CRYPTOGRAPHY

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CRYPTOGRAPHY

• Lecture 5

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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 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 A C D E F G H I J K L M N O P Q R S T U V W
X Y Z A B D E F G H I J K L M N O P Q R S T U V W
X Y Z A B C E F G H I J K L M N O P Q R S T U V W
X Y Z A B C D F G H I J K L M N O P Q R S T U V W
X Y Z A B C D E G H I J K L M N O P Q R S T U V W
X Y Z A B C D E F H I J K L M N O P Q R S T U V W
X Y Z A B C D E F G I J K L M N O P Q R S T U V W
X Y Z A B C D E F G H J K L M N O P Q R S T U V W
X Y Z A B C D E F G H I K L M N O P Q R S T U V W
X Y Z A B C D E F G H I J L M N O P Q R S T U V W
X Y Z A B C D E F G H I J K M N O P Q R S T U V
W X Y Z A B C D E F G H I J K L N O P Q R S T U
V W X Y Z A B C D E F G H I J K L M O P Q R S T
U V W X Y Z A B C D E F G H I J K L M N P Q R S
T U V W X Y Z A B C D E F G H I J K L M N O Q R
S T U V W X Y Z A B C D E F G H I J K L M N O P
R S T U V W X Y Z A B C D E F G H I J K L M N O
P Q S T U V W X Y Z A B C D E F G H I J K L M N
O P Q R T U V W X Y Z A B C D E F G H I J K L M
N O P Q R S U V W X Y Z A B C D E F G H I J K L
M N O P Q R S T V W X Y Z A B C D E F G H I J K
L M N O P Q R S T U W X Y Z A B C D E F G H I J
K L M N O P Q R S T U V X Y Z A B C D E F G H I
J K L M N O P Q R S T U V W Y Z A B C D E F G H
I J K L M N O P Q R S T U V W X Z 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
SAVEMEPLEASE plain text CRYPTOGRAMCR
keyword URTTFSVCEMUV enciphered The first
letter, S is encrypted using the row beginning
with C The second letter, A is encryted using the
row beginning with R The third letter, V is
encrypted using the row beginning with Y The
fourth letter, E, is encrypted using the row
beginning with P. And so on . . .
You can use http//www.simonsingh.net/The_Black_Ch
amber/v_square.html
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Breaking the Vigenere cipher

• It wasn't until 1854, over two hundred years
  later, that the Vigenère Cipher was finally
  cracked by the British cryptographer Charles
  Babbage. Babbage employed a mix of cryptographic
  genius, intuition and sheer cunning to break the
  Vigenère Cipher. Amazingly, his work was never
  published in his lifetime, and it was over a
  hundred years later, in the 1970's, that his
  technique was finally made public.

This slide and the next few copied directly from
Simon Singhs website.
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Vigenere cipher the unbreakable code

• The strength of the Vigenère Cipher is that the
  same letter can be encrypted in different ways.
  For example, if the keyword is KING, then every
  plaintext letter can be encrypted in 4 ways,
  because the keyword contains 4 letters. Each
  letter of the keyword defines a different cipher
  alphabet in the Vigenère Square. Whole words will
  be enciphered in different ways - the word 'the'
  could be enciphered as DPR, BUK, GNO and ZRM
  depending on its position relative to the
  keyword. Although this makes cryptanalysis
  difficult, it is not impossible.

This slide and the next few copied directly from
Simon Singhs website.
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Breaking the Vigenere cipher the unbreakable
code

• The important point to note is that if there are
  only four ways to encipher the word 'the', and
  the original message contains several uses of the
  word 'the', then it is inevitable that some of
  the four possible encipherments will be repeated
  in the ciphertext. This is demonstrated in the
  following example, in which the line "The Sun and
  the Man in the Moon", has been enciphered using
  the Vigenere cipher and the keyword KING.

This slide and the next few copied directly from
Simon Singhs website.
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Breaking the Vigenere cipher

• KINGKINGKINGKINGKINGKING keyword
• THESUNANDTHEMANINTHEMOON plaintext
• DPRYEVNTNBUKWIAOXBUKWWBT cipher
• The letters BUK repeat after 8 letters. This
  suggests that the number of letters in the
  keyword is a factor of 8. So, the keyword has 2,
  4, or 8 letters.

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Breaking the Vigenere cipher

• The word 'the' is enciphered as DPR in the first
  instance, and then as BUK on the second and third
  occasions. The reason for the repetition of BUK
  is that the second 'the' is displaced by 8
  letters with respect to the third 'the', and 8 is
  a multiple of the length of the keyword. In other
  words, the second 'the' was enciphered according
  to its relationship to the keyword, and by the
  time we reach the third 'the', the keyword has
  cycled round exactly twice, to repeat the
  relationship.

