What are digital keys?

All common approaches to digital signatures use what is called Public Key Cryptography. In Public Key Cryptography, there are two keys: one public and one private. To create a signature, the first hash is produced of the original data, and then the private key is used to encrypt that hash. That encrypted hash, along with other information, such as the encryption method used to become part of the signature, are attached to the original data.

This is where the public key comes into play. The mathematical link between the public key and the private key allows the public key to decrypt the hash, and then the hash can be used to check the data. Thus, two things can now be checked: who signed the data and that the data that was signed has not been altered. The following is a diagrammatic representation of the same:

This form of cryptography is critical to blockchain technology. Through hashing and digital signatures, a blockchain is able to record information both on actions (movement of tokens) as well as prove who initiated those actions (via digital signatures). 

Let's create an example of how this would look. Jeremy and Nadia wish to send messages to each other securely. Each publishes a public key. Jeremy's will look something as follows (using an RSA algorithm with 1,024 bits):

-----BEGIN PUBLIC KEY-----
MIGeMA0GCSqGSIb3DQEBAQUAA4GMADCBiAKBgH+CYOAgKsHTrMlsaZ32Gpdfo4pw
JRfHu5d+KoOgbmYb0C2y1PiHNGEyXgd0a8iO1KWvzwRUMkPJr7DbVBnfl1YfucNp
OjAsUWT1pq+OVQ599zecpnUpyaLyg/aW9ibjWAGiRDVXemj0UgMUVNHmi+OEuHVQ
ccy5eYVGzz5RYaovAgMBAAE=
-----END PUBLIC KEY-----

With that key, he will keep private another key, which looks as follows:

-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

In the meantime, Nadia will do the same, resulting in the following two keys:

-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDHWwgTfI5Tic41YjUZqTmiKt+R
s5OMKIEdHPTyM8FZNaOBWIosFQbYk266V+R7k9odTnwCfi370GOt0k5MdTQilb9h
bK/lYiavIltgBd+1Em7xm7UihwO4th5APcg2vG4sppK41b1a9/I5E6P/jpQ320vF
BMuEtcnBoWawWcbXJwIDAQAB
-----END PUBLIC KEY-----

This is her private key:

-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

With these keys, Jeremy decides to send a message to Nadia. He uses her key and encrypts the following message: I love Bitcoin, which results in the following data:

EltHy0s1W1mZi4+Ypccur94pDRHw6GHYnwC+cDgQwa9xB3EggNGHfWBM8mCIOUV3iT1uIzD5dHJwSqLFQOPaHJCSp2/WTSXmWLohm5EAyMOwKv7M4gP3D/914dOBdpZyrsc6+aD/hVqRZfOQq6/6ctP5/3gX7GHrgqbrq/L7FFc=

Nobody can read this, except Nadia. Using the same algorithm, she inputs this data and her private key, and gets the following message:

I love Bitcoin.

We'll discuss more about this topic in Chapter 4, Cryptography and the Mechanics Behind Blockchain.