In cryptocurrencies, a private key allows a user to gain access to their wallet. The person who holds the private key fully controls the coins in that wallet. For this reason, you should keep it secret. And if you really want to generate the key yourself, it makes sense to generate it in a secure way.

Here, I will provide an introduction to private keys and show you how you can generate your own key using various cryptographic functions. I will provide a description of the algorithm and the code in Python.

Do I need to generate a private key?

Most of the time you don’t. For example, if you use a web wallet like Coinbase or Blockchain.info, they create and manage the private key for you. It’s the same for exchanges.

The same private key, written in different formats. Why exactly 32 bytes? Great question! You see, to create a public key from a private one, Bitcoin uses the ECDSA, or Elliptic Curve Digital Signature Algorithm. More specifically, it uses one particular curve called secp256k1. Of course you can use Elliptic Curve cryptography to do public key encryption, that is, a method with a public key and a private key; anyone with the public key can encrypt, but only someone with the private key can decrypt. One way would be to use the Integrated Encryption System. It's does most everything for you (allowing the encryption of.

Mobile and desktop wallets usually also generate a private key for you, although they might have the option to create a wallet from your own private key.

So why generate it anyway? Here are the reasons that I have:

• You want to make sure that no one knows the key
• You just want to learn more about cryptography and random number generation (RNG)

What exactly is a private key?

Formally, a private key for Bitcoin (and many other cryptocurrencies) is a series of 32 bytes. Now, there are many ways to record these bytes. It can be a string of 256 ones and zeros (32 * 8 = 256) or 100 dice rolls. It can be a binary string, Base64 string, a WIF key, mnemonic phrase, or finally, a hex string. For our purposes, we will use a 64 character long hex string.

Why exactly 32 bytes? Great question! You see, to create a public key from a private one, Bitcoin uses the ECDSA, or Elliptic Curve Digital Signature Algorithm. More specifically, it uses one particular curve called secp256k1.

Now, this curve has an order of 256 bits, takes 256 bits as input, and outputs 256-bit integers. And 256 bits is exactly 32 bytes. So, to put it another way, we need 32 bytes of data to feed to this curve algorithm.

There is an additional requirement for the private key. Because we use ECDSA, the key should be positive and should be less than the order of the curve. The order of secp256k1 is FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141, which is pretty big: almost any 32-byte number will be smaller than it.

Naive method

So, how do we generate a 32-byte integer? The first thing that comes to mind is to just use an RNG library in your language of choice. Python even provides a cute way of generating just enough bits:

Looks good, but actually, it’s not. You see, normal RNG libraries are not intended for cryptography, as they are not very secure. They generate numbers based on a seed, and by default, the seed is the current time. That way, if you know approximately when I generated the bits above, all you need to do is brute-force a few variants.

When you generate a private key, you want to be extremely secure. Remember, if anyone learns the private key, they can easily steal all the coins from the corresponding wallet, and you have no chance of ever getting them back.

So let’s try to do it more securely.

Cryptographically strong RNG

Along with a standard RNG method, programming languages usually provide a RNG specifically designed for cryptographic operations. This method is usually much more secure, because it draws entropy straight from the operating system. The result of such RNG is much harder to reproduce. You can’t do it by knowing the time of generation or having the seed, because there is no seed. Well, at least the user doesn’t enter a seed — rather, it’s created by the program.

In Python, cryptographically strong RNG is implemented in the secrets module. Let’s modify the code above to make the private key generation secure!

That is amazing. I bet you wouldn’t be able to reproduce this, even with access to my PC. But can we go deeper?

Specialized sites

There are sites that generate random numbers for you. We will consider just two here. One is random.org, a well-known general purpose random number generator. Another one is bitaddress.org, which is designed specifically for Bitcoin private key generation.

Can random.org help us generate a key? Definitely, as they have service for generating random bytes. But two problems arise here. Random.org claims to be a truly random generator, but can you trust it? Can you be sure that it is indeed random? Can you be sure that the owner doesn’t record all generation results, especially ones that look like private keys? The answer is up to you. Oh, and you can’t run it locally, which is an additional problem. This method is not 100% secure.

Now, bitaddress.org is a whole different story. It’s open source, so you can see what’s under its hood. It’s client-side, so you can download it and run it locally, even without an Internet connection.

So how does it work? It uses you — yes, you — as a source of entropy. It asks you to move your mouse or press random keys. You do it long enough to make it infeasible to reproduce the results.

Are you interested to see how bitaddress.org works? For educational purposes, we will look at its code and try to reproduce it in Python.

Quick note: bitaddress.org gives you the private key in a compressed WIF format, which is close to the WIF format that we discussed before. For our purposes, we will make the algorithm return a hex string so that we can use it later for a public key generation.

