Re: Manual hashing
From: AE (hidden_at_nospam.com)
Date: 06/29/04
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Date: Tue, 29 Jun 2004 20:32:30 +0200
Here yet another suggestion I tried today: It's based on error
correcting codes.
I'm using the string "mokkongshen" as an example.
1) convert characters and numbers to decimal numbers
For english text I'd use the following well known scheme to convert
frequent characters to single digits and less frequent characters to
pairs of digits.
1 2 3 4 5 6 7 8 9 0
a e i n o r s t
9 b c d f g h j k l m
0 p q u v w x y z # .
. is the stop symbol as used in a telegram
# is necessary to switch between numbers and characters.
Every number is represented by itself, repeated once, so there's no
collission between a number and this character.
The resulting number sequence is:
90 5 98 98 5 4 95 7 96 2 4
It's easier for me to do additions with numbers than
with characters and numbers. Else I would have omitted this step.
2) Write this number sequence in the smallest square it fits.
Our example happens to fit exactly in a 4x4 square.
In other cases it might be necessary to fill the square with
sequences of 09 (a combination that doesn't make sense at the end of
a string and that doesn't make sense when being repeated so no danger
a string could be replaced with a string where just 09 is appended.
Sum the rows and columns modulo 10.
9059 3
8985 0
4957 5
9624 1
0405
This is my compression step. Larger sequences should be split into
several squares of at most 9x9 - this makes calculation less
error-prone and preservers in the checksum of every square the
entropy of typical english text.
3) Repeat this step with one or more squares that are filled in a
different way. Don't simply change rows and colums - I'm filling them
once diagonal and once in a spiral.
9098 6 9059 3
5859 7 7968 0
9476 6 5429 0
9524 0 9458 6
2737 0784
Generally it's simple to find a second square that produces the same
checksum as the first one and that way to produce collissions.
Adding these additional squares it should be more puzzling for the
attacker to produce collissions.
4) Concatenate the resulting digits to numbers - and sum the rows of
each square and the columns of each square.
3051 + 6760 + 3006 = 12817
0405 + 2737 + 0784 = 03926
The concatenation of row-sum and column-sum is the checksum:
0392612817
This is simply a different compression step that doesn't commute with
addition modulo 10.
In this special example compression is not as good as requested, but for
larger texts results will be better.
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