What is a digital signature?
A digital signature is exactly what it sounds like: a way for individuals to digitally sign a document so that a recipient can verify that it was the individual who signed and not another person.
What is a digital signature used for?
It’s like if I have a secret password that controls my money. I want to send some money to another person. I can prove to them that it’s my money if I show them my password, but if I do that, they will know my password and have the ability to control my money. So digital signatures use cryptography so that I can show someone my lock. And only my key can open the lock. I don’t need to show them my key, all I need to do is show them that I have the ability to unlock that lock because they know that only my key can unlock that lock. So that’s what a digital signature is.
Why is a digital signature secure?
Cryptographic hash functions are used to prove that a digital signature is valid. The recipient is given a SHA-256 Output and half of an input. Remember, I mentioned that one input will always result in the the same output, but two different inputs will not result in the same output. So when someone takes the public input and combines it with their secret input, then puts it into the SHA-256 hash function, they get a specific output. And in this way, the digital signature has been verified without giving up the secret input.
How do digital signatures work?
Digital signatures use elliptical curve mathematics, which is covered in another section. Elliptical curves allow one person to choose a starting point and then perform a one way operation to create a second point such that it is it not possible to find the first point from the finial derived point.
If you want an explanation of how digital signatures work specifically in Bitcoin, Coindesk provides a great beginner friendly explanation. Check it out here.
The following diagram comes from the Bitcoin Whitepaper, written by Satoshi Nakamoto. It explains how digital signatures are utilized within the Bitcoin blockchain.