This slide and the next few copied directly from
Simon Singhs website.
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Breaking the Vigenere cipher

• Babbage's vital breakthrough was to realize that
  repetitions in the ciphertext indicated
  repetitions in the plaintext and that the space
  between such repetitions hinted at the length of
  the keyword.

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Breaking the Vigenere cipher

• Once the length of the keyword is determined,
  the message can be broken up into the
  corresponding number of messages, each one is a
  caesar shifted cipher, and amenable to frequency
  analysis.
• This is how Babbage cracked the Vigènere Cipher.

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Breaking the Vigenere cipher
Babbage defined a series of steps to crack the
Vigenère Cipher. Let us try to decipher a sample
ciphertext. We know that it is enciphered using
the Vigenère Cipher, but we know nothing about
the original message or the keyword. http//www.s
imonsingh.net/The_Black_Chamber/cracking_example.h
tml

This slide and the next few copied directly from
Simon Singhs website.
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Breaking the Vigenere cipher

RIKVBIYBITHUSEVAZMMLTKASRNHPNPZICSWDSVMBIYFQEZUBZP
BRGYNTBURMBECZQKBMBPAWIXSOFNUZECNRAZFPHIYBQEOCTTIO
XKUNOHMRGCNDDXZWIRDVDRZYAYYICPUYDHCKXQIECIEWUICJNN
ACSAZZZGACZHMRGXFTILFNNTSDAFGYWLNICFISEAMRMORPGMJL
USTAAKBFLTIBYXGAVDVXPCTSVVRLJENOWWFINZOWEHOSRMQDGY
SDOPVXXGPJNRVILZNAREDUYBTVLIDLMSXKYEYVAKAYBPVTDHMT
MGITDZRTIOVWQIECEYBNEDPZWKUNDOZRBAHEGQBXURFGMUECNP
AIIYURLRIPTFOYBISEOEDZINAISPBTZMNECRIJUFUCMMUUSANM
MVICNRHQJMNHPNCEPUSQDMIVYTSZTRGXSPZUVWNORGQJMYNLIL
UKCPHDBYLNELPHVKYAYYBYXLERMMPBMHHCQKBMHDKMTDMSSJEV
WOPNGCJMYRPYQELCDPOPVPBIEZALKZWTOPRYFARATPBHGLWWMX
NHPHXVKBAANAVMNLPHMEMMSZHMTXHTFMQVLILOVVULNIWGVFUC
GRZZKAUNADVYXUDDJVKAYUYOWLVBEOZFGTHHSPJNKAYICWITDA
RZPVU
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Breaking the Vigenere cipher

RIKVBIYBITHUSEVAZMMLTKASRNHPNPZICSWDSVMBIYFQEZUBZP
BRGYNTBURMBECZQKBMBPAWIXSOFNUZECNRAZFPHIYBQEOCTTIO
XKUNOHMRGCNDDXZWIRDVDRZYAYYICPUYDHCKXQIECIEWUICJNN
ACSAZZZGACZHMRGXFTILFNNTSDAFGYWLNICFISEAMRMORPGMJL
USTAAKBFLTIBYXGAVDVXPCTSVVRLJENOWWFINZOWEHOSRMQDGY
SDOPVXXGPJNRVILZNAREDUYBTVLIDLMSXKYEYVAKAYBPVTDHMT
MGITDZRTIOVWQIECEYBNEDPZWKUNDOZRBAHEGQBXURFGMUECNP
AIIYURLRIPTFOYBISEOEDZINAISPBTZMNECRIJUFUCMMUUSANM
MVICNRHQJMNHPNCEPUSQDMIVYTSZTRGXSPZUVWNORGQJMYNLIL
UKCPHDBYLNELPHVKYAYYBYXLERMMPBMHHCQKBMHDKMTDMSSJEV
WOPNGCJMYRPYQELCDPOPVPBIEZALKZWTOPRYFARATPBHGLWWMX
NHPHXVKBAANAVMNLPHMEMMSZHMTXHTFMQVLILOVVULNIWGVFUC
GRZZKAUNADVYXUDDJVKAYUYOWLVBEOZFGTHHSPJNKAYICWITDA
RZPVU
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Breaking the Vigenere cipher

• Figure out the frequency tables for
• this message (show file)
• See what length the keyword is 7 is a good
  guess.

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Breaking the Vigenere cipher

• It seems probable that the keyword is 7 letters
  long. For the time being let us call the keyword
  L1-L2-L3-L4-L5-L6-L7. The letter L1 defines one
  row of the Vigenère square, and effectively
  provides a monoalphabetic substitution cipher
  alphabet for the first letter of the plaintext,
  and also the 8th 15th 22nd  letters, etc. So if
  we take the corresponding letters in the
  ciphertext, we know they have been encrypted
  using the same row of the Vigenère square, and we
  can work out which row by using frequency
  analysis, because each row of the square is
  equivalent to one monoalphabetic cipher. This
  polyalphabetic cipher consists of cycling between
   7 monoalphabetic ciphers.

