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Bitcoin uses point multiplication on the Elliptic Curve secp256k1 to generate a public key from a private key. Basically, this curve has a defined Generator point G, and a method for 'adding' two points together in a way to get a new point (EC Point Addition). Because the key pair is mathematically related, whatever is encrypted with a Public Key may only be decrypted by its corresponding Private Key and vice versa. For example, if Bob wants to send sensitive data to Alice, and wants to be sure that only Alice may be able to read it, he will encrypt the data with Alice's Public Key. Let’s walk through the process step by step and build our our own Elixir module to generate private keys and public addresses. What are Private Keys and Public Addresses? A Bitcoin private key is really just a random two hundred fifty six bit number. As the name implies, this number is intended to be kept private. Using SSH public-key authentication to connect to a remote system is a robust, more secure alternative to logging in with an account password or passphrase. SSH public-key authentication relies on asymmetric cryptographic algorithms that generate a pair of separate keys (a key pair), one 'private' and the other 'public'.

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To sign an assembly with a strong name, you must have a public/private key pair. This public and private cryptographic key pair is used during compilation to create a strong-named assembly. You can create a key pair using the Strong Name tool (Sn.exe). Key pair files usually have an.snk extension.

Generate RSA keys with SSH by using PuTTYgen

Elixir Generate Public And Private Keys In Linux

One effective way of securing SSH access to your cloud server is to usea public-private key pair. This means that a public key is placed onthe server and a private key is placed on your local workstation.Using a key pair makes it impossible for someone to log in by using justa password, as long as you set up SSH to deny password-basedauthentication.

This article provides steps for generating RSA keys by using PuTTYgen onWindows for secure SSH authentication with OpenSSH.

Elixir Generate Public And Private Key Encryption

Generate keys

In Windows, use PuTTYgen to generate your public and private keys.

1. If needed, download PuTTYgen from the PuTTY download page.(PuTTYgen might have been installed previously with PuTTY or WinSCP.)
2. Launch the program, and then click the Generate button.The program generates the keys for you.
3. Enter a unique key passphrase in the Key passphrase andConfirm passphrase fields.For additional information about using passphrases,see Log in with a SSH Private Key on Windows.
4. Save the public and private keys by clicking the Save public keyand Save private key buttons.
5. From the Public key for pasting into OpenSSH authorized_keys filefield at the top of the window, copy all the text (starting with ssh-rsa)to your clipboard by pressing Ctrl-C.You need this key available on your clipboard to paste eitherinto the public key tool in the Control Panel or directly into theauthorized keys on your cloud server.

Use the key pair

You can use the RSA key pair in the following ways.

Specify your SSH key when creating a new cloud server

When you create a cloud server, you can assign a public key from the list of keys.If your key is not already in the list, you may add it, and then assign it.

Add a new public key to the list

1. Under Advanced Options on the Create Server page, click Manage SSHKeys.
2. Select public key for the cloud server from the SSH Keys listand click Add Public Key.
3. Enter the key name, select the region, and paste the entire publickey into the Public Key field. Then click Add Public Key.
4. Go back to the Create Server page, and confirm that your key is listedin the SSH Key list.

Assign a public key

1. Under Advanced Options on the Create Server page, select the publickey you want to use from the SSH key drop-down menu.
2. When you are done specifying the all the other details for the server,click Create Server.

Assign your SSH Key to an existing cloud server

To make use of your newly generated RSA key pair, you must tell PuTTY touse it when connecting to your cloud server.

1. To edit the file (or create it), run the following command on the cloud server:

2. Paste the text onto its own line in the file.

   You must have the key available in your clipboard to paste it. The key and itsassociated text (the ssh-rsa identified at the start and the comment at the end)must be on one line in the file. If the text is word-wrapped onto multiple linesan error might occur when connecting.

3. If you created the authorized_keys file, change its permissionsafter you’re done editing it by running the following command:

4. Open PuTTY, and go to the SSH > Auth section.

5. Browse to the location of the key file, and load the private key.

6. Go to the Session page, and save the session. This saves the configurationso that PuTTY uses the key every time that you connect to your cloudserver.

After you save your session, your key is loaded automatically when youconnect to your server.

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In order to be able to create a digital signature, you need a private key. (Its corresponding public key will be needed in order to verify the authenticity of the signature.)

In some cases the key pair (private key and corresponding public key) are already available in files. In that case the program can import and use the private key for signing, as shown in Weaknesses and Alternatives.

In other cases the program needs to generate the key pair. A key pair is generated by using the KeyPairGenerator class.

In this example you will generate a public/private key pair for the Digital Signature Algorithm (DSA). You will generate keys with a 1024-bit length.

Generating a key pair requires several steps:

Create a Key Pair Generator

The first step is to get a key-pair generator object for generating keys for the DSA signature algorithm.

As with all engine classes, the way to get a KeyPairGenerator object for a particular type of algorithm is to call the getInstance static factory method on the KeyPairGenerator class. This method has two forms, both of which hava a String algorithm first argument; one form also has a String provider second argument.

A caller may thus optionally specify the name of a provider, which will guarantee that the implementation of the algorithm requested is from the named provider. The sample code of this lesson always specifies the default SUN provider built into the JDK.

Put the following statement after the

line in the file created in the previous step, Prepare Initial Program Structure:

Initialize the Key Pair Generator

The next step is to initialize the key pair generator. All key pair generators share the concepts of a keysize and a source of randomness. The KeyPairGenerator class has an initialize method that takes these two types of arguments.

The keysize for a DSA key generator is the key length (in bits), which you will set to 1024.

The source of randomness must be an instance of the SecureRandom class that provides a cryptographically strong random number generator (RNG). For more information about SecureRandom, see the SecureRandom API Specification and the Java Cryptography Architecture Reference Guide .

Elixir Generate Public And Private Key

The following example requests an instance of SecureRandom that uses the SHA1PRNG algorithm, as provided by the built-in SUN provider. The example then passes this SecureRandom instance to the key-pair generator initialization method.

Some situations require strong random values, such as when creating high-value and long-lived secrets like RSA public and private keys. To help guide applications in selecting a suitable strong SecureRandom implementation, starting from JDK 8 Java distributions include a list of known strong SecureRandom implementations in the securerandom.strongAlgorithms property of the java.security.Security class. When you are creating such data, you should consider using SecureRandom.getInstanceStrong(), as it obtains an instance of the known strong algorithms.

Generate the Pair of Keys

Elixir Generate Public And Private Key With Putty Generator Oracle Cloud

The final step is to generate the key pair and to store the keys in PrivateKey and PublicKey objects.