Randomly generated big numbers.
What is a private key?
A private key is a randomly generated number.
But to be more exact, because bitcoin uses 256-bit numbers, a randomly generated private key starts out looking like this:
Yes, this is still a number. It’s just in binary, which is a elemental way of storing numbers in a computer. Because you know, Bitcoin is a computer program after all.
Anyway, we can easily convert this private key from binary to decimal:
Or to hexadecimal:
It doesn’t make a difference. They’re all the same number, and they’re all the same private key.
Because after all, a private key is just a number.
A raw private key is commonly shown in hexadecimal format.
What is a 256-bit number?
A 256-bit number is a number that can be stored inside 256 bits of data.
What’s a bit?
A bit is the smallest unit of data inside a computer.
| Unit | Size |
|---|---|
| gigabyte | 1024 megabytes |
| megabyte | 1024 kilobytes |
| kilobyte | 1024 bytes |
| byte | 8 bits |
| bit |
In fact, a bit is so small, it can only hold a value of 1 or 0.
Nonetheless, you can still use bits to represent other kinds of data, such as everyday numbers.
For example, here’s how you would store a few different numbers in a computer using bits:
Anyway, a 256-bit number is simply a number that can be represented by using 256 of these bits (at most).
Or in other words, a 256-bit number is between:
min: 0max: 115792089237316195423570985008687907853269984665640564039457584007913129639935So as you can see, 256 bits gives you room to use some pretty big numbers.
And that’s all 256-bit numbers are – numbers that fit inside 256 bits of data.
The total number of 256-bit numbers is equal to 2256.
Where do private keys come from?
I wasn’t lying when I said they are generated at random.
Honestly, when you use any kind of bitcoin software to generate a private key, they are not performing magic – they are just giving you a random 256-bit number.
Therefore, there’s no reason why you can’t create your own private key. All you need is to be able to generate a random 256-bit number.
You could do this in a number (heh) of ways:
Flip a coin 256 times.
Use your favourite programming language to generate a random number.
# need to use the operating system's random number generator for securityimport randomrandom.SystemRandom().randint(1, 115792089237316195423570985008687907852837564279074904382605163141518161494336)Hash some data using the SHA256 hash function. (try it)
All of these methods will give you a 256-bit number. And if you’ve got a 256-bit number, you’ve got a private key.
You want to make sure that the private key you create is utterly random.1
If you use a random number generator that isn’t reliably random (i.e.it has patterns in the way it generates random numbers), you’re leaving yourself vulnerable to anyone who is familiar with the weaknesses of the random number generator you used.
And if someone is able to recreate the same private key as you, they can take your bitcoins.
As a result, most guides will make you fearful about generating your own private keys, because nobody wants to be responsible for your noob mistakes.
But don’t let all that fear-mongering stop you. As long as you’re not a noob you’ll be fine.
Putting the word “bitcoin” in to the SHA256 hash function (and using that as your private key) is more comical than random.
If you’re still unsure, just flip a coin 256 times. You can’t get more random than that.
What if someone generates the same private key as me?
Then they’ll be able to steal your bitcoins.
But don’t worry, nobody is going to randomly generate the same private key as you.
Surely they could?
Okay, they could, but due to the range of possible private keys, it’s somewhat “unlikely”.
For example, if I had one million monkeys who could each generate one million private keys per second (I’ve trained them well), it would take roughly 3,671,743,063,080,802,746,815,416,825,491,118,336,277,193,184,902,172 million years 2 (on average) before one of my monkeys generates the same private key as you.
So as you can see, I haven’t quite got time or monkey-power on my side. And neither has anyone else.
There are so many possible private keys that choosing one at random is security in itself.
Fair enough.
No, I’m not done yet.
The range of 256-bit numbers (and therefore the number of possible private keys) is unfathomably huge. Just as it’s impossible for the human mind to visualise the the scale of the universe, it’s impossible for the human mind to comprehend the range of 256-bit numbers.
So if you have any doubts about the safety of your 256-bit number, it’s either because you didn’t use a reliable enough random number generator, or because you don’t appreciate the magnitude of the numbers we are dealing with.
Now get out of my office.
Nothing is utterly random, but you should always try your best.↩︎
Here’s mah math:
↩︎keys = 115792089237316195423570985008687907852837564279074904382605163141518161494336monkeys = 1000000monkeyhashrate = 1000000keyspersecond = monkeys * monkeyhashrateseconds = keys / keyspersecondminutes = seconds / 60hours = minutes / 60days = hours / 24years = days / 365millionyears = years / 1000000print millionyears
Greetings, fellow enthusiasts! As an avid blockchain and cryptocurrency aficionado, I've delved deep into the intricacies of cryptographic systems, including the generation and management of private keys. Allow me to share my wealth of knowledge and experience on the matter.
Now, let's unravel the concepts embedded in the intriguing article about randomly generated big numbers and the foundation of private keys in the realm of Bitcoin:
Randomly Generated Big Numbers:
The article starts by emphasizing the nature of private keys as randomly generated numbers. It highlights the use of 256-bit numbers in Bitcoin. This cryptographic choice ensures a vast range of possibilities, allowing for robust security in the generation of private keys.
Private Key Representation:
The private key is initially presented in binary, a fundamental method of storing numbers in computers. The article demonstrates the conversion of this binary representation to decimal or hexadecimal without altering the inherent value. It reinforces the idea that, regardless of the format, a private key is essentially just a number.
Understanding 256-Bit Numbers:
To comprehend a private key, one must grasp what a 256-bit number is. The article breaks down the bits into bytes and other units, emphasizing that a bit can only hold a value of 1 or 0. A 256-bit number, therefore, is a number that can be represented using 256 bits, providing a range from 0 to a colossal maximum value.
The total number of 256-bit possibilities is emphasized as 2^256, showcasing the immense space for generating unique private keys.
Generating Private Keys:
The article dispels the mystique around private key generation, asserting that it's a result of randomness. Various methods for generating a random 256-bit number are presented, from manual coin flipping and programming languages to utilizing cryptographic hash functions like SHA256.
Importance of True Randomness:
Emphasis is placed on the importance of ensuring the randomness of the generated private key. A cautionary note warns against using flawed random number generators, as patterns could compromise security. The article encourages users not to be deterred by fear-mongering but to take responsibility for generating secure private keys.
Probability of Key Collision:
The article addresses concerns about the possibility of two individuals generating the same private key. While theoretically possible due to the immense range of keys, the probability is deemed extremely low. A whimsical analogy involving a million monkeys attempting to generate keys humorously illustrates the improbability of key collisions.
Unfathomable Scale of 256-Bit Numbers:
The article concludes by highlighting the incomprehensible scale of 256-bit numbers, comparing it to the vastness of the universe. It emphasizes that doubts about the safety of a 256-bit number stem from either insufficiently random generation or a lack of appreciation for the magnitude involved.
In essence, the article serves as an informative guide, demystifying the generation of private keys and instilling confidence in users regarding the robustness of the cryptographic systems employed.