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Breaking the Vigenere cipher

• Now we perform a frequency analysis of the
  portion of the ciphertext corresponding to each
  of the shifts. This should give us a good idea of
  the keyword.

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HW5a breaking a Vigenere cipher message

Use the Vigenere cipher to encrypt a longish
message. Then swap with other groups and try to
break the code. Remember that you will need some
computational help . . . Or a lot of time and
brain power.
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Ciphers

• Monoalphabetic ciphers are easy to encode, but
  also easy to break.
• Polyalphabetic ciphers are hard to break, but
  also hard to use.
• Something in the middle
• Homophonic substitution ciphers

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Ciphers

• Monoalphabetic ciphers each letter in the
  plaintext is encoded by only one letter from the
  cipher alphabet, and each letter in the cipher
  alphabet represents only one letter in the
  plaintext.
• Polyalphabetic ciphers each letter in the
  plaintext can be encoded by any letter in the
  cipher alphabet, and each letter in the cipher
  alphabet may represent different letters from the
  plaintext each time it appears.

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Example Homophonic Ciphers

• 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
• 09 48 13 01 14 10 06 23 32 15 04 26
  22 18 00 38 94 29 11 17 08 34 60 28
  21 02
• 12 81 41 03 16 31 25 39 70 37
  27 58 05 95 35 19 20 61 89
  52
• 33 62 45 24 50 73 51
  59 07 40 36 30 63
• 47 79 44 56 83 84
  66 54 42 76 43
• 53 46 65 88
  71 72 77 86 49
• 55 68 93 91
  90 80 96 69
• 78 57
  99 75
• 92 64
  85
• 74
  97
• 82
• 87
• 98

Encode letters which are more frequent by more
possible numbers. We therefore need more than 26
cipher symbols. Each letter in plaintext has
several ciphertext representations, but each
ciphertext letter only represents one plaintext
letter. So this is still a type of
monoalphabetic cipher, but it is not amenable to
frequency analysis.
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Homophonic Ciphers
The homophonic cipher is still a type of
monoalphabetic cipher, mainly because once the
cipher alphabet is set, it does not change. It is
not amenable to frequency analysis, but it is
breakable by digraph analysis. For example, the
letter Q is a funny letter in English it always
appears in combination with a u QU, so if we find
a letter which is only ever followed by a small
number (2-4) of letters, we can assume they make
a QU pair.
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HW6b Homophonic Ciphers
97 68 55 65 99 22 99 95 23 90 59 88 13 62 83 38
56 44 77 88 19 22 63 62 56 27 00 29 82 11 82 62
61 80 57 30 50 12 91 67 35 24 06 08 51 09 77 27
99 58 99 33 84 38 56 12 48 24 75 88 62 62 88 95
39 98 35 48 63 43 83 49 88 19 58 99 43 38 87 40
31 82 13 85 24 83 97 23 16 29
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Digraph ciphers
A digraph cipher encrypts by substituting each
digraph (i.e. pair of letters) in the message
with a different digraph or symbol. In the
digraph cipher shown here, each plaintext digraph
is substituted with a digraph from the square.
For example, 'as' is encrypted by finding the
intersection of the column headed by 'a' with the
row headed by 's', which gives us NO. So, the
plaintext digraph 'as' is substituted with the
ciphertext digraph NO. This digraph cipher much
harder to break than a single letter cipher,
because the codebreaker has to identify the true
value of 676 digraphs, as opposed to struggling
with just 26 letter substitutions.
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Digraph ciphersThe Great Cipher of the Rossingols
A digraph cipher encrypts by substituting each
digraph (i.e. pair of letters) in the message
with a different digraph or symbol. In the
digraph cipher shown here, each plaintext digraph
is substituted with a digraph from the square.
For example, 'as' is encrypted by finding the
intersection of the column headed by 'a' with the
row headed by 's', which gives us NO. So, the
plaintext digraph 'as' is substituted with the
ciphertext digraph NO. This digraph cipher much
harder to break than a single letter cipher,
because the codebreaker has to identify the true
value of 676 digraphs, as opposed to struggling
with just 26 letter substitutions.
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Digraph ciphersThe Great Cipher of the Rossingols
This cipher was only broken 200 years later, by
Etiemme Bazeries. He used frequency analysis to
figure out what the most common digraphs were in
the messages and compared them to the most common
digraphs. But this did not lead him far. The
code was not all digraphs, some letters were used
too. And the Rossingols were sneaky they
introduced pitfalls such as a number that
represented neither a letter nor a digraph, only
an instruction to delete the previous letter.
Bazeries managed to make headway by identifying
the cluster 124-22-125-46-345 several times and
postulating that this represented les-en-ne-mi-s.
This crucial breakthough allowed him to complete
new words by knowing parts, thus identifying more
symbols and in turn figuring out more words.