16.3. Architecture of Public Key Cryptosystem

So, let us see the architecture of public key cryptosystem. So, in this system, the receiver will have 2 keys, a key which we call us public key, pk available in the public domain. And there will be another key, sk which will be secret key and available only with the receiver. Now in this system, any person who wants to encrypt a message for this receiver will look for the copy of the public key in some public domain, say for example, a telephone directory or the homepage of the receiver.

In a public key cryptosystem, the architecture consists of two keys for the receiver: a public key (pk) and a secret key (sk). The public key is accessible to everyone, while the secret key is kept private and known only to the receiver. This allows anyone to encrypt messages meant for the receiver using the public key. The encrypted message can then only be decrypted by the receiver using their secret key.

Imagine you have a locker at a bank. The public key is like the bank's address which anyone can find to send letters (encrypted messages), but only you have the key (the secret key) that opens that locker to read the letters.

Once the public key copy is available to the sender and sender has the plain text m, he will use the encryption algorithm and produce a cipher text or the scrambled text which is communicated to the receiver. Receiver upon receiving the scrambled text, will now use a different key, namely the secret key which is available only with the receiver and he will decrypt and recover back the message m.

After the sender obtains the public key, they can take a message (plain text) and use an encryption algorithm to convert it into ciphertext, which is a scrambled version of the original message. This ciphertext is then sent to the receiver. When the receiver gets the ciphertext, they use their secret key to decrypt this message and retrieve the original plain text.

Continuing with our bank locker analogy, when someone sends you a letter, they lock it in the box using your public address (public key). When you receive the locked box, you use your personal key (secret key) to unlock it and read your letter inside.

And now the security property that we require here is that if there is a third party an attacker, who knows the description of the public key, who knows the description of the encryption algorithm, who knows the description of the decryption algorithm and who also knows the description of the cipher text, should not be able to figure out what exactly in the underline message.

For a public key cryptosystem to be secure, it is crucial that even if an attacker knows the public key, the encryption and decryption algorithms, and the ciphertext, they cannot decipher the original message. This requirement ensures that the secret key remains unknown and while the encryption process is public, the actual content of the message stays private.

Imagine a treasure box locked with your special key (secret key). Even if someone sees the box (ciphertext) and knows how it's locked (encryption method), they can’t open it because they don’t have your key. The contents inside remain safe and private from prying eyes.

So, the analogy that I can give here is the following, you can imagine that receiver has created multiple copies of a padlock, all of which can be opened using a single key. And now, the public key is nothing but copies of that padlocks, but in an open state.

This analogy simplifies the concept of public and secret keys. The receiver creates many padlocks (public keys) that anyone can use to secure their messages by locking the padlocks. However, only the receiver possesses the unique key (secret key) that can open these locks and reveal the messages. This demonstrates the core functionality of a public key cryptosystem.

Think of a mailbox where you have a special key. Anyone can drop their letters into that mailbox (encrypt a message using a public key), but only you can open the mailbox to retrieve your letters (decrypt messages using your secret key). This represents how public and secret keys work in a public key cryptosystem.

It has got tremendous potential in the sense that, now the whole problem of key distribution is easily solved. If I am a receiver, and if I am an amazon, for instance, I do not have to worry, who is the potential sender, he can be any entity from the world.

Public key cryptosystems address the key distribution problem effectively. Users can publish their public keys online and any potential sender can use it to send secure messages without needing to establish a secret key agreement beforehand. This method simplifies the process of secure communication.

Consider how you can send a birthday invitation digitally. Instead of every guest needing a special secret code to RSVP, they simply find your public email address (public key), and can respond whenever they want, without needing to coordinate beforehand.

So, even though Diffie and Hellman thought about this architecture, this new system, they failed to give a concrete instantiation. Namely, a concrete encryption algorithm, concrete decryption algorithm, a concrete mechanism of coming up with a public key and a concrete mechanism of coming up with a secret key.

The foundational ideas behind public key cryptography were introduced by Diffie and Hellman, but they did not develop a fully functional encryption system. Their work paved the way for later developments, where actual encryption algorithms and mechanisms for generating public and secret keys were designed.

Imagine an idea for a new type of lock that’s incredibly safe. However, until someone figures out how to make the key and produce the lock in a real-world setting, the idea itself remains just an interesting concept without practical use.

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