18.1.2. Private Key or Symmetric Key Encryption

In symmetric key encryption, it is ensured that a common key is already shared between Sita and Ram by some mechanism, say, by running a key agreement protocol and no one else apart from Sita and Ram knows the value of that key.

Symmetric key encryption works on the principle that both parties (in this case, Sita and Ram) share a common secret key, which they use for both encrypting and decrypting messages. This key must be securely shared using a key agreement protocol before any secure communication occurs.

Think of symmetric key encryption like a secret handshake between two friends. Once they've agreed on the handshake (the common key), they can communicate secretly without anyone else being able to understand their conversation.

Sita has some message abstracted as a binary string, we call her message as plain text. We want to design an encryption algorithm which takes a message m and the key k both of which are binary strings. It should produce another binary string which we call a ciphertext.

The encryption process transforms the plain text message into a ciphertext using the encryption algorithm and the shared key. This ciphertext appears as a random sequence of bits to an observer and is sent to Ram. Upon receipt, Ram utilizes a decryption algorithm—along with the same key—to convert the ciphertext back into the original plain text message.

Imagine Sita writes a message, puts it in a box, and locks it. The locked box represents the ciphertext. When Ram receives the locked box, he uses the same key to unlock it (the decryption process) and read Sita's message.

If there is a third party or Ravana, who knows the public description of your algorithm but does not know the value of key then even after observing the communication happening between Sita and Ram, Ravana should not be able to decode the message.

The security of symmetric key encryption relies on the secrecy of the key. Even if an unauthorized party (like Ravana) knows the encryption algorithm, they cannot decipher the messages without the key. This principle ensures privacy in communications.

Imagine if Ravana peeks at the locked box and sees it is closed. He knows that Sita sent something to Ram but cannot open the box without the specific key that both Sita and Ram possess, keeping the contents a secret.

How at the first place they can do that? […] The Turing Award winner, Diffie and Hellman, proved this belief to be incorrect, by coming up with their seminal key exchange protocol.

Before Sita and Ram can communicate securely, they need to establish a common key over a public channel without compromising its secrecy. The key exchange protocol devised by Diffie and Hellman allows Sita and Ram to collaboratively generate a key that remains private, even when communicated over insecure channels.

It's akin to two friends wanting to meet at a secret location without anyone else knowing where they're going. They publicly agree on a plan (the key exchange protocol) that enables them to covertly decide on the location without revealing it to anyone else who could be listening.

They observed that there are plenty of tasks in this universe which are asymmetric, they are asymmetric in the sense, they are very easy to compute in one direction but extremely difficult to reverse back.

The key exchange protocol utilized this principle of asymmetry, where certain mathematical operations are easy to perform but challenging to reverse. This forms the foundation of secure key exchanges, ensuring that even if an observer sees the exchanged messages, they cannot easily determine the original keys.

Consider how easy it is to lock a door but how difficult it becomes to unlock it without the key. The key exchange mechanism uses this concept to secure communication—what is easy for Sita and Ram is almost impossible for anyone else trying to decipher their communication.

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