RSA - Can you create a public key from a private key?

Question

I am creating an encryption strategy for a lab project and want to know if there exists the capability to create a public key from just the private key?

Otherwise, can the public key only be created at the same time as the private key from some key generator?

P.S. A quick google didnt really help.

Answer 1

Depends on the algorithm. With RSA, you cannot, with EC you can. However, the public key is usually always stored together with the private key (not the other way around, though, of course), so this is not really a problem (if you have the private key, the same file also includes the public key).

Answer 2

Extracting public RSA key from a private key from the command line

Command line comparison to show there is no difference between a public RSA key and an extracted key if you ignore whitespace.

1. Generate public private key pairing under home directory with no passphrase and no coment.

   ssh-keygen -t rsa -f ~/id_rsa -N '' -C ""

2. Generate public key into file 'extracted_public_key'

   ssh-keygen -y -f '/home/vagrant/id_rsa' > extracted_public_key

3. Diff public key with 'extracted_public_key' file ignoring white space.

   diff -b id_rsa.pub extracted_public_key

Ignoring whitespace at the end of id_rsa.pub there is no difference between a public key and an extracted key.