Tactics available to help prove security of a new system?
Prove resistance to differential cryptanalysis.

For example, this presentation: Provable security against Impossible Differential Cryptanalysis. Or this paper:  ProvableSecurity Against a Differential Attack (1995)
Prove resistance to linear cryptanalysis.

For example: On Measuring Resistance to Linear Cryptanalysis
Run a bunch of statical tests against the cipher. 

For example: Cryptographic Randomness Testing of Block Ciphers and Hash Functions