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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. 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. In Python, cryptographically strong RNG is implemented in the secrets module. That is amazing. But can we go deeper? There are sites that generate random numbers for you. We will consider just two here.
One is random. Another one is bitaddress. Can random. Definitely, as they have service for generating random bytes. But two problems arise here. Can you be sure that it is indeed random? The answer is up to you. Now, bitaddress. 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.
For educational purposes, we will look at its code and try to reproduce it in Python. Bitaddress creates the entropy in two forms: by mouse movement and by key pressure. 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 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 bytes from window. 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. 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.
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. Here we put some bytes from cryptographic RNG and a timestamp. Notice that we use secrets. First, we need to generate byte number using our pool. Instead, there is a shared object that is used by any code that is running in one script. What does that mean for us? It means that at each moment, anywhere in the code, one simple random.
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. You can see it yourself. The key is random and totally valid. Moreover, each time you run this code, you get different results.
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