title: Encrypt with private key and decrypt with public key
body: <p>What I'd like to know is simple.
  Can I use OpenSSL to encrypt a string "hello" with a private key then send it to everyone who can decrypt it with the public key to retrieve the original string.</p>
  
  <p>I've searched all around and can't really find anything.</p>
  
  <p>Mathematically I can use the private exponent and public modulus to perform an encryption then use the public exponent and public modulus to perform the decryption.</p>
  
  <p>Can I do this with OpenSSL?</p>
  
  <p>I've read that this is considered signing. 
  Then how can I sign with my private key and receive the original data from the signed file with just the public key?</p>
  
  <p>I've read a lot of the responses on the web and they're all vague. 
  Can anyone give me clear solutions?</p>
  
  <p>If it is possible to encrypt with a private key and decrypt with public can anyone give me an example on how to do it with the openssl tool? Or do I have to write my own implementation?</p>