Security protocols

If you send a user-controlled number ``I'' and your peer replies with I + 1 encrypted by K and then gives you a number ``J'', is there any way to find J + 1 encrypted by K if you do not know the K?

Using AES + ECB btw, I am wondering if one can use something like that for authentication.

Use the I+1 reply to find K, obviously.

You mean just by knowing the input and output deducing which method was used to generate the output from the input, that is to say the source code of the encryption function, without having access to it?
Maybe if you have a great list of input-output pairs you could try regressing it somehow.

I don't think you can't reverse engineer an encryption algorithm from one example. it's not like you can just do K(I+1)/I * J. presumably the encryption is actually encryption. gnomesayin

I would just iterate over every known encryption function or combination thereof, in order of popularity, to see which one it was.

You can do that exactly if the scheme is malleable. You can also use encryption for authentication but please don't try to write your own authentication scheme if you don't know about malleability, it will probably fail horribly in some way.

>>6
It might be a good learning experience, though.

>>7
What are you going to learn? It is easy to design something you yourself can't break, so unless you find someone to cryptanalyze it (which will be next to impossible even if the system is hot garbage) your experience will be that of gluing some blackboxes together in a way you don't really understand. A textbook on cryptography like Vanstone will teach you much more.

The comparison is not that appropriate, but imagine trying to learn mathematics by tackling a Millenium problem. Sure, you might learn something in the process, but it'll be much less than you could get from a book and most likely you're just going to waste your time on a method of proof that provably does not work. (≈ a class of system that is broken in general)