encrypts to David (11)
• Charlie encrypts to Eve (12)
• David encrypts to Alice (13)
• David encrypts to Bob (14)
• David encrypts to Charlie (15)
• David encrypts to Eve (16)
• Eve encrypts to Alice (17)
• Eve encrypts to Bob (18)
• Eve encrypts to Charlie (19)
• Eve encrypts to David (20)

Answer: 20 separate encrypted messages

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Question 2: For a group of 100 people, how many separate encryptions per message?

Show Answer

formula: n × (n-1)

For 100 people: 100 × 99 = 9,900

Answer: 9,900 separate encrypted messages

That's almost 10,000 encryptions for ONE message

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Question 3: If you send 100 messages in a 100-person group, how many total encryptions?

Show Answer This

9,900 encryptions per message × 100 messages = 990,000 total encryptions

Almost 1 million encryptions just for 100 messages

This is the n² problem - it explodes quickly

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🔢 The Math

The n² Problem

For a group of n people, sending one message to everyone requires:

$Encryptions = n \times (n - 1)$

Let's see how fast this grows:

Group Size (n)	Encryptions Per Message	For 100 Messages
2	2	200
3	6	600
4	12	1,200
5	20	2,000
10	90	9,000
20	380	38,000
50	2,450	245,000
100	9,900	990,000
1,000	999,000	99,900,000

See how it explodes?

For 1,000 people, you'd need almost 1 million encryptions per message

That's 100 million encryptions for 100 messages

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💡 Why This Matters

Real-World Impact

Imagine WhatsApp with 1 million users:

Naive approach: Encrypt to each person separately
- For 1 group chat of 50 people = 2,450 encryptions
- For 10,000 group chats = 24,500,000 encryptions
- Per message

Server load:
- Too many encryptions = slow
- Too many encryptions = expensive
- Too many encryptions = users leave

MLS Solution:

MLS approach: Encrypt once for group
- For 1 group chat of 50 people = 1 encryption
- For 10,000 group chats = 10,000 encryptions
- Per message

That's 2,450x LESS work

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✅ Quick Check

Can you explain the whisper game problem to a 5-year-old?

Try saying this out loud:

"Imagine you're playing whisper game with 10 friends. You tell your secret to each person separately. For 10 friends, you have to whisper 10 times But if you could put all 10 friends in one room, you'd only need to whisper once!"

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🎓 Key Takeaways

✅ Whisper game = Each person gets their own version
✅ Current group chat = Encrypt separately to each person
✅ n² problem = Encryptions grow exponentially
✅ 100 people = 9,900 encryptions per message
✅ MLS solution = Encrypt once, everyone gets it
✅ Efficiency = O(n²) vs O(n) big difference

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🎉 What You'll Learn Next

Now you understand the problem Next, we'll learn what makes secure group messaging work:

🎖️ Continue: The Three Rules

We'll learn about the three security rules every group chat must follow

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Now you understand why group encryption is hard. Next: The rules for secure group messaging