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Episode 12 – Breaking a substitution code European section – Season 3

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Episode 12 – Breaking a substitution code

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ibn ’omran ibn Ismail al-Kindi (9th century).

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Letter frequencies in English

0 2 4 6 8 10 12 14

a b c d e f g h i j k l m n o p q r s t u v w x y z

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53‡‡†305))6∗;4826)4‡.)4‡);806∗;48†8

$60))85;1‡(;:‡∗8†83(88)5∗†;46(;88∗96

∗?;8)∗‡(;485);5∗†2:∗‡(;4956∗2(5∗–4)8

$8∗;4069285);)6†8)4‡‡;1(‡9;48081;8:8‡

1;48†85;4)485†528806∗81(‡9;48;(88;4 (‡?34;48)4‡;161;:188;‡?;

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Symbol frequencies in the cipher

8 ; 4 ‡ ) ∗ 5 6 † 1

33 26 19 16 16 13 12 11 8 8

0 9 2 : 3 ? $ – .

6 5 5 4 4 3 2 1 1

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8 = e

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8 e

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8 e

;48 =

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8 e

;48 = the

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8 ; 4 e t h

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8 ; 4 e t h

;48;(88;4 =

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8 ; 4 e t h

;48;(88;4 = thet.eeth =

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8 ; 4 e t h

;48;(88;4 = thet.eeth = the tree th

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8 ; 4 ( e t h r

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8 ; 4 ( e t h r

the tree ;4(‡?34

=

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8 ; 4 ( e t h r

the tree ;4(‡?34

= the tree thr‡?3h

=

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8 ; 4 ( e t h r

the tree ;4(‡?34

= the tree thr‡?3h

= the tree through

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8 ; 4 ( ‡ ? 3 e t h r o u g

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8 ; 4 ( ‡ ? 3 e t h r o u g

†83(88 =

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8 ; 4 ( ‡ ? 3 e t h r o u g

†83(88 = †egree =

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8 ; 4 ( ‡ ? 3 e t h r o u g

†83(88 = †egree = degree

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8 ; 4 ( ‡ ? 3 †

e t h r o u g d

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8 ; 4 ( ‡ ? 3 †

e t h r o u g d

;46(;88∗=

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8 ; 4 ( ‡ ? 3 †

e t h r o u g d

;46(;88∗= th6rtee∗=

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8 ; 4 ( ‡ ? 3 †

e t h r o u g d

;46(;88∗= th6rtee∗= thirteen

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8 ; 4 ( ‡ ? 3 † 6 ∗

e t h r o u g d i n

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8 ; 4 ( ‡ ? 3 † 6 ∗

e t h r o u g d i n

53‡‡†=

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8 ; 4 ( ‡ ? 3 † 6 ∗

e t h r o u g d i n

53‡‡†= 5good =

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8 ; 4 ( ‡ ? 3 † 6 ∗

e t h r o u g d i n

53‡‡†= 5good = A good

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8 ; 4 ( ‡ ? 3 † 6 ∗ 5

e t h r o u g d i n a

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8 ; 4 ( ‡ ? 3 † 6 ∗ 5

e t h r o u g d i n a

’A good glass in the bishop’s hostel in the devil’s seat forty-one degrees and thirteen minutes northeast and by north main branch seventh limb east side shoot from the left eye of the

death’s-head a bee-line from the tree through the shot fifty feet out.’

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About five of the letters should have a frequency less than 1 per cent, they probably represent j, k, q, x and z.

One of the letters should have a frequency greater than 10 percent, and it probably represents e.

0 4 8 12

a b c d e f g h i j k l mn o p q r s t u v w x y z

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If the plaintext doesn’t reveal itself immediately, which is often the case, then focus on pairs of repeated letters.

In English the most common repeated letters are ss, ee, tt, ff, ll, mm and oo.

If the ciphertext contains any repeated characters, you can assume that they represent one of these.

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More complex use of statistics can be conceived, such as considering counts of pairs of letters, or triplets (trigrams), and so on.

For instance, q and u nearly always occur together in that order in English, even though q itself is rare.

Also,th is the most common bigram, and the the most common trigram.

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One of the most useful skills for a cryptanalyst is the ability to identify words, or even entire phrases, based on experience or sheer guesswork. Any such word or phrase is known as a crib.

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Al-Kindi

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Blaise de Vigenère

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Charles Babbage

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Alan Turing

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Ralph Merkle, Martin Hellman, Whitfield Diffie

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Adi Shamir, Ronald Rivest, Len Adleman

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Phil Zimmermann

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Clifford Cocks

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Georges Perec

Episode 12 – Breaking a substitution code

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