Cryptography/Generate a keypair using OpenSSL

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.

Other popular ways of generating RSA public key / private key pairs include PuTTYgen and ssh-keygen.

Generate an RSA keypair with a 2048 bit private key
Execute command: "openssl genpkey -algorithm RSA -out private_key.pem -pkeyopt rsa_keygen_bits:2048" (previously “openssl genrsa -out private_key.pem 2048”)

e.g. $ openssl genpkey -algorithm RSA -out private_key.pem -pkeyopt rsa_keygen_bits:2048 ....................................................................+++ ....................................................+++

Make sure to prevent other users from reading your key by executing  afterward.

Extracting the public key from an RSA keypair
Execute command: " "

e.g. $ openssl rsa -pubout -in private_key.pem -out public_key.pem writing RSA key

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 private 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.

Viewing the key elements
Execute command: " "

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. (The Base64 PEM encoded version of all that data is identical to the private_key.pem file).

Password-less login
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". 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 tools can make use of the password-protected keys.