> (and instead use the Suite A ciphers -- it's impossible for others to break them if they don't know anything about them, right?)

It is possible to break an unpublished cipher. Just more difficult, because you've got to figure out the algorithm as well as the key. As long as it is similar to existing algorithms, you can try and look for differences.

For example, American cryptanalysts broke the Japanese Purple cipher during World War II entirely from encrypted messages. It was only at the end of the war that they managed to recover parts of one machine from the Japanese embassy in Berlin. No complete machine was ever found.

(In contrast, Enigma machines were captured, so cryptanalysts could directly examine the mechanism and use this knowledge to look for weaknesses.)

Of course, if the algorithm is completely novel, and bears no resemblance even to any principle used in published cipher, then it's a lot more secure. It would be hard to even begin to analyze it.

That said, it's unlikely the NSA has truly novel algorithms. They recruit from the general public like everyone else. There principle advantage is that they're big (working for the NSA is appealing) and can classify in-house breakthroughs.