A digital signature to prove ownership

Blockchain makes heavy use of digital signatures to authenticate transaction initiators. The following points are relevant here:

Blockchain networks use modern data encryption technology. This is the foundation of the users’ digital signatures.
Popular public blockchain networks like Bitcoin or Ethereum use the “public key-private key encryption”.
Users have two keys. One is the public key, which can be shared with others. The other is the private key, which users should always keep secret.
Users encrypt the message using the public key, whereas they decrypt the encrypted message using the private key. Read more about this in “What is public-key cryptography?”.
The public key is mathematically related to the private key.
One can use the encryption algorithm to easily create the public key from the private key. However, the reverse is simply impractical. Creating a private key from a public key will require so much computing power that today’s computers will literally take billions of years to complete. I touched on this point in an earlier article called “Quantum computing: will it kill blockchain?”.
Cryptocurrencies are mathematical money. A digital coin is, in effect, just a piece of information.
When cryptocurrency users get a blockchain wallet to store their cryptocurrencies, they set up their public and private keys. A good example is “eth-lightwallet”. From that point onwards, they only need to secure their private key.
They can sign their transactions using their digital signature, and that completes the authentication process.
Proving the ownership of a digital coin actually boils down to proving the ownership of that piece of information. Digital signatures and wallets enable users to guard this information.
Now, look beyond cryptocurrencies. You will find the same concept of user authentication using digital signatures in enterprise blockchains.
Enterprise blockchains like Hyperledger Fabric (Fabric) don’t operate cryptocurrencies. However, these networks still deal with information. Users create this information. There are other users that consume the information. Note: Fabric uses digital signatures and even provides a “Hardware Security Model” (HSM), i.e., hardware-based enhanced security for digital signatures. Read more about this in “Pros and cons of Hyperledger Fabric for blockchain networks”.