< Cryptography
Sep 30, 2016 In this paper, we introduce a generalized algorithm over RSA that is advanced, adaptable and scalable in using a number of primes. Our algorithm uses 2 k prime numbers with secure key generation involving additional complexity, making it computationally infeasible to determine decryption key. A user can use 4, 8, 16, 32. 5.9 Public Key Cryptography; The RSA System Ever since written communication was used, people have been interested in trying to conceal the content of their messages from their adversaries. This has led to the development of techniquesof secretcommunication,ascienceknownascryptogra-phy. Sep 30, 2019 To generate RSA keys using the RSAGenerateKeys function, call it in the following sequence of steps: Establish the pseudorandom number generator and prime number generator. Define the RSA private key type 2 in successive calls to the RSAGetSizePrivateKeyType2 and RSAInitPrivateKeyType2 functions with desired values of factorPBitSize.
Download and install the OpenSSL runtimes. If you are running Windows, grab the Cygwin package.
OpenSSL can generate several kinds of public/private keypairs.RSA is the most common kind of keypair generation.[1]
Other popular ways of generating RSA public key / private key pairs include PuTTYgen and ssh-keygen.[2][3]
Generate an RSA keypair with a 2048 bit private key[edit]
Execute command: 'openssl genpkey -algorithm RSA -out private_key.pem -pkeyopt rsa_keygen_bits:2048'[4] (previously “openssl genrsa -out private_key.pem 2048”)
e.g.
Make sure to prevent other users from reading your key by executing chmod go-r private_key.pem afterward.
Extracting the public key from an RSA keypair[edit]
Execute command: 'openssl rsa -pubout -in private_key.pem -out public_key.pem'
e.g.
A new file is created, public_key.pem, with the public key.
It is relatively easy to do some cryptographic calculations to calculate the public key from the prime1 and prime2 values in the public key file.However, OpenSSL has already pre-calculated the public key and stored it in the private key file.So this command doesn't actually do any cryptographic calculation -- it merely copies the public key bytes out of the file and writes the Base64 PEM encoded version of those bytes into the output public key file.[5]
Viewing the key elements[edit]
![Primes Primes](/uploads/1/2/6/0/126017793/116759351.png)
Execute command: 'openssl rsa -text -in private_key.pem'
All parts of private_key.pem are printed to the screen. This includes the modulus (also referred to as public key and n), public exponent (also referred to as e and exponent; default value is 0x010001), private exponent, and primes used to create keys (prime1, also called p, and prime2, also called q), a few other variables used to perform RSA operations faster, and the Base64 PEM encoded version of all that data.[6](The Base64 PEM encoded version of all that data is identical to the private_key.pem file).
Password-less login[edit]
Often a person will set up an automated backup process that periodically backs up all the content on one 'working' computer onto some other 'backup' computer.
Because that person wants this process to run every night, even if no human is anywhere near either one of these computers, using a 'password-protected' private key won't work -- that person wants the backup to proceed right away, not wait until some human walks by and types in the password to unlock the private key.Many of these people generate 'a private key with no password'.[7]Some of these people, instead, generate a private key with a password,and then somehow type in that password to 'unlock' the private key every time the server reboots so that automated toolscan make use of the password-protected keys.[8][3]
Further reading[edit]
- ↑Key Generation
- ↑Michael Stahnke.'Pro OpenSSH'.p. 247.
- ↑ ab'SourceForge.net Documentation: SSH Key Overview'
- ↑'genpkey(1) - Linux man page'
- ↑'Public – Private key encryption using OpenSSL'
- ↑'OpenSSL 1024 bit RSA Private Key Breakdown'
- ↑'DreamHost: Personal Backup'.
- ↑Troy Johnson.'Using Rsync and SSH: Keys, Validating, and Automation'.
- Internet_Technologies/SSH describes how to use 'ssh-keygen' and 'ssh-copy-id' on your local machine so you can quickly and securely ssh from your local machine to a remote host.
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How to Generate a Public/Private KeyPair for Use With Solaris Secure Shell
Users must generate a public/private key pair when their site implementshost-based authentication or user public-key authentication. For additionaloptions, see the ssh-keygen(1) manpage.
Before You Begin
Determine from your system administrator if host-based authenticationis configured.
Generate Rsa Key Pair
- Start the key generation program.where -t is the type of algorithm, one of rsa, dsa, or rsa1.
- Specify the path to the file that will hold the key.Bydefault, the file name id_rsa, which represents an RSAv2 key, appears in parentheses. You can select this file by pressing the Return key. Or, you can type an alternative file name.The file name of the public key is created automatically by appendingthe string .pub to the name of the private key file.
- Type a passphrase for using your key.This passphraseis used for encrypting your private key. A null entry is stronglydiscouraged. Note that the passphrase is not displayed when youtype it in.
- Retype the passphrase to confirm it.
- Check the results.Check that the path to the keyfile is correct.At this point, you have created a public/private key pair.
- Choose the appropriate option:
- If your administrator has configuredhost-based authentication, you might need to copy the local host's publickey to the remote host.You can now log in to the remote host.For details, see How to Log In to a Remote Host With Solaris Secure Shell.
- Type the command on one line with no backslash.
- When you are prompted, supply your login password.
- If your site uses user authentication with public keys, populateyour authorized_keys file on the remote host.
- Copy your public key to the remote host.Type thecommand on one line with no backslash.
- When you are prompted, supply your login password.Whenthe file is copied, the message “Key copied” is displayed.
- (Optional) Reduce the prompting for passphrases.For a procedure, see How to Reduce Password Prompts in Solaris Secure Shell. For more information, see the ssh-agent(1) and ssh-add(1) man pages.
Example 19–2 Establishing a v1 RSA Key for a User
Generate Rsa Key 200 Primes In Order
In the following example, the user cancontact hosts that run v1 of the Solaris Secure Shell protocol. To be authenticated by v1hosts, the user creates a v1 key, then copies the public key portion to theremote host.