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.
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.
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.
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.
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.
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.
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.
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.
Generating a private key is only a first step. 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.
I am doing a presentation on Bitcoins and I was looking for some calculations to make people feel safe about the private key encryption. Please first answer, how long in bytes the private key is, then how many combinations of numbers it will contain, and then what is the fastest computer or network of supercomputers and how long it would take to crack a private key using that computer. I think the result would be very educational based on my own calculations. Thank you.
A Bitcoin private key is a random 256-bit number. However, the public key reveals some information about the private key. The best known algorithms for breaking ECDSA require O(sqrt(n)) operations. That means 2^128 operations would be needed to break a Bitcoin account.
A Bitcoin private key (ECC key) is an integer between one and about 10^77. This may not seem like much of a selection, but for practical purposes it's essentially infinite.If you could process one trillion private keys per second, it would take more than one million times the age of the universe to count them all. Even worse, just enumerating these keys would consume more than the total energy output of the sun for 32 years. This vast keyspace plays a fundamental role in securing the Bitcoin network.
There is a vanitygen utility (check out exploitagency's version which is improved fork of samr7's version) which can give you the estimates how long it takes to find the private key for the given pattern (see: vg_output_timing_console()). Some special cases (like repeated characters) are more difficult than the other.
The difficult of finding a vanity address depends on its exact structure (leading letters and numbers) and how likely such an output is given the algorithms involved, which can consist of several pivots where the difficulty suddenly changes. bitcoin wiki
It's worth to note, that the above-generated address has 34 bytes, but the first character is just the network identifier (for bitcoin it's usually 1 or 3), and the last 4 bytes is just a checksum. For more details about the address, see this bitcoin wiki page.
Many will give lots of excuses why this is not relevant, but the fact is that the party line of "it is effectively impossible to crack bitcoin private keys" is a demonstrably false statement. Keys have been cracked, and it did not billions of billions of years.
The point Is that your bitcoin folks telling you how secure it is based on 10P already have the basic math wrong by 15-30 times because they evidently don't know as much as they think. The improvements are not dependent on Moore's Law either , the recent advancements and present limitations have to do with an entirely different Law which is what NV Link solved as best it could and improved computing time so well , This is just today's example of how their theory of a billion billion years is already wrong by a factor of 15-30 and will continue to become wrong each year at a much higher rate than they assume. In 30 years or less bitcoin at it's present level will be easily cracked by anyone who has 40 to 50,000 dollars to spend (in todays money) or can use any number of University or Corporate Supercomputers.
Anyone who actually believes that 50 year old technology is going to keep something digitally secure 50 years later is frankly not the kind of person you should be paying ANY attention to at all ... Does that mean bitcoin is dangerous today ? Not really but if the same folks are in charge of it's security in 30 years, are the same clueless people that are on here right now it will be.
Secure Shell is one of the most common network protocols, typically used to manage remote machines through an encrypted connection. However, SSH is prone to password brute-forcing. Key-based authentication is much more secure, and private keys can even be encrypted for additional security. But even that isn't bulletproof since SSH private key passwords can be cracked using John the Ripper.
Key-based authentication, on the other hand, uses cryptography to ensure secure connections. A key pair is generated consisting of a public and private key. The private key should be kept secret and is used to connect to machines that have the matching public key.
The public key is used to encrypt communication that only the associated private key can decrypt. This makes it nearly impossible for hackers to compromise SSH sessions unless they have access to the private key.
The next thing we need to do is generate a public/private key pair. The ssh-keygen utility can easily take care of this for us. Use the default location, which will create the file in our home directory:
At this point, we need to get the private key (id_rsa) on our local machine. This can happen through a variety of scenarios, like if we had read access due to LFI or even command injection allowing us to execute certain commands.
In this tutorial, we learned about SSH key-based authentication and how to crack private key passwords. First, we created a new user on the target system and generated an SSH key pair. Next, we obtained the private key from the target and used ssh2john to extract the hash. Finally, we cracked the private key password and used it to connect to the target.
Anyone can easily access any account, as long as the private key is valid. The user does not need to provide the public key or go through any other authentication steps. This applies to both Ethereum and Solana, or any other blockchain.
Ethereum private key is a 32 bytes/256 bits data often represented as a 64 hexadecimal character string. Theoretically, any string can be used as a private key. Most wallets and blockchains support generating private keys from seed/mnemonic phrases, which are first defined in BIP-32, BIP-39, and BIP-44.
Joe Carrigan: [00:01:38] Dave, this week, I found a really interesting article from Sophos. What Sophos did was they worked with a company called CipherTrace to track sextortion emails from September 1 of last year to January 31 of this year, 2020. And what CipherTrace does is they are a cryptocurrency tracking company. Their mission is to help banks with anti-money laundering operations because one of the big fears is that cryptocurrency can be used as money laundering. But CipherTrace takes a look at the block chain. And actually, one of the drawbacks of cryptocurrencies like Bitcoin is that it is a public ledger. So everybody can see where everything goes on the bitcoin blockchain. And CipherTrace capitalizes on that and helps banks make sure they're not helping criminals launder money.
Joe Carrigan: [00:04:23] Over the course of this campaign, these actors used 50,000 bitcoin addresses, and only 261 of them received bitcoin during this timeframe, from September to the end of January. And the total amount of bitcoin they received was 51 bitcoin, or $473,000 - in the article. I don't know how they're calculating the value of bitcoin. I mean, that is such a wildly fluctuating value it doesn't... 2b1af7f3a8