Bitaddress: the specifics

Bitaddress creates the entropy in two forms: by mouse movement and by key pressure. We’ll talk about both, but we’ll focus on the key presses, as it’s hard to implement mouse tracking in the Python lib. We’ll expect the end user to type buttons until we have enough entropy, and then we’ll generate a key.

Bitaddress does three things. It initializes byte array, trying to get as much entropy as possible from your computer, it fills the array with the user input, and then it generates a private key.

Bitaddress uses the 256-byte array to store entropy. This array is rewritten in cycles, so when the array is filled for the first time, the pointer goes to zero, and the process of filling starts again.

The program initiates an array with 256 bytes from window.crypto. Then, it writes a timestamp to get an additional 4 bytes of entropy. Finally, it gets such data as the size of the screen, your time zone, information about browser plugins, your locale, and more. That gives it another 6 bytes.

After the initialization, the program continually waits for user input to rewrite initial bytes. When the user moves the cursor, the program writes the position of the cursor. When the user presses buttons, the program writes the char code of the button pressed.

Finally, bitaddress uses accumulated entropy to generate a private key. It needs to generate 32 bytes. For this task, bitaddress uses an RNG algorithm called ARC4. The program initializes ARC4 with the current time and collected entropy, then gets bytes one by one 32 times.

This is all an oversimplification of how the program works, but I hope that you get the idea. You can check out the algorithm in full detail on Github.

Doing it yourself

For our purposes, we’ll build a simpler version of bitaddress. First, we won’t collect data about the user’s machine and location. Second, we will input entropy only via text, as it’s quite challenging to continually receive mouse position with a Python script (check PyAutoGUI if you want to do that).

That brings us to the formal specification of our generator library. First, it will initialize a byte array with cryptographic RNG, then it will fill the timestamp, and finally it will fill the user-created string. After the seed pool is filled, the library will let the developer create a key. Actually, they will be able to create as many private keys as they want, all secured by the collected entropy.

Initializing the pool

Here we put some bytes from cryptographic RNG and a timestamp. __seed_int and __seed_byte are two helper methods that insert the entropy into our pool array. Notice that we use secrets.

Seeding with input

Here we first put a timestamp and then the input string, character by character.

Generating the private key

This part might look hard, but it’s actually very simple.

First, we need to generate 32-byte number using our pool. Unfortunately, we can’t just create our own random object and use it only for the key generation. Instead, there is a shared object that is used by any code that is running in one script.

Generate Public Key From Ecdsa Private Key Code

What does that mean for us? It means that at each moment, anywhere in the code, one simple random.seed(0) can destroy all our collected entropy. We don’t want that. Thankfully, Python provides getstate and setstate methods. So, to save our entropy each time we generate a key, we remember the state we stopped at and set it next time we want to make a key.

Second, we just make sure that our key is in range (1, CURVE_ORDER). This is a requirement for all ECDSA private keys. The CURVE_ORDER is the order of the secp256k1 curve, which is FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141.

Finally, for convenience, we convert to hex, and strip the ‘0x’ part.

In action

Let’s try to use the library. Actually, it’s really simple: you can generate a private key in three lines of code!

You can see it yourself. The key is random and totally valid. Moreover, each time you run this code, you get different results.

Conclusion

As you can see, there are a lot of ways to generate private keys. They differ in simplicity and security.

Generating a private key is only a first step. Mitsushiba driver for mac. The next step is extracting a public key and a wallet address that you can use to receive payments. The process of generating a wallet differs for Bitcoin and Ethereum, and I plan to write two more articles on that topic.

If you want to play with the code, I published it to this Github repository.

I am making a course on cryptocurrencies here on freeCodeCamp News. The first part is a detailed description of the blockchain.

I also post random thoughts about crypto on Twitter, so you might want to check it out.

In the previous article, we looked at different methods to generate a private key. Whatever method you choose, you’ll end up with 32 bytes of data. Here’s the one that we got at the end of that article:

60cf347dbc59d31c1358c8e5cf5e45b822ab85b79cb32a9f3d98184779a9efc2

/nfs-shift-2-unleashed-cd-key-generator.html. We’ll use this private key throughout the article to derive both a public key and the address for the Bitcoin wallet.

Generate Public Key From Ecdsa Private Key Code

What we want to do is to apply a series of conversions to the private key to get a public key and then a wallet address. Most of these conversions are called hash functions. These hash functions are one-way conversions that can’t be reversed. We won’t go to the mechanics of the functions themselves — there are plenty of great articles that cover that. Instead, we will look at how using these functions in the correct order can lead you to the Bitcoin wallet address that you can use.

Elliptic Curve Cryptography

The first thing we need to do is to apply the ECDSA or Elliptic Curve Digital Signature Algorithm to our private key. An elliptic curve is a curve defined by the equation y² = x³ + ax + b with a chosen a and b. There is a whole family of such curves that are widely known and used. Bitcoin uses the secp256k1 curve. If you want to learn more about Elliptic Curve Cryptography, I’ll refer you to this article.

