[Cryptography] Unicity distance of Playfair

[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.

				Bear

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