DoChen, there are a few types of crypto that solve different problems, and so are different. The two prime number thing (RSA-like) tries to solve the problems of authentication with its public and private keys, but is hard to do (when you have the keys) versus easy to crack (factor). It's a good way to send keys used for other things, in other words. A one-time pad is pretty darn good if you only use it once, and everyone knows where to start in it - but how to get the key to someone safely?
Turns out the
Diffie-Hellman thing had a lousy way of choosing the primes in the first place and has a backdoor due to that - but it's still enough to keep amateurs out.
Believe me, though - anyone with a good list of all the primes of the two popular sizes used there could make a fortune by agreeing to NOT sell it. I've thought of doing that, but it kinda paints a target on your back, or forces one back into government service. It would be a lotta disks, but computers that could fill them are now in territory where one could actually afford them.
It's a big world in that zone, anyone who want more should probably go buy Applied Cryptography and some other works of Bruce Schneieir. There's plenty of good crypto free, but it's just the crypto routine - you have to do the rest. As Bruce and many others point out, most leaks aren't from someone breaking the crypto itself - there are side channel attacks, poor implementations that leave the plaintext around somewhere, and the ultimate side-channel attack - the rubber hose till you give up the key.
I know that in staying under the radar here, even with the like minded we don't talk about how much we dislike what the PTB are doing - we know anyway. We don't talk about how big the food or PM stash is becoming, we already know or see it when we visit. We talk on the porch away from cars and celphones when we do.
We go out and have a beer and shoot our guns (either before or after grilling the steaks), but don't act like knuckle dragging camo-wearing white supremacist skinheads, which is easy, because we aren't. We aren't revolutionaries. Just ready if someone else does. If TSHTF, we won't be the guys throwing it - we'll be the guys wiping it off people after.
Just some normal guys, maybe a little better off than average - but not too rich-appearing even if we are, we love collecting all our neato tools, having a little extra everything...being able to be sufficient in whatever we can accomplish that in, and so forth. It's amazing how few words that can take, and none at all in public about
why, to get there and be pretty completely under all radars - even the other neighbors.
It's like a club no one knows exists till they get invited in, and that happens because they obviously already qualify. Then all it takes is a glance and a nod - pretty hard to intercept.
All simple ciphers are trivial to crack because in most cases, it's now possible to automate plaintext detection when it works - most people don't use enough layers or forget certain nasty gotchas. You can just toss it to a bank of machines and wait, but that's rarely needed - there are other ways in, and something being crypto is the main flag you need to get interested in it in the first place, which is why steganography is also popular.
In that technique, you can just replace the least significant bits of say, audio or picture data with your stuff - since most stuff is way over-precise, you don't notice there's a message in it at all, which of course, is the point. You could encrypt it too if you wanted to, of course, making it harder for someone to be sure there was anything there that wasn't just noise. But you're still leaving
traffic out there to be analyzed, and I'm sure if you send the same few pix back and forth enough, someone will figure out something is going on - so it's work to get right. All this stuff is.
So, if you need to hide a few messages to a few people, you really have to be sending a lot to a lot of people...all the time, so there's nothing special about those few that's easily picked up on. Goes all too deep for the tastes of most.
Bruce doesn't talk much about crypto these days, but his blog goes way back, and his books are industry references.
Here's a little free stuff. The code is out there online for it.