[Cryptography] Unicity distance of Playfair

[mok-kong shen]

Am 25.03.2016 um 01:38 schrieb Ray Dillinger:
>
>
> On 03/24/2016 04:17 PM, mok-kong shen wrote:
>> Am 24.03.2016 um 22:41 schrieb Ray Dillinger:
>
>>> It doesn't matter.  The cipher produces one output letter per
>>> input letter.  The letter in this case is the basic unit of
>>> encryption.  This is true with almost all hand ciphers.
>
>> Sorry, I don't yet understand the "purpose" of your mentioning this
>> general fact, for another similar general fact for most ciphers
>> is that they produce one output bit per input bit and the bit is the
>> "most" basic unit of all encryption. The unit of processing is
>> another basic unit and for Playfair it happens to be 2 characters
>> in each step.
>
> You don't have to know how a particular cipher works to calculate
> the Unicity distance.  Every cipher that has the same key length
> will have the same unicity distance when used to encrypt English.
> So thinking of pairs is strictly a distraction here.
>
> Using different units will not affect the unicity distance any
> more than the difference between measuring a distance in miles
> or kilometers affects the distance.  I got my answer in letters
> because I worked the problem using bits of information per letter
> to calculate the redundancy of English text.
>
> The number of different possible keys is easiest to calculate
> using letters, and the redundancy of English text is available
> as a measure per letter.  That made working with letters easiest.
>
> If you want, You can measure the unicity distance in bits
> instead, and at 4.64 bits per Playfair character, it's going
> to be about 120 bits.  If you want to measure it in pairs it's
> going to be about 13 pairs.  The number of possible keys does
> not change in either case.
>
> In each case it's the same amount of information because the
> redundancy of English scales exactly according to the size
> units you're measuring it in.

Your sentence "Every cipher that has the same key length will have
the same unicity distance when used to encrypt English." is IMHO
evidently a "consequence" of these "ciphers" which have been examined
all have alphabet of size 26 (excepting Playfair, which we are arguing
here). So your logic is apparently problematical here.

Anyway, your post of 24.03. employed the term "aphabet". In a post
of mein to J. Leichter I used the hypothetical (because impractical)
case of digraphic Vigenere. Do you agree at all that in that case
the "alphabet" is 26**2 instead of 26?

M. K. Shen