Two caveats on the commentary about a symmetric key algorithm with a
trapdoor being a public key algorithm.

1) The trapdoor need not be a good public key algorithm, it can be flawed
in ways that would make it unsuited for use as a public key algorithm. For
instance being able to compute the private key from the public or deduce
the private key from multiple messages.

2) The trapdoor need not be a perfect decrypt. A trapdoor that reduced the
search space for brute force search from 128 bits to 64 or only worked on
some messages would be enough leverage for intercept purposes but make it
useless as a public key system.

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