The art of concealment
Lesson 3
The art of hiding a message is a very an ient s ien e, whi h has taken various forms and has improved greatly during the ages, espe ially sin e the information age. One of the referen e books about the s ien e of ryptography is The Code Book, by Simon Singh. Extra ts from this book were read on the BBC. Here are some of them.
I. Julius Caesar 1
[...℄
2
The substitution ypher turns the original message into an en iphered
3
message by substituting ea h letter with a dierent one. So every A in
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the original message may be repla ed with P, every B with K and so on.
5
In ee t, the original alphabet is being rearranged into what is known
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as the ypher alphabet. 1. Name two books ontaining information about the substitution ipher. 2. Try to ypher the following texts using an
n + 10
substitution ipher, whi h
th letter to the right of it (resubstitutes for ea h letter of the alphabet the 10 turning to the beginning when you get to the end of the alphabet) :
Oui-Oui. (Noddy, Enid
All hildren, ex ept one, grow up. (Peter Pan, J. M.
Blyton
)
Barrie
)
3. Using the same ipher, uns ramble the message
SDGKC KZVOK CEBOD YLEBX (Fahrenheit 451, Ray
Bradbury
)
II. Ane shift iphers We start by en oding ea h letter by its numeri al position in the alphabet, from 0 to 25. We then repla e a position
n with the number 3n + 4.
2 ! 3 2 + 4 = 10, while 8 ! 3 8 + 4 = 28 whi h is interpreted as 2 (28 = 26 + 2). Whenever the result of the omputation is larger than 26 we So for example
keep subtra ting 26 until it be omes smaller. Finally we repla e the numbers with the letters they stand for. Première Euro
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1. Fill in the following substitution alphabet for the
3n + 4 ipher.
A
B
C
D
E
F
G
H
I
J
K
L
M
E
H
K
N
Q
T
W
Z
C
F
I
L
O
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
R
U
X
A
D
G
J
M
P
S
V
Y
B
2. Cipher the following text using this rule.
It was love at first sight. (Cat h-22, Joseph
Heller
)
3. De ipher the following message, that has been oded using this rule.
CJZCR ICLLG JUXZQ DQ (Andrew
Alberti's Cipher Disk
Wiles
, 23 June 1993)
Blet hley Park Museum exhibit
III. Every possible rearrangement 1
There are over 400 million million million million ways of rearranging the
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letters of the alphabet, and so an enemy odebreaker annot hope to de-
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ipher an inter epted message by he king every possible rearrangement.
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In fa t, if an agent ould he k one of the possible rearrangements every
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se ond it would take roughly a billion times the age of the universe to
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he k all of them. 1. a) If our alphabet had only three letters, how many ways would there be of
rearranging them ?
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b) The same question if it had only four letters.
) Can you explain where the 400 million. . . omes from ? 2. a) If an agent ould he k one of the possible rearrangements every se ond
how many years would it take him to do it ? b) How does that orrespond to Simon Singh's al ulation ?
IV. Breaking the ode For over a millennium an ient s holars onsidered that the substitution ipher was unbreakable. The breakthrough o
urred in the East and required a brilliant
ombination of linguisti s, statisti s and religious devotion. The 8
th entury AD heralded the golden age of the Islami ivilization. Arab theo-
logians were interested in establishing the hronology of the revelations ontained in the Qu'ran, and they did this by ounting the frequen y of words and letters
ontained in ea h revelation. The great mathemati ian Al-Kindi made the apparently inno uous observation that some letters were more ommon in Arabi than others. He used this observation to devise a de iphering method. 1
Al-Kindi's ode-breaking te hnique is most easily explained by imagining
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a message originally written in English whi h has then been en rypted
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and whi h has fallen into the hands of an enemy odebreaker. Al Kindi
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advised the odebreaker to look for the most ommon letter in the en-
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rypted text. If the most ommon letter is, say, W, then this probably
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represents the letter E, be ause E is the most ommon letter in English,
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a
ounting for roughly 13 % of all letters. Similarly the se ond most
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ommon letter in the en rypted text probably represents T, and the
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third probably represents A, the se ond and third most ommon letters
10
in English.
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This te hnique, known as frequen y analysis, relies on linguisti s and
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mathemati s as well as a ertain level of guile, guess work and intuition. 1. Can you imagine situations when this te hnique would not be of mu h use for
the odebreaker ? 2. Can you imagine a te hnique to improve the substitution ipher ?
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