[Cryptography] Unicity distance of Playfair

[mok-kong shen]

Am 24.03.2016 um 03:47 schrieb Ray Dillinger:
>
>
> On 03/22/2016 11:14 AM, mok-kong shen wrote:
>> Anyway, I should appreciate it very much, if someone could privide
>> me a terse recipe, listing which computations are to be done in order
>> to obtain the unicity-distance of Playfair. (I am attempting to
>> determine whether a certain suggested variant of Playfair provide
>> performance advantages or not and suppose that the unicity-distance
>> could be a useful measure for that purpose.)
>
>
> Okay, here's your terse recipe:
>
> Keybits/Redundancy = Unicity.
>
> Keybits = number of bits required to count all the possible keys.
>
> Redundancy = RepBits - InfoBits
>
> RepBits = Number of bits required to count the units of the encoding
> InfoBits = Amount of information conveyed by each unit of the encoding
>
> Using Playfair we either can't distinguish IJ, or we can't
> distinguish YZ.  That makes it a 25-character alphabet.
>
> Log2 of 25 is RepBits, the number of bits required to count the
> units of encoding.  It's about 4.64.
>
> InfoBits is the number of bits of information conveyed per unit
> of the alphabet used.  In English, it's estimated to be about 1.5.
> This is unaffected by the indistinguishability of an IJ pair
> or a YZ pair because there are approximately no words you could
> confuse for each other due to ambiguity between those pairs -
> ie, those particular distinctions don't measurably _contribute_
> to the information conveyed per character.
>
> Redundancy = (RepBits - InfoBits) = (4.64 - 1.4) = 3.24.
>
> Playfair has 25! possible keys because there are 25 different
> boxes in the grid to fill with letters (one of them gets to be
> both I and J, or else one of them gets to be both Y and Z).  It
> takes about 83.7 bits to count 25! different keys, so keybits
> is 83.7.
>
> 83.7 / 3.24 = about 25.8333.  Rounding to the nearest whole
> number, therefore Playfair has about 26 character Unicity
> distance.
>
> This means that, *on average*, given a Playfair key and 26
> letters of ciphertext, you can tell whether or not it's the
> right key.
>
> Given the ciphertext, though, it's a lot harder to *find* the
> correct key with Playfair than it is with a number of other
> 'hand' ciphers whose Unicity distance is larger. Unicity
> distance is not a measure of security.

One point I don't yet understand: You wrote: "Using Playfair we
either can't distinguish IJ, or we can't distinguish YZ." Clearly
you refer 'IJ' to input and 'YZ' to output. But 'IJ' has a (variable)
space of 25*25 (like 'I' has a space of 25), isn't it? So 'IJ'
would be an alphabet of 25*25 in my current view.

M. K. Shen