Quote: "...easy to create a crypto scheme that appears to be rock solid, but that contains a fatal weakness..."
@JohnFen Usual assumption here is that encryption is ALWAYS based on mathematics, prime numbers, and so on (like RSA,PGP). Look up the Beale Papers. Two out of three documents have remained private for more than one hundred years.
Why is this? The cipher texts were not created using mathematics or prime number schemes. They were created using a book cipher, and the book used for the message which was deciphered has been found, but the book used for the other two messages is still unknown......despite lots of effort over the intervening time.
Now there's another problem for the so-called "good guys". Even if the "bad guys" use priate ciphers with a "fatal weakness", they still have the advantage that they can read messages immediately....while the "good guys" will need to wait a while to decipher the message....maybe weeks, maybe months, or in the case of the Beale messages....over a century!!!
Here's an example of a message enciphered with a book cpher....it no doubt has a "fatal weakness"...so you can publish the plain text when you've figred it out.