How to get plain text from several ciphered messages in depth
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1) INTRODUCTION
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Perhaps, the superposition method is the most powerful cryptanalysis one.
It was invented by Auguste Kerckhoffs. To use it, it is necessary to have 
several messages which were enciphered with the same key. The number of 
messages need to be placed over each other, "in depth". All letters of 
each column are ciphered by the same alphabet!

With a cipher machine like Enigma, it is necessary to have more than a dozen 
messages to have any hope of finding the solution. But, in case of cipher 
machines which use an additive method (as an Hagelin serie C cipher machine),
only two messages in depth are sufficent. Naturally the more messages in 
depth you have, the easier it is.

The Hagelin serie C cipher machine encryption formula is:
   In the same column, for a single letter:
           cipher1 = ((key + slide) - plain1) % 26   
           cipher2 = ((key + slide) - plain2) % 26
   We can calculate difference (delta):
           DELTA = cipher1 - cipher2 = plain2 - plain1
           plain2 = DELTA + plain1

We know cipher1 and cipher2. If we guess plain1 (or plain2) we can calculate
the letter plain2 (or plain1).
In short, if we guess a probable word in the good position, plain text
will appear (a word or the begining of a word or the ending of a word).


2) GUESSING A PROBABLE WORD AT THE BEGINNING OF THE MESSAGE
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Assume to have these three enciphered messages "in depth":
     No. 1 - FZGYU LMIJE LMXSS EXHNG SJFKG MOEZO AOUGY
     No. 2 - FZGYR ZFDRM MZJRV TQZGV GRTQS PTXAG ONTGY
     No. 3 - XYTUR QLCSW LTBYG QXHNU OVQZA AEXNR HBGGY

We guess that the 3rd message begins by the word "BIRDS". Try to decipher
the 1st message:
       F - X = B - ? =  5 - 23 =  1 - ? = 8  => ? = 1 - 8 = -7 = 19 = T
       Z - Y = I - ? = 25 - 24 =  8 - ? = 1  => ? = 8 - 1 = 7 = H
       G - T = R - ? =  6 - 19 = 17 - ? = 13  => ? = 17 - 13 = 4 = E
       Y - U = D - ? = 24 - 20 =  3 - ? = 4  => ? = 3 - 4 = -1 = 25 = Z
       U - R = S - ? = ...

Then, the 1st message begins by the word "THE". We are on the good track!


3) SEARCHING A PROBABLE WORD SOMEWHERE IN THE MESSAGE
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We believe that the probable word "WHEEL" is in the 2nd message, but we
don't know where. We need to try this word in all positions and verify if 
plain text appears in other texts.

For example, if we scan the 2nd message with probable string "ZWHEELZ",
we find the following strings in the 1st message:
   ...
   06 SRPMFYL
   07 UEPFRXY
   08 HEIRQKC
   09 HXUQDOO
   10 AJTDHAS
   11 MIGHTER   (Hooray !!!)

We have found several things:
- The string "ZWHEELZ" appears in the 2nd message at the 11th position.
- The string "MIGHTER" appears in the 1st message at the 11th position.  
  Perhaps it is bordered by "Z": "ZMIGHTERZ" ?
- We can search for plain text at the 11th position in other messages:
  in the 3rd message, we found "FEATHER".
 
Generally, when we find new plain text, it is the ending or begining of 
a word. If we guess the whole word, we can verify our hypothesis in other
messages. If our hypothesis is true perhaps we can find new plain text again.
Step by step we can reconstruct all the plain texts.


4) BIGRAPHS FREQUENCY METHOD
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[Excerpt of TICOM DF-120 (German method to get plain text from messages in
depth)]
... At the point following the "Z" in both messages, a new word has to begin.
We seek out in the next two positions all the bigraphs which could yield, in
both messages at the same time, possible English words or good abbreviations
...


5) EXAMPLES OF PROBABLE WORDS
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Examples of probable words or probable strings:
- The figures: "ONE" (or "ZONEZ"), "TWO", "THREE", "FOUR", ...

- Signs or abbreviations: "PAREN" (or "ZPARENZ"), "DASH", "QUOTE",
"CMA" [meaning "comma"], "PD" [period], "CLN" [meaning "column"], "XXX", ...

- Short words: THE (or "ZTHEZ"), AND (or "ZANDZ"), HAS (or "ZHAS"), 
FOR (or "ZFORZ"), THAT (or "ZTHATZ"), OFTEN (or "ZOFTENZ"), 
WITH (or "ZWITHZ"), NEVER (or "ZNEVERZ"), IN (or "ZINZ), TO (or "ZTOZ"), ...

- Beginning or ending of words: -TION (or "TIONZ"), -MENT (or "MENTZ"), 
-ING (or "INGZ"), THER- (or "ZTHER"), ...

With experience, a depth of two messages can be solved easily.