The Case Against Steganography In Perceptually Encoded Media

[georgemw at speakeasy.net]

On 14 Sep 2002 at 12:32, Peter Wayner wrote:


> It's also important to remember that there are many tricks that avoid 
> making changes in the usual way. I'm currently very intrigued with 
> the potential to rearrange lists of items. (You can try out an applet 
> here: http://www.wayner.org/books/discrypt2/sorted.php)
> 

There's an error in the way youconvert arrangements into
numbers.  On your page you have

<quote>
A Strange Notation 
Before beginning, we need to introduce one slightly strange 
notation, a flexible base, where the ith digit can be any value 
between 0 and i+1. The digits are enumerated from right to 
left so the smallest value, the one with the least significance 
on the right, is digit 0. It can be either a 0 or a 1. The next 
digit to its left, the one with next-to-least significance, is digit 
1 and it can be either a 0, a 1, or a 2.

Here's a value in the flexible base: 321. Each digit is set to it's 
maximum value. What is this value in base 10? To figure this 
out, first find the multiple assigned to each digit. That is, how 
much each digit contributes to the final value. In base 10, the 
multiple assigned to digit 1 is 10 and the multiple assigned to 
digit 2 is 100. To put it simply, the multiple of digit i is 10i in 
base ten and 2i in base two. What is the multiple of each digit 
in this flexible base? In the fixed bases, each digit's multiple 
increases by another factor of the base for each new digit. In 
this example, each digit has a different value. The 0 digit can 
only take two values, 0 or 1. The 1 digit can take three values, 
0, 1 or 2. The multiple of digit i is (i+1)!. You can check it 
out. What is 321 in base ten? That's 
1*(1!)+2*(2!)+3*(3!)=1+4+18=23. 
 </quote>

There's no reason for the factorials in the notation, the multiple
of digit i should be i, not i!, so the value of any permutation of
n items should be something from 0 to n!-1.  for example,
for 3 items what you should have is

permutation	value
123		0
132		1
213		2
231		3
312		4
321		5
  

> I guess it's important not to let an obsessive attention to 
> mathematical perfection  prevent you from accomplishing something 
> cool. After all, every RSA key can be factored eventually, but we 
> still use the system because it's practically secure.
> 
> -Peter
> 
George