Establishing Trust Between Computers

In the Middle Ages, kings used a royal seal to prove a document came from them. A royal seal was simply an elaborate design that was pressed into melted wax that sealed the letter. In order to open the letter, the receiver had to break the wax seal. It was assumed that once broken, the seal couldn’t be put back together again.

Royal Wax Seal

The seal had 2 purposes as follows:

1. 1. The seal’s elaborate design validated the letter had come from the king.
2. 2. If the wax seal was intact, it was assumed that no one else had opened the letter.

In modern times, cryptographic keys are used as the royal seal and we don’t need to be kings or queens to have our own keys.

It is useful to think of keys as coming in pairs – a private key and a public key. The public key actually comes from the private key but they are not the same number. The neat part is that you can generate multiple public keys from a private key which is very useful for Bitcoin transactions as we’ll see below.

Another important characteristic is that creating a public key from a private key is a one-way function. In other words, you can’t get the private key back from the public key.

Explain One-Way Function Cryptography as ELI5?

Wikipedia describes a one-way function as easy to calculate if you know the input but hard to reverse-engineer if you don’t know the input.

Bitcoin has a lot of complex math but to show the idea, we’ll use a simpler example.

Let’s use remainders as an example. Let’s say our equation is: divide by 10 and use the remainder for the public key.

In this example, we’ll say our private key is 297. Now according to the equation we need to divide by 10 and use the remainder.

297 / 10 = 29 with a remainder of 7.

So our private key is 297 and our public key is 7.

Can we figure out the private key from the public key? Well, sorta but it could take many iterations to find.

If we know the equation and the public key, the private key could be 7, 17, 27, 37, 47, 57 … and so on up into the millions. You would need to check every one to see if it is the private key. You get the picture and this is a simple example. With large numbers it just isn’t worth it.

Another use of one-way cryptographic functions is with hash functions. Hash functions are used to represent a number with a smaller number. In the example above, 123456 could be represented by 6 as well.

Back to Private and Public Keys

Either key can decode a message that was encoded with the other key. Normally, a private key is used to encode the message and a public key is used to decode the message.

If Alice is sending Bob a message, she will send him the public key initially.

Then Alice will write a message.

Hi Bob. 
This is Alice and when you decode this message with the 
public key, you'll see it is me and can verify this message came
from me.
Alice

Then Alice will encrypt the message with her private key giving this:

-----BEGIN PGP MESSAGE-----
Version: OpenPGP v2.0.8
Comment: https://sela.io/pgp/
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=8TVh
-----END PGP MESSAGE-----

Using the RSA public and private key generator.

Alice will then send the encrypted message to Bob. If it is intercepted, it won’t be readable.

When Bob receives the message, he unscrambles the message with the public key Alice sent him earlier. Bob can trust that the message came from Alice because Alice’s public key unscrambles the message.

… which gets us back to how private and public keys are used in Bitcoin transactions…

Private and Public Keys in Bitcoin Transactions

So how are private and public keys used in Bitcoin transactions? Answer: They are used to establish trust.

Trust

Each transaction has

• inputs
• outputs
• a signature

Inputs

The inputs are the outputs from previous transactions. The sum of these inputs should add up to the outputs.

Outputs

The receiver must provide a Bitcoin address to the sender. The sender’s public key is converted with a hashing function into a Bitcoin address. The hashing function shortens the public key and obscures it to help prevent hacks until the full public key is revealed.

A Signature

To prove that the inputs of the transaction belong to the sender, the public key that created the Bitcoin address is revealed. This public key is passed through the hashing function to confirm the hashed result matches the Bitcoin address.

The private key is used to create a signature. The same public key that is revealed above can be used to decode the signature. If the public key decodes the signature it proves that the private key was used to encode the signature.  Notice that the private key never has to be revealed so it stays secret the entire time.

This is similar to the wax seal establishing trust as described above.

Using A Computer to Verify

As we discussed above, a Bitcoin Node verifies the sender has a legitimate Bitcoin balance to send in a transaction by

1. Verifying the Bitcoin address used by the inputs to the transaction match the public key.
2. Verifying the public key can decode the signature – which means the sender owns the private key as well.

Bitcoin Transaction Example

At the beginning of this transaction, assume Alice has 2 Bitcoin and Bob has no Bitcoin.

To start, Bob needs to tell Alice where to send the Bitcoin. He will normally generate a receive address from his Bitcoin wallet. The receive address is a special form of a generated public key.