Public Key Generation What's It Look Like
The public key is created automatically What does a CSR look like? Most CSRs are created in the Base-64 encoded PEM format. This format includes the '-BEGIN CERTIFICATE REQUEST-' and '-END CERTIFICATE REQUEST-' lines at the begining and end of the CSR. A Private Key Generates a Public Key Which Generates an Address. A public key is obtained by subjecting a private key to a set of mathematical operations defined in a set of standards known as Elliptic Curve Cryptography (ECC). Whereas a private key is an integer, a public key is a 2D coordinate composed of two integers. Key Generator: A key generator (keygen) is a cryptographic tool used to generate product keys, which are unique alpha-numeric sequences that tell an installer program that the user that initiated the install owns a license of the software. A key generator tries to generate a correct product key that allows the installation of the software to. What is a Pem file and how does it differ from other OpenSSL Generated Key File Formats? (which includes the public key but not the private. But it worked like. Feb 26, 2018 GPG is the Gnu Privacy Guard and it is an implementation of OpenPGP (Open Pretty Good Privacy). It is an encryption technique that was originally developed for use in. With modern versions of OpenSSH, the knownhosts file on the client contains a hash of the server name and public key, rather than the name and the public key directly. The reason for only storing a hash is that if someone obtains a copy of this file (e.g. Leaked backup), they can't discover which servers are recorded, i.e. They can't discover which sites you connected to. 4.3 Git on the Server - Generating Your SSH Public Key. In order to provide a public key, each user in your system must generate one if they don’t already have one. This process is similar across all operating systems. First, you should check to make sure you don’t already have a key. The public keys look something like this.
In today’s electronic world where everything is done online, “trust” is hard to come by. Conversations can be snooped on, credit card numbers can be stolen, identities can be exchanged and unseen eyes are everywhere. Imagine business emails being maliciously read by competitors, company’s proposals being leaked and even crucial corporate information being tampered with…
This is where cryptography plays a crucial role, and important transactions have to be encrypted with strong algorithms to prevent leakage of information. We will discuss the basics of cryptography, public key cryptography, the RSA algorithm and the ‘PuTTYgen’ program (which is used to create and public and private keys) in this paper.
It is a commonly known fact that the field of cryptography involves two major models – the symmetric cipher model and the asymmetric cipher or public key cipher model. The major difference between the two models is that the symmetric cipher model uses the same key to encrypt and decrypt messages, and the asymmetric cipher model uses different keys for encryption and decryption. Some popular symmetric algorithms are DES (Data Encryption Standard), AES (Advanced Encryption Standard) and Blowfish. Similarly popular asymmetric cipher algorithms are RSA (which stands for Ron Rivest, Adi Shamir, and Leonard Adleman, who designed the algorithm), ElGamal and DSS (Digital Signal Standard).
That generates a 2048-bit RSA key pair, encrypts them with a password you provide and writes them to a file. You need to next extract the public key file. You will use this, for instance, on your web server to encrypt content so that it can only be read with the private key. Export the RSA Public Key to a File. This is a command that is. Openssl rsa -in private.pem -outform PEM -pubout -out public.pem. A separate public key file is not created at the same step though. To extract public key from the private key file into separate public key file you use your openssl rsa -in private.pem -pubout -out public.pem command. When you produce a public key this way, it is extracted from the private key. To do so, I have to generate a PKCS#1 RSA key pair in PEM format for signing and verification. I've tried using OpenSSL v.1.0.1. But the public key generated is a X.509 PEM. Here's the openssl command I used to generate the keys: Private Key: openssl genrsa -out nameofprivatekey.pem 1024 Public Key. OpenSSL can generate several kinds of public/private keypairs. RSA is the most common kind of keypair generation. Other popular ways of generating RSA public key / private key pairs include PuTTYgen and ssh-keygen. 1 Generate an RSA keypair with a 2048 bit private key. Openssl generate rsa key pair pem.
