Is this Possible?

From: Myrddin Emrys (myrddin_at_iosys.net)
Date: 06/24/03 

Date: 24 Jun 2003 01:15:49 -0700

I'm a novice at cryptography, so I apologize if this could be answered
in Crypto-101. If it can, please direct me to the appropriate website
or publication.

I wish to encrypt an IP:PORT datum, 6 bytes. I do not wish the
encrypted form to be longer than 8 bytes. I need to be able to reform
the original result after an arbitrary length of time with no
additional data. The encrypted chunks will have a massive degree of
duplication, but I wish the encrypted results to be as random as
possible. I need it to be impossible for an attacker, given the
hundreds or thousands of encoded chunks, to be able to break the
cypher.

I don't think this is possible. From what I understand, any algorithm
could be brute-forced, due to the limited dataset... only 64 bits, 48
of which are highly insecure (easily guessed, frequently duplicated).
Also, if you carry the concept to the extreme, it sounds ludicrous:
Can I encode 0-9 as a 2 digit string (00-99) such that inputting 0
over and over gets me seemingly random results, but from those random
results I can reconstruct the number 0 each time. It seems obvious
that this is false... the dataset, to allow encoding all 10 results,
would mean that encoding 0 over and over would only give 10 different
results, because the other 90 need to be used for encoding 1-9.

To make it secure, local storage would be required that 'remembered'
every such cypher sent out. You could then do a truly random XOR on
the 6 bytes, remember the result and match it to the XOR that would
get the original back, and pass it out. When you get encrypted results
back, you could test (possibly multiple) results that match the cypher
to see which one returns a valid IP:PORT (valid IP:PORTS will be an
extremely limited set, under 1000, so accidental matches wil be
minimal).

Am I wrong? Is there a way of encoding thousands of (very repetetive)
6 byte datums so that the cyphers produce different results for the
same input, but are recoverable without additional data beyond the
cypher? Would increasing the cypher result from 8 bytes to 14 bytes
(giving me 64 bits of secure data) make it secure, or does the massive
repetition (hundreds of thousands of encodings of the same value)
undermine the security to too great an extent? Assuming I'm shooting
for equivalent-to-DES-64 level security (where brute-force is the only
solution), how many extra bytes (or bits) beyond the 6 to be encoded
are necessary to maintain security?

Because (for example) 100K cyphers of the same datum will be available
to the decoder, does that mean I need an additional log2(100000) bits
to maintain the same level of security as having 1 cypher out there?

Finally, I'm not actually worried about what algorithm to use at the
moment... I'm sure that can be researched, and I have many to choose
from. I'm concerned more with the theoretical limits that exist.

Thank you for your time, and I hope this is an interesting question.

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