While most cryptanalytic methods in ``real-life'' scenarios are based on partial information, it is best to examine a symmetric system as one would a ``black box''. The following tests come to mind:

**Entropy of output**- How random is the output given general input? One can measure the extent to which the output contains redundancies (as measured by Shannon's theory of information) for different inputs and keys.
**Diffusion of input variations**- Is the effect of small changes in the input localised? One can examine a large number of input pairs which differ by the same small change; is the change in the resulting output (for a fixed key) in the same place or does it ``diffuse''?
**Diffusion of key variations**- Is the effect of small changes in the key localised? One can examine (over a large number of inputs) how two keys that differ by a small amount cause variation in the output. Is this difference ``diffuse''?
**Weak inputs and keys**- Are there some simple inputs which have a lot of symmetry that produce output from which the key can be computed?

**Symmetries**- The cryptographic operations should ``break symmetry''. If not then it may be possible to show that each key has an ``inverse'' key and such an inverse may be easily computable.
**Small order**- The cryptographic functions may be such that iterating them may cause the resulting permutation to be one which is easily recognised.
**Partial Reverse-engineering**- Is it possible to build simple black-boxes (ones that are ``crackable'') that give output that has considerable overlap with the given black-box?