Public Key Cryptography
The key concepts in public key cryptography are plain text, encryption algorithm, cipher text, decryption algorithm and the recovered text. In addition, we make use of the most important component of public key cryptography to encrypt and decrypt the text – the public and private keys. If one key is used to encrypt the text, the other key is used to decrypt the text. The public and private keys are mathematically connected. The public keys are normally managed by a trustworthy third party person. Some of the required features of public key cryptography are listed below:
- The private key should be infeasible to be generated through the public key.
- Both the private and public keys should be easy to generate.
- Person ‘X’ (also popularly known as ‘Bob’) should easily be able to encrypt a message and send it to person ‘Y’ (also popularly known as ‘Alice’) using person ‘Y”s public key.
- Similarly, person ‘Y’ should easily be able to decrypt the message using their private key.
- A hacker should find it impossible to recover the original text in spite of knowing the ciphertext and the public key.
Public key cryptography solves two of the symmetric cipher model’s drawbacks:
- The key distribution problem, which in the symmetric model is to figure a way to distribute the keys when a lot of people are involved. This is solved in the asymmetric model by having “key-value” pair.
- The authentication problem (verifying that the message indeed came from where it should have come from), which is solved in the asymmetric key model by making use of “digital signatures”.
We will next see the RSA algorithm, which uses public key cryptography and is the basis of the PuTTYgen program.
RSA Algorithm
As already stated, ‘RSA’- stands for Ron Rivest, Adi Shamir and Leonard Adleman, who designed the algorithm. Most cryptographic algorithms involve tremendous amount of mathematics and the RSA algorithm is no exception. The mathematics behind the RSA algorithm are explained below in a lucid and easy to understand form. The basic idea behind the RSA algorithm is that it:
- “is a block cipher;
- it uses very large prime numbers for key generation; and
- the generated keys are mathematically linked.” (Walsh College, 2010)
There are three steps in the RSA algorithm:
Public Key Generation What's It Look Like Meme
- generating the public and private keys
- encrypting the message
We will see a brief gist of generating the public and private keys in this paper.
Generating the public and private keys:
- For the RSA algorithm to be highly successful, two large prime numbers are chosen (‘u’ and ‘v’)
(n=u * v)
- Totient of the product is calculated as:
Φ(n)= (u-1) (v-1) where ‘Φ’ is the Greek symbol ‘phi’.
- Next, we need to find values for ‘P’ and ‘Q’ after which the two large prime numbers can be abandoned.
P * Q = 1(mod Φ(n))
The only condition here is that both ‘P’ and ‘Q’ must be relatively prime to Φ(n). Two numbers are relatively prime, if they have no common factors apart from 1.
For example,
GCD (15,10) = 5
GCD (18,10) =2
GCD (21, 10) = 1
Now, 21 and 10 are relatively prime to each other or co-prime to each other.
Step (d) seems to be a bit more complicated than it actually looks. This can be simplified and re-written, assuming ‘P’ to be 7:
7 * Q = K * Φ(n) + 1, where ‘K’ can be any number.
Now ‘P’ and ‘R’ are the public keys and ‘Q’ and ‘R’ become the private keys. (Prime Number Hide-and-Seek: How the RSA Cipher Works)
Explaining the RSA algorithm with an example:
- We take two small prime numbers, 5 and 11, for this example.
- “Φ(55) = (5 – 1) * (11 – 1) = 4 * 10 = 40.
- Now, we need to find numbers (‘P’ and ‘Q’) to fit the equation:
P * Q = 1 (mod 40).
Now, ‘P’ and ‘Q’ must be relatively prime to 40. (Prime Number Hide-and-Seek: How the RSA Cipher Works) - If ‘P’ is considered as 7, and the unfamiliar modular mathematics are removed and replaced with a highly understandable equation,
7 * Q = K * 40 + 1,
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We next consider ‘Q’ to be 23 which is the next prime number close to 40. ‘P’ and ‘Q’ should also not be congruent to mod 40.
The equation now becomes,
7 * 23 = 161
And ‘K’ now becomes ‘4’.
So, the primary keys are 7 and 55 and private keys are 23 and 55.
