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== Mini UGGs ==
In classical [[cryptography]], the '''trifid cipher''' is a cipher invented around 1901 by [[Felix Delastelle]], which extends the concept of the [[bifid cipher]] to a third dimension, allowing each symbol to be [[transposition cipher#Fractionation|fractionated]] into 3 elements instead of two. That is, while the bifid uses the [[Polybius square]] to turn each symbol into coordinates on a 5 × 5 (or 6 × 6) square, the trifid turns them into coordinates on a 3 × 3 × 3 cube. As with the bifid, this is then combined with [[transposition cipher|transposition]] to achieve [[confusion and diffusion|diffusion]]. However a higher degree of diffusion is achieved because each output symbol depends on 3 input symbols instead of two. Thus the trifid was the first practical [[substitution cipher#Polygraphic substitution|trigraphic substitution]].


== Operation ==
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Several variants probably exist: Below is one example but most decoders work slightly differently: they use TABLE,ROW,COLUMN. The principle remains the same but the result will be completely different. The Dutch version of this page has another example. And there are also different ways to fill out a keyword in the tables: spread out horizontally or fill up one table first.
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First, a [[substitution cipher|mixed alphabet]] cubic analogue of the Polybius square is drawn up:
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{| border="2" cellpadding="4"
! colspan="4" | Layer 1 ||
! colspan="4" | Layer 2 ||
! colspan="4" | Layer 3
|-
! || 1 || 2 || 3 || || || 1 || 2 || 3 || || || 1 || 2 || 3
|-
| '''1''' || F || J || O || || '''1''' || V || Z || L || || '''1''' || E || U || Q
|-
| '''2''' || R || X || C || || '''2''' || G || D || P || || '''2''' || N || H || A
|-
| '''3''' || Y || B || S || || '''3''' || M || W || T || || '''3''' || . || K || I
|}


In theory, the message is then converted to its [[Cartesian coordinate system|coordinate]]s in this grid; in practice, it is more convenient to write the triplets of trits out in a table, like so:
== Mens UGG Kenton Slippers ==
{| border="1" cellpadding="4"
| F 111 || C 132 || W 223 || U 321
|-
| R 112 || S 133 || L 231 || H 322
|-
| Y 113 || V 211 || P 232 || K 323
|-
| J 121 || G 212 || T 233 || Q 331
|-
| X 122 || M 213 || E 311 || A 332
|-
| B 123 || Z 221 || N 312 || I 333
|-
| O 131 || D 222 || . 313 ||
|}
Then the coordinates are written out vertically beneath the message:
'''T R E A T Y E N D S B O E R W A R .'''
2 1 3 3 2 1 3 3 2 1 1 1 3 1 2 3 1 3
3 1 1 3 3 1 1 1 2 3 2 3 1 1 2 3 1 1
3 2 1 2 3 3 1 2 2 3 3 1 1 2 3 2 2 3
They are then read out in rows:


2 1 3 3 2 1 3 3 2 1 1 1 3 1 2 3 1 3 3 1 1 3 3 1 1 1 2 3 2 3 1 1 2 3 1 1 3 2 1 2 3 3 1 2 2 3 3 1 1 2 3 2 2 3
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Then divided up into triplets again, and the triplets turned back into letters using the table:
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213 321 332 111 312 313 311 331 112 323 112 311 321 233 122 331 123 223
''' M  U  A  F  N  .  E  Q  R  K  R  E  U  T  X  Q  B  W'''
In this way, each [[ciphertext]] character depends on three [[plaintext]] characters, so the trifid is a trigraphic cipher. To decrypt, the procedure is simply reversed.


== Dimensions ==
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As the bifid concept is extended to higher dimensions, we are much less free in our choice of parameters.
 
Since <math>2^3 = 8 < 26 < 27 = 3^3</math>, our cube needs to have a side length of at least three in order to fit in the 26 letters of the alphabet. But if we go even to 4, then our symbol set would have <math>4^3 = 64</math> symbols, which is probably too much for classical cryptography. Thus, the trifid is only ever implemented with a 3 &times; 3 &times; 3 cube, and each coordinate is indicated by a [[ternary|trinary digit]], or trit. Incidentally, note that since this gives us 27 symbols, we will have one extra. In the example above, the period or full-stop was used.
 
If we increase the dimensions further to four, noting that <math>2^4 = 16 < 26</math>, we still need a side length of 3 - giving a symbol set of size <math>3^4 = 81</math>, far more than we need. If we go one step further, to five dimensions, then we only need a side length of 2, since <math>2^5 = 32 > 26</math>. But such a [[binary numeral system|binary]] encoding - 5 [[bit]]s - is what occurs in [[Baudot code]] for telegraphic purposes. Breaking letters into bits and manipulating the bits individually is the hallmark of modern cryptography. Thus, in a sense, the trifid cipher can be thought to stand on the border between classical cryptography's ancient [[Polybius square]], and the binary manipulations of the modern world.
 
== See also ==
Other ciphers by Delastelle:
* [[Four-square cipher]] (related to [[Playfair cipher|Playfair]])
* [[Bifid cipher]] (similar to trifid)
 
{{Cryptography navbox | classical}}
 
[[Category:Classical ciphers]]

Latest revision as of 21:03, 3 December 2014

Mini UGGs

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