Schneier on Security

Clive Robinson • February 6, 2020 11:10 AM

@ Erik,

This feels like the contrapositive

It might feel like that, but it’s not.

The shorter the message is the harder it is to work out what it’s meaning is. This is because of the lack of structure to test for. The longer the message or the more messages sent under the same key the more structure is revealed. But that may not be sufficient, thus the more messages you need under other keys to determine the methods used.

Eventually sufficient structure is revealed such that an unambiguous method is revealed and from this key schedules etc can be worked out.

The less traffic the less certainty…

For instance one way to attack a pencil and paper cipher if you suspect it is a transposition cipher from a frequency analysis is to “anagram” it out looking for repeated pattern lengths that will reveal the size of the transposition blocks.

But you would be led down a false path if infact it was a polyalphabetic substitution cipher that used a method to modify the ciphertext to have the same or sufficiently similar statistics to transposed plaintext.

So I could use a simple method of transcoding where I convert the normal plaintext alphabet (A..Z) into a variable size alphabet with a much flatter statistic (0..7,80-99) then use a numeric One Time Pad (OTP) to encrypt the transcoded plaintext into equiprobable ciphertext. This I then transcode back into the normal plaintext alphabet (A..Z) with statistics sufficiently similar to normal plaintext for the assumed language in use.

If you try to anagram the transcoded ciphertext you will find some patterns possibly even what you think are messages[1] but they will be meaningless. The shorter the message within reason the more likely you are to find what you think are partial patterns but your time will be wasted. Because the actual strength of the system is the “equiprobable plaintext” of the OTP.

There is a limit for any encipherment system where it is not possible to be certain you have a valid message or not. Rather than type in an explanation of “Unicity distance”, I’ll give a link instead,

https://en.wikipedia.org/wiki/Unicity_distance

[1] The problem with unbounded random text is that beyond a certain size it will always have some kind of patterns to be found. Worse as we know from “Bible Code Hunters” you will find hidden messages in any sizable block of text.

Clive Robinson • February 7, 2020 9:58 AM

@ Random Comment,

The puzzle is way above my current brainpower and intellect but i’m guessing if computers have not solved it already, it’s because there is a variable missing to them.

On the assumption the plaintext and ciphertext are the same length and that the plain text is one or more sensible English language phrases it could be “brute forced” into all the messages that would fot that length.

How fast the whole message could be done is not exactly relevant[1], because as each word is assumed correct various tests can be performed for relevance to the transform from ciphertext to plaintext[2]. If there is a “method” and not just random luck then the level of confidence you have on the message goes up.

Thus the real battle is keeping not the plaintext secret but the method secret. That is making the space the method works in to large or complex to be found with any given length of message below certain limits.

The Germans tried to do this with their Lorenz cipher machine in essence all it was was a stream cipher where the stream was generated by short pattern cycles. Any one pattern cycle would have been obvious if the message was twice as long as the pattern cycle. So the designers used another pattern the length of which was prime to the first cycle. This produced a much longer cycle which was as long as the product not the sum of the two pattern cycles. The designers figured if they kept adding pattern cycles at some point the method would not be visable despite the length of the message.

It was broken because somebody made a mistake[3]. Two long messages using the same key setting were sent, the difference in length was smallish but apparent and the ciphertexts started off the same then diverged. This gave information about the encryption method that had untill that point not been available.

The problem with this statue is there is just one short message under this unknown encipherment method. Even giving hints such as short parts of the plaintext does not realy help in discovering the method.

[1] See a certain well known social media sight brute forcing it’s name for a secret Tor service identifier.

[2] Look up the “sawbuck” cryptanalysis technique for one simple example, given in Bauer F.L. — Decrypted Secrets: Methods and Maxims of Cryptology ISBN 978-3-662-03452-1.

[3] The reason was the operator sent the equivalent of “Message Number 123” in one message and as the equivalent of “Message No 123” in the other message. Upto that point the two ciphertexts had been the same as you would expect then they diverged again as you would expect. The British having got both ciphertexts and assuming they were the same message went through them and worked out how to seperate the two key streams and then the various periods in use in the encryption method. It was a work of some genius and long hours by the fruits of this work that gave rise to Tommy Flowers developing the first electronic based automatic cryptanalysis machine COLOSUS, that he was wise enough to make more flexible by making it programable. Thus technically the first electronic computer.

https://www.codesandciphers.org.uk/lorenz/fish.htm