The RSA algorithm is tough to crack if the keys are long. RSA keys are typically between 1024 – 2048 bits long, and a key length of 1024 bits is mostly sufficient for most calculations.
Attacks against RSA:
There are four different types of attacks that are possible against the RSA algorithm.
- Brute force: This is trying different types of combinations to crack the keys. It is very difficult to crack the algorithm when the keys are large.
- Mathematical attacks: This is equivalent to factoring the two large primes, which again has not been successful.
- Timing attacks: The timing attack depends on the running time of the decryption algorithm.
- Chosen ciphertext attacks: This type of attack is aimed at the properties of the algorithm. (Stallings)
Public Key Generation What's It Look Like Real
We will next move onto PuTTygen – a program for generating public and private keys.
PuTTY
“PuTTY is an SSH and telnet client, developed originally by Simon Tatham for the Windows platform. PuTTY is open source software that is available with source code and is developed and supported by a group of volunteers.” (Download PuTTY) It is used to generate public and private keys.
The PuTTY program can be downloaded from this link:
http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html.
The following screenshot shows the opening screen of the PuTTY program.
Before we move onto the other aspects of ‘PuTTYgen’ program, we will briefly divert to the topic of SSH. We can see from the above screenshot, that there are SSH-1 RSA and SSH-2 RSA and SSH2-2 DSA keys to generate. We will see a brief explanation of SSH next.
SSH
SSH is secure shell network protocol that is basically used to connect two networked computers securely. By means of SSH, the two computers can be used to perform remote and secure command login, secure data communication and other secure network services. SSH “connects, via a secure channel over an insecure network, a server and a client running SSH server and SSH client programs, respectively.[1] The protocol specification distinguishes between two major versions that are referred to as SSH-1 and SSH-2.” (Secure Shell)
Retracing back to the PuTTY gen program, we can generate public and private keys by moving the mouse cursor constantly over the blank area.
The following screenshot shows the result of generating the public and private key pair:
As we can see, we have generated SSH-2 RSA keys of length 1024 bits. The public and private keys can be saved as .txt files for later use. If the keys are generated using a length of 2048 bits, security will be enhanced, but at the cost of decreased performance.
The ‘passphrase’ field is optional, but it is better used. It is used to encrypt the private key in case it falls into wrong hands. The use of passphrase is explained in the University of Waterloo website which states that the private key is like a debit card and the passphrase is the PIN that is used to guard it.
“With SSH private keys, if somebody manages to acquire it, they will not be able to use it until they’ve figured out your passphrase. A private key without a passphrase is like a credit card, once they acquire it they can immediately use it.” (SSH Public Key authentication)
Application of the keys generated:
The keys that are generated can be used for SSH authentication with OpenSSH. The public key is the one that will be stored on the server. The private key will be the key that will be stored on one’s own computer. Instead of using the traditional username and password to login, the SSH client will authenticate your private key with the public key which was stored on the server.
Conclusion
This paper discussed the basics of cryptography and the necessities of cryptography, followed by the public key cryptography. We next moved onto the mathematics behind the RSA algorithm and concluded with the PuTTY program, which is used to generate public and private keys. Using public and private keys for authentication may be the future for online login into various websites.
Bibliography
Download PuTTY. (n.d.). Retrieved April 28, 2014, from putty.org: http://www.putty.org/
Prime Number Hide-and-Seek: How the RSA Cipher Works. (n.d.). Retrieved April 28, 2014, from muppetlabs.com: http://www.muppetlabs.com/~breadbox/txt/rsa.html#11
Secure Shell. (n.d.). Retrieved April 29, 2014, from en.wikipedia.org: http://en.wikipedia.org/wiki/Secure_Shell
SSH Public Key authentication. (n.d.). Retrieved from Waterloo Cheriton School of Computer Science: https://cs.uwaterloo.ca/cscf/howto/ssh/public_key/
Cryptography and Network Security. In W. Stallings.
Walsh College. (2010). Retrieved from Walsh College.
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.
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.
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. 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.