A couple examples of using asymmetric RSA signing and encryption using Ruby's OpenSSL libraries.

encryption-decryption.rb

require 'openssl'

key = OpenSSL::PKey::RSA.new(2048)
p encrypted_string = key.public_encrypt('my plaintext string', OpenSSL::PKey::RSA::PKCS1_OAEP_PADDING)
p decrypted_string = key.private_decrypt(encrypted_string, OpenSSL::PKey::RSA::PKCS1_OAEP_PADDING)

sign-verify.rb

require 'openssl'

key = OpenSSL::PKey::RSA.new(2048)
data = 'my string to sign'
p signature = key.sign(OpenSSL::Digest::SHA256.new, data)

pubkey = key.public_key

if pubkey.verify(OpenSSL::Digest::SHA256.new, signature, data)
  puts 'the signature is valid'
else
  puts 'the signature is invalid'
end