Re: Triangulation Cryptography - Statistical Cryptanalysis Attack.

From	"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups	sci.crypt
Subject	Re: Triangulation Cryptography - Statistical Cryptanalysis Attack.
Date	2021-09-17 13:39 -0700
Organization	Aioe.org NNTP Server
Message-ID	<si2udf$94r$2@gioia.aioe.org> (permalink)
References	(5 earlier) <si2lv0$kr0$1@gioia.aioe.org> <22751d32-7d5e-43ce-9060-6b0fa3ba4bbdn@googlegroups.com> <si2nut$1i95$1@gioia.aioe.org> <15d4e9a7-59f7-47ea-9840-aa266dc7f781n@googlegroups.com> <si2qd0$ln9$1@gioia.aioe.org>

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On 9/17/2021 12:30 PM, Max wrote:
> On 17.09.21 21:09, austin obyrne wrote:
>> On Friday, 17 September 2021 at 19:49:04 UTC+1, Max wrote:
>>> On 17.09.21 20:35, austin obyrne wrote:
>>>> On Friday, 17 September 2021 at 19:15:02 UTC+1, Max wrote:
>>>>> On 17.09.21 20:04, austin obyrne wrote:
>>>>>> On Friday, 17 September 2021 at 18:32:18 UTC+1, Max wrote:
>>>>>>> On 17.09.21 19:11, austin obyrne wrote:
>>>>>>> [..]
>>>>>>>>
>>>>>>>> As I see I don't think combinatorics is valid as a method in 
>>>>>>>> vector cryptography
>>>>>>>> .- OK in scalar data that have magnitude but not with vectors ( 
>>>>>>>> that have direction as well as magnitude).
>>>>>>> You don't use "directions". They are, at best, an "emergent 
>>>>>>> property" of
>>>>>>> your vectors. Your vectors are sufficiently defined by their x, y 
>>>>>>> and
>>>>>>> z-values. As these values are integers, I can easily map them / 
>>>>>>> encode
>>>>>>> them to a single integer (143, 752, 12) simply becomes 143752012.
>>>>>>>
>>>>>>> Still wondering, where do the 9! come from? I think, this is wrong.
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> AOB
>>>>>>>>
>>>>>>>
>>>>>>> Cheers,
>>>>>>>
>>>>>>> Max
>>>>>> Each column (of the 7) can be filled in 9! ways i.e. nine 
>>>>>> factorial ways.
>>>>>> (The possibility space must consider filling all 9 places in every 
>>>>>> possible way)
>>>>>> There are 7 'columns' => 9^7
>>>>>> There are 3 sets of 7 integers as coefficients of i, j, k => 
>>>>>> (9!^7) ^3 = 9! ^ 21
>>>>>> in words - nine factorial to the power of twenty one.
>>>>> I asked, where the 9! comes from, not the 21. Why do you think, each
>>>>> column can be filled in 9! ways?
>>>>> If we're talking digits, then each spot in a 7-digit-number can be
>>>>> filled in 10 ways. So, there are 10^7 possible combinations.
>>>>>
>>>>>>
>>>>>> AOB
>>>>>>
>>>>> So, there are 10^7 possible combinations.
>>>> Zero (0) doesn't count anywhere n the first column= > 9 only ways
>>> Yes, it does. Or do you only allow for vector coefficients greater or
>>> equal to 100? 7 would be 007. Same with all the following digits. 700 is
>>> a valid value, too.
>>>> - Doesn't happen in my work but you may have a point to argue in 
>>>> other cases
>>>> .- Better settle for 9 all round - hence 9! - agreed ?
>>> No. Even if there were 9 possible values per digit, that would be
>>> 9*9*9*...*9 aka 9^n. 9! would be 9*8*7*6*5*4*3*2*1, only applicable, if
>>> each digit in a 9-digit-number would have to be unique and also not
>>> allowed to be 0.
>>>
>>>
>>>>
>>>> AOB
>>>>
>> This is beyond argument - it is a standard result => n places can be 
>> filled in n! ways - I've been using this on trust for many years
>>
>> In our case these is no point in filling a place in the first 
>> column.with zero - okay in all the others of course  => total = ( 9! + 
>> 10!^6) ^3 in a single ciphertext item comprised of 3 x 7digit 
>> integers. - please check.
> 
> Yes, there is. If you want to express a k digit number with n digits and 
> n > k > 0 , you have to fill up the left n-k digits with zeros. There is 
> no other way to express 7 as a 3-digit-number than 007.

Sorry for butting in, but what about:

124 = 1 + 2 + 4 = 7

;^)

Thread

Triangulation Cryptography  - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 09:07 -0700
  Re: Triangulation Cryptography  - Statistical Cryptanalysis Attack. Leo <usenet@gkbrk.com> - 2021-09-17 16:17 +0000
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-17 17:34 +0100
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 02:28 -0700
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 09:36 -0700
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 09:14 -0700
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. 711 Spooky Mart <711@spooky.mart> - 2021-09-24 15:14 -0500
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-24 21:57 +0000
  Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-17 17:23 +0100
  Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 18:44 +0200
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 10:11 -0700
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 19:32 +0200
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-17 18:43 +0100
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 11:04 -0700
          Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 20:14 +0200
            Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 11:35 -0700
              Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 20:49 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 12:09 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 21:30 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-17 13:39 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 22:44 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-17 13:55 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. 711 Spooky Mart <711@spooky.mart> - 2021-09-24 15:33 -0500
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-17 20:42 +0100
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 22:25 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. wizzofozz <oxxxxxxxxxxxs@gmail.com> - 2021-09-17 22:56 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-17 23:11 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. wizzofozz <oxxxxxxxxxxxs@gmail.com> - 2021-09-17 23:53 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Max <maxturv26@gmx.net> - 2021-09-18 00:16 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-18 00:12 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 01:56 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 10:09 +0100
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 02:25 -0700
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-17 20:57 +0000
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. wizzofozz <oxxxxxxxxxxxs@gmail.com> - 2021-09-17 23:03 +0200
                Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. wizzofozz <oxxxxxxxxxxxs@gmail.com> - 2021-09-17 22:47 +0200
            Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-17 20:54 +0000
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. austin obyrne <ao402468@gmail.com> - 2021-09-17 11:23 -0700
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-17 20:50 +0000
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-17 20:46 +0000
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-17 13:56 -0700
  Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 02:41 -0700
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 10:55 +0100
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 03:34 -0700
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-18 12:26 +0000
          Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 14:02 +0100
            Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 06:17 -0700
              Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 14:28 +0100
              Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 14:51 +0100
              Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-18 16:20 +0000
            Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Rich <rich@example.invalid> - 2021-09-18 16:18 +0000
  Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 06:24 -0700
    Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 14:31 +0100
      Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. MM <mrvmurray@gmail.com> - 2021-09-18 06:44 -0700
        Re: Triangulation Cryptography - Statistical Cryptanalysis Attack. Richard Heathfield <rjh@cpax.org.uk> - 2021-09-18 15:20 +0100

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