By applying the ECDSA to the private key, we get a 64-byte integer. This consists of two 32-byte integers that represent the X and Y of the point on the elliptic curve, concatenated together.

For our example, we got: 1e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7b73ff919898c836396a6b0c96812c3213b99372050853bd1678da0ead14487d7.

In Python, it would look like this:

Note: as you can see from the code, before I used a method from the ecdsa module, I decoded the private key using codecs. This is relevant more to the Python and less to the algorithm itself, but I will explain what are we doing here to remove possible confusion.

In Python, there are at least two classes that can keep the private and public keys: “str” and “bytes”. The first is a string and the second is a byte array. Cryptographic methods in Python work with a “bytes” class, taking it as input and returning it as the result.

Now, there’s a little catch: a string, say, 4f3c does not equal the byte array 4f3c, it equals the byte array with two elements, O&lt;. And that’s what codecs.decode method does: it converts a string into a byte array. That will be the same for all cryptographic manipulations that we’ll do in this article.

Public key

Once we’re done with the ECDSA, all we need to do is to add the bytes 0x04 at the start of our public key. The result is a Bitcoin full public key, which is equal to: 041e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7b73ff919898c836396a6b0c96812c3213b99372050853bd1678da0ead14487d7 for us.

Compressed public key

But we can do better. As you might remember, the public key is some point (X, Y) on the curve. We know the curve, and for each X there are only two Ys that define the point which lies on that curve. So why keep Y? Instead, let’s keep X and the sign of Y. Later, we can derive Y from that if needed.

The specifics are as follows: we take X from the ECDSA public key. Now, we add the 0x02 if the last byte of Y is even, and the byte 0x03 if the last byte is odd.

In our case, the last byte is odd, so we add 0x03 to get the compressed public key: 031e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7. This key contains the same information, but it’s almost twice as short as the uncompressed key. Cool!

Previously, wallet software used long, full versions of public keys, but now most of it has switched to compressed keys.

Encrypting the public key

From now on, we need to make a wallet address. Whatever method of getting the public key you choose, it goes through the same procedure. Obviously, the addresses will differ. In this article, we will go with the compressed version.

What we need to do here is to apply SHA-256 to the public key, and then apply RIPEMD-160 to the result. The order is important.

SHA-256 and RIPEMD-160 are two hash functions, and again, we won’t go into the details of how they work. What matters is that now we have 160-bit integer, which will be used for further modifications. Let’s call that an encrypted public key. For our example, the encrypted public key is 453233600a96384bb8d73d400984117ac84d7e8b.

Here’s how we encrypt the public key in Python:

Adding the network byte

The Bitcoin has two networks, main and test. The main network is the network that all people use to transfer the coins. The test network was created — you guessed it — to test new features and software.

We want to generate an address to use it on the mainnet, so we need to add 0x00 bytes to the encrypted public key. The result is 00453233600a96384bb8d73d400984117ac84d7e8b. For the testnet, that would be 0x6f bytes.

Checksum

Now we need to calculate the checksum of our mainnet key. The idea of checksum is to make sure that the data (in our case, the key) wasn’t corrupted during transmission. The wallet software should look at the checksum and mark the address as invalid if the checksum mismatches.

To calculate the checksum of the key, we need to apply SHA-256 twice and then take first 4 bytes of the result. For our example, the double SHA-256 is 512f43c48517a75e58a7ec4c554ecd1a8f9603c891b46325006abf39c5c6b995 and therefore the checksum is 512f43c4 (note that 4 bytes is 8 hex digits).

The code to calculate an address checksum is the following:

Getting the address

Finally, to make an address, we just concatenate the mainnet key and the checksum. That makes it 00453233600a96384bb8d73d400984117ac84d7e8b512f43c4 for our example.

That’s it! That’s the wallet address for the private key at the start of the article.

But you may notice that something is off. You’ve probably seen a handful of Bitcoin addresses and they didn’t look like that. Well, the reason is that they are encoded with Base58. It’s a little bit odd.

Here’s the algorithm to convert a hex address to the Base58 address:

What we get is 17JsmEygbbEUEpvt4PFtYaTeSqfb9ki1F1, a compressed Bitcoin wallet address.

Conclusion

The wallet key generation process can be split into four steps:

• creating a public key with ECDSA
• encrypting the key with SHA-256 and RIPEMD-160
• calculating the checksum with double SHA-256
• encoding the key with Base58.

Depending on the form of public key (full or compressed), we get different addresses, but both are perfectly valid.

Here’s the full algorithm for the uncompressed public key:

If you want to play with the code, I published it to the Github repository.

I am making a course on cryptocurrencies here on freeCodeCamp News. The first part is a detailed description of the blockchain.

I also post random thoughts about crypto on Twitter, so you might want to check it out.