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comment Are there standards for transport layer security using only symmetric keys?
Probably so, which is why I mentioned CyaSSL which is designed for embedded. There is also MatrixSSL which also supports PSK.
comment Tactics available to help prove security of a new system?
+1, and I completely agree with the sentiment here, but want to make an addendum to "The hard bit is to design a cipher that no one else can break." - the really hard part is doing this while having something that is at all competitive from an implementation perspective. It wouldn't be that hard for someone with a decade or so of experience to come up with an algorithm that would be secure if you used, say, 10000 rounds, but which would probably not be secure if you wanted it to be as fast as, say, Rijndael or Twofish. Of course most such people know enough not to bother doing such things...
comment Should DES be avoided when developing new systems?
It might be worth distinguishing between CBC and CTR in terms of the problems that are encountered with an n bit cipher. As I understand it, after 2**(n/2) CBC blocks, one can expect to start extracting information about the plaintext, whereas with CTR the only change is that you can distinguish the keystream from a uniform random string, because you would expect to see a collision after 2**(n/2) blocks, but wouldn't with CTR. Obviously the best solution regardless is to use a cipher with a larger block, but I do think these are very different failure modes.
comment Replacing the Rijndael S-Box?
I assume your question has an implicit "holding other cryptographic properties constant", since an sbox of [1,2,...,255,0] has cycle type 256, but would make a fairly poor sbox. You may want to make this explicit.