Some days you just wake up curious. Today when this video showed up in my feed, I had some questions about TLS protocol.

This took my down a rabbit hole of how Symmetric Key Derivation algorithms work. I’m sharing a succinct and paraphrased version of that conversation with gpt-4o:

Q: You are an expert in TLS protocol. Which keys are used to encrypt my HTTPS traffic?

  • Neither the public key nor the private key (asymmetric keys used to sign and validate certs) directly encrypts the actual traffic.
  • They are used during the handshake to establish a symmetric key.
  • The symmetric session key is then used to encrypt the actual data.

Q: Can you dive deeper into how symmetric session keys are used to encrypt traffic?

… Yes, the actual traffic is encrypted, but not with public/private keys. It’s encrypted using a symmetric encryption algorithm (like AES) after the TLS handshake is complete.

Let’s dive deeper into how this works:

1. Purpose of Public/Private Keys (Asymmetric Encryption)

  • Used only during the handshake phase of a TLS connection.
  • Enables:

Why not use public/private keys for actual data encryption?

  • Performance: Asymmetric encryption is computationally expensive and slower.
  • Security Best Practices: Symmetric encryption is faster and more suitable for large data volumes like website content.

2. Actual Traffic Encryption (Symmetric Encryption)

Once the handshake is complete:

  • A shared symmetric key (or a set of keys) is agreed upon.
  • From then on, all HTTP traffic is encrypted with this symmetric key, using algorithms like:

🔑 How Is the Symmetric Key Established?

It depends on the key exchange algorithm:

Modern TLS (using ECDHE):

  • Both sides generate ephemeral key pairs (private + public).
  • They exchange public parts.
  • Each side uses their private key + the other’s public key to derive the same shared secret (via elliptic curve math).
  • This shared secret is passed through a Key Derivation Function (KDF) to generate:

Q: What are the characteristics of symmetric keys?

🛡️Summary

  • 🔁 Same key is used for both encryption and decryption
  • ⚡ Very fast and efficient
  • 🔢 Typically 128–256 bits (longer = more secure)
  • 🔒 Must be securely exchanged or derived
  • 🌐 Used in TLS to encrypt actual traffic after handshake
  • 🔧 Common algorithms include AES and ChaCha20

Q: How difficult is it to get hold of session keys and why is it difficult?

🛡️Summary

  • ☠️ Session key compromise is fatal — all traffic can be decrypted
  • 🛡️ Extremely difficult to obtain the session key
  • 🧠 Session key is never sent, is ephemeral, exists only in RAM, and is derived via secure ECDHE math
  • 🚫 Attacker’s best chances are malware, memory scraping, or exploiting bugs (which are rare and detectable)

Q: You mentioned earlier that both parties use the same session key. However you also say that keys are never actually transmitted. How is that possible?

✅ Short Answer:

  • Yes, both client and server use the same session key(s).
  • But this session key is never transmitted over the network.
  • Instead, both parties independently derive the same session key, using secure mathematical operations during the key exchange phase.

🔑 Summary: Same Key, But Not Shared Explicitly

  • 🔑 Symmetric session key is the same on both client and server
  • 📵 It is never transmitted over the network
  • 🧮 Each party derives it using ECDHE math on exchanged public keys and their own private key
  • 🔐 Security benefit: even if someone intercepts all traffic, they can’t compute the key without a private key

Q: How is it possible that same exact secret is generated when a public key and a different private key (which could be anything) goes into a mathematical function?

That’s an excellent and deep question — and it’s the heart of Elliptic Curve Diffie-Hellman (ECDH) key exchange.

It does seem strange at first:

How can two parties, each using a different private key, and the other’s public key, end up computing the exact same secret?

Let’s walk through it mathematically but intuitively.

🔐 TL;DR:

  • The shared secret is the result of a scalar multiplication of elliptic curve points.
  • Due to the commutative nature of the math (like a × b = b × a), both parties arrive at the same result independently.
  • The result is the same because of how elliptic curve point multiplication works.

🔐 Final Insight

ECDH works because both parties use their own private key + the other’s public key to derive the same point — and the math ensures that the result is identical.

They don’t need to know each other’s private keys — they just rely on shared public information and the hard math problem underneath.

— Conversation Over —

That last bit about ECDH algorithm was fascinating! I hope you got to learn something from this as well.