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Private Keys, Public Keys, and Digital Signatures
What do all these terms mean?
Here& #39;s a high level overview of the basics, and how they help us do cool things especially in bitcoin
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What do all these terms mean?
Here& #39;s a high level overview of the basics, and how they help us do cool things especially in bitcoin
A Private Key is just secret number
Thats all
It& #39;s just a really large random number - so large that it can& #39;t be guessed by anyone
Thats all
It& #39;s just a really large random number - so large that it can& #39;t be guessed by anyone
In bitcoin, private keys can be any number between 0 and 2^256
To get a sense of how many choices there are, 2^256 is roughly the number of atoms in the known universe
To get a sense of how many choices there are, 2^256 is roughly the number of atoms in the known universe
So if you use a good random number generator to pick a number between 0 and 2^256, it& #39;s basically impossible for anyone to guess what the number is
Once you have a Private Key, you can then calculate its Public Key
You do this by multiplying the Private Key by a set number that everyone has agreed upon (we call this set number G - the "Generator" point)
You do this by multiplying the Private Key by a set number that everyone has agreed upon (we call this set number G - the "Generator" point)
Now there are a couple important catches here..
This isn& #39;t regular multiplication...
Its a fancy type of multiplication that uses a special number system (which I won& #39;t get into here)
In this number system, multiplication is easy, but DIVISION is IMPOSSIBLE
This isn& #39;t regular multiplication...
Its a fancy type of multiplication that uses a special number system (which I won& #39;t get into here)
In this number system, multiplication is easy, but DIVISION is IMPOSSIBLE
The important point is that if you have a just Public Key, there is no way to figure out the Private Key
You can& #39;t just divide it by G, because in this number system, division is impossible
(This number system is an Elliptic Curve over a Finite Field, aka "fancy math")
You can& #39;t just divide it by G, because in this number system, division is impossible
(This number system is an Elliptic Curve over a Finite Field, aka "fancy math")
Let& #39;s not go too far into the math, but let& #39;s recap:
- Private key is a secret number
- Public key is also basically a number, and you get it by multiplying the private key by G
- Division is impossible, so you cannot figure out the Private Key if you only know the Public Key
- Private key is a secret number
- Public key is also basically a number, and you get it by multiplying the private key by G
- Division is impossible, so you cannot figure out the Private Key if you only know the Public Key
The nice thing about Public Keys is that you can safely share them with everyone
So they function kind of like your digital identity
So they function kind of like your digital identity
So what can we do with this now?
Imagine I own 1 Bitcoin and I& #39;d like to send it to my friend @SahilBloom
In order to send this coin, I need a way to "prove" to the network that I am the rightful owner of this coin and authorize it& #39;s transfer
Imagine I own 1 Bitcoin and I& #39;d like to send it to my friend @SahilBloom
In order to send this coin, I need a way to "prove" to the network that I am the rightful owner of this coin and authorize it& #39;s transfer
This is where Digital Signatures come into play
I first create a message (in this case its a bitcoin transaction) that says:
"I, the owner of Danny& #39;s Public Key, authorize the sending of this 1 Bitcoin to the owner of Sahil& #39;s Public Key"
I first create a message (in this case its a bitcoin transaction) that says:
"I, the owner of Danny& #39;s Public Key, authorize the sending of this 1 Bitcoin to the owner of Sahil& #39;s Public Key"
Now I need to prove to everyone that I created this message
This proof is called a Digital Signature.
I basically just put my Private Key and the Message into an equation, and out pops another number - the Signature!
This proof is called a Digital Signature.
I basically just put my Private Key and the Message into an equation, and out pops another number - the Signature!
The cool thing about this number (Signature), is that anybody can look at the Signature, the Message, and the Public Key, plug them into another simple equation..
If the math checks out, they can be 100% sure that the owner of the private key is the one who created the signature
If the math checks out, they can be 100% sure that the owner of the private key is the one who created the signature
In other words, the Signature is mathematical proof that owner of the Private Key has authorized the Message!
Those are the basics of Private Keys, Public Keys, and Digital Signatures
These elements of cryptography are used everywhere in software and the internet (not just bitcoin), and are a great example of the powers the fancy math gives us
These elements of cryptography are used everywhere in software and the internet (not just bitcoin), and are a great example of the powers the fancy math gives us
Unfortunately I& #39;ve hand-waved over the wonderful math that makes this all possible...
For more info on that, you can research "Elliptic Curves over Finite Fields"
The Math isn& #39;t too complicated, it& #39;s just very different from what they teach us in school
For more info on that, you can research "Elliptic Curves over Finite Fields"
The Math isn& #39;t too complicated, it& #39;s just very different from what they teach us in school
Hope that was helpful!
Let me know if I got anything wrong - I really appreciate all the feedback in the commentshttps://abs.twimg.com/emoji/v2/... draggable="false" alt="đ" title="Grinsendes Gesicht" aria-label="Emoji: Grinsendes Gesicht">
Let me know if I got anything wrong - I really appreciate all the feedback in the comments
