Re: Triangulation Cryptography - Statistical Cryptanalysis Attack.

From	Rich <rich@example.invalid>
Newsgroups	sci.crypt
Subject	Re: Triangulation Cryptography - Statistical Cryptanalysis Attack.
Date	2021-09-17 20:46 +0000
Organization	A noiseless patient Spider
Message-ID	<si2urq$srl$3@dont-email.me> (permalink)
References	<438ad408-35cb-4e67-968d-9c0b67861b31n@googlegroups.com> <si2glu$3nn$1@gioia.aioe.org>

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Max <maxturv26@gmx.net> wrote:
> On 17.09.21 18:07, austin obyrne wrote:
>> Given that the ciphertext is comprised of groups of 3 x seven-digit 
>> integers.  It follows that the sample space is of the order of (9 
>> factorial)^21 in any attack.  This is 362880^21- an enormous number 
>> that can even be made emuch larger if needs be.
> 
> 9 factorial?  I'd like to see that math.  Is there any point in your 
> cipher where each number from 1 to 9 has to appear exactly once?  I 
> hope all values are independent from one another.

As with most things that Austin posts, his math is comically wrong.

So, now it is "seven digit integers".  Well, "seven digit integers" can 
represent 10,000,000 possible numbers.

Now, I switch to some "bc" work to do the math.

Three "seven digit" integers then are:

  10000000*10000000*10000000*3
  3000000000000000000000

Possible combinations.

Now, define a factorial function (this is direct from the bc manpage):

  define f (x) {
    if (x <= 1) return (1);
    return (f(x-1) * x);
  }

And then compute (9 factorial)^21:

  f(9)^21
  56888396215740878371932195299255658329404794388858314473940721862532\
  2895127819048683463338098688000000000000000000000

Hmm, that number is significantly longer than the first.  How much 
longer (at this size, I'm just letting BC do integer arithmetic, with 
numbers this big, no one cares if the answer has a decimal value)?

  (f(9)^21)/(10000000*10000000*10000000*3)
  18962798738580292790644065099751886109801598129619438157980240620844\
  0965042606349561154446032896

So Austin's math is wrong by a factor of 189,627,987,385,802,927,906,\
440,650,997,518,861,098,015,981,296,194,381,579,802,406,208,440,965,\
042,606,349,561,154,446,032,896 times.

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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