I was wondering how secure public private key encryption methods are.
If two individuals were sending emails back and forth forever, where each person would encrypt the body of the email they were sending with the other person's public key, would anyone be able to decrypt the body of those emails after a while?
I'm assuming that each person creates their own private-public key pair and then if you wanted to send someone an email you would grab their public key and encrypt your message before sending it to them. They would then decrypt it with their own private key.
Wikipedia (http://en.wikipedia.org/wiki/Public-key_cryptography) claims that its effectively impossible to decrypt email if all you know is the public key. But is this really true? What if you had the resources of the NSA, are they not able to brute force the decryption?