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?
Public-key cryptography security given NSA resources
security;encryption
The entire internet security is based on the presumption that factoring prime numbers is NP-hard, as it has yet to be proven mathematically that it is (But centuries of looking indicate its not trivial).  If the NSA has figured out a way to do it more efficiently, then RSA is broken. If the NSA  (or anyone else) have broken RSA - they unlikely to use the exploit on you, as the value of people not knowing they have the ability far exceeds any value you as an individual hold (Read the stories of the allies in WWII letting the Germans 'win some' - at the cost of lives, so as not to tip them off that Enigma was cracked). If they do use the exploit, they will manufacture a plausible story as to how the information was cracked by something like guessing the key, exploiting a flaw in the implementation etc This is where the statistics come into play - if the NSA gets lucky a statistically significant number of times, it will be noticed, so they need to get lucky just enough not to get noticed. Other exploits (a gun to your head, a big bag of cash etc) are cheaper and as effective. The NSA is more likely to persuade your co conspirator to just give them any info they want....In summary - If the NSA is interested, you can't be certain you can stop them, and can not be certain that you have succeeded. If you have an unlucky streak, maybe it was the NSA.... Best and only practical bet is not to upset the NSA and end up on their radar.... 