CRYPTOGRAPHY

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CRYPTOGRAPHY

• Lecture 4

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(No Transcript)
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Mono-alphabetic Substitution Cipher

• Allow any permutation of the alphabet
• Each letter is replaced by a different letter or
  symbol
• Roughly 288 possibilities checking 1 billion
  per second, would take 12 billion years
• Too many possibilities to break by brute force!
  This is a major strength of the substitution
  cipher.

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Mono-alphabeticSubstitution Cipher

• The major weakness frequency analysis can help
  break this kind of cipher.
• But unlimited substitution ciphers require
  exchange of a lot of information the entire
  alphabet!
• A good key would be something you can look up in
  a book.

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Frequency Analysis
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Problem 4a Monoalphabetic Substitution cipher
SK BKGKC FBTKCHZWBT W ZXUBA HM SKOO, WBT EWQK
UZ MFC MSB, WH SXKB SK XWGK TUHJMGKCKT UZ DMC
MFCHKOGKH
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Problem 4b Mono-alphabetic Substitution cipher
CGXTOUNZL NQ UDOU HDNTD BCJONLQ HDCL ZLC DOQ
WZBMZUUCL CACBEUDNLM DC KCOBLCG NL QTDZZK.
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Problem 4c Mono-alphabetic Substitution cipher
UWZEZ VTPUW ZBEIK WVRWT UPUZT UWPUV YZFZE PAIQB
SISVT RBFZE TZJPR UNIKW PUUWZ GAVFZ ETZVT YBEPA
SKWIV UVTWZ EZVUK VNNVA TUPAU NISVT PCCZP
EPASQ ZEZCN PRZSQ ITBOZ UWVAX ZFZAO BEZQV HPEEZ
PASVA ZJCNV RPQNZ UWZEZ VTPAB UWZEU WZBEI KWVRW
TUPUZ TUWPU UWVTW PTPNE ZPSIW PCCZA ZS
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What can we do to improve the substitution cipher?
In 1460 Battista Alberti wrote an essay on what
he believed to be a new form of cipher use two
or more cipher alphabets alternately to encrypt a
message.
ABCDEFGHIJKLMNOPQRSTUVWXYZ plain
text GHIJKLMNOPQRSTUVWXYZABCDEF cipher1 RSTUVWXYZA
BCDEFGHIJKLMNOPQ cipher2
Lets encrypt the statement IT IS WAY TOO EARLY
IN THE DAY TO BE DOING THIS OK OJ CRE KUF KRXCE
ZT KNV JRE KU SK UUZTX ZYOJ 12 34 567 890 12345
67 890 123 45 67 89012 3456
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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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What can we do to improve the substitution cipher?
Alberti was followed by Johannes Trithemius (born
1462) and Giovanni Porta (born 1535) who
developed his ideas. Finally, Vigenere put all
these ideas together. Lets take a whole table
of Caesar shift alphabets. The first row will
have a Caesar shift of 1, the second of 2, etc.
Each letter in the plaintext message can be
enciphered by a different row.
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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
Vigenere cipher Start with a table of Caesar
shift alphabets.
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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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Vigenere cipher

• The Vigenere cipher is a polyalphabetic cipher.
• Frequency analysis does not apply.
• Enormous number of possible keys
• It was then neglected for 2 centuries it is
  hard to break but also hard to encrypt.

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Vigenere cipher the unbreakable code

• At first glance the Vigenère Cipher appears to be
  unbreakable, due to its use of up to 26 different
  cipher alphabets. Ciphers like this, which use
  more than one cipher alphabet are known as
  Polyalphabetic Ciphers. These can be incredibly
  difficult to decipher, because of their
  resistance to letter frequency analysis. Indeed,
  over time, the Vigenère cipher became known as
  'Le Chiffre Undechiffrable', or 'The Unbreakable
  Cipher'.

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

• 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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Next time . . .How Babbage cracked the
undecipherable cipher.
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HW 4a Vigenere

• 1. Encrypt the sentence Simon Singh is a
  singularly talented writer using the keyword
  CODE
• 2. Encrypt 1 message (at least 100 words long)
  using a chosen keyword. Swap and try to crack it.

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HW 4b Monoalphabetic Substitution cipher
NBSQF VKLUV GZSGN BGVZQ SZMCR GZUVG RHABI FHSVW
XGZMT VLMVE LQSGV LSGVQ TRUVM RGLKC GRHCV ZQZMC
NRMVG VXZMM LSNRH HSGVQ VMVUV QDZHZ AZQTZ RMAVS
SVQCQ RUVMG RHGVZ QSRMN VPVVO HNVZM CGRNR MLMVN
BGVZQ SRMGR NGRHS GLFTG SHZMC HVMHV HTFRC VHGVK
LUVHN BGVZQ SELQL MXVRS DZHGR HLDMR XGVQR HGGRH
AVXZF HVRMN VRSAR CVHGR HGVZQ SGRHD LFMCQ VXVRU
VCEQL NNBHR TGSNB GVZQS DZHDL FMCVC DRSGG RHDLF
MCVCG VZQSE LQZHE QLNNV LMGRN GRHGF QSCRC KRTGS
HLHSR KKNVS GLFTG SRMNV GRHGF QSCRC HNZQS ALSGV
JFZKG FQSRM SGRHX GZMTV HLFTG SLFQA KRHHN BSQFV
KLUVG ZSGNB GVZQS ZMCRG ZUVGR H
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HW 4c Mono-alphabetic Substitution cipher
826821526251162515231172625148114  
14826232621111161411615142623722526  
14826168262326172213262514826232621111  
11221614231252212142221622161827182625  
8262326116252026232671782152625148114  
14826232621111161411615142623722526  
252610711112512011  
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Websites which help
http//www.geocities.com/cryptogramcorner/ http/
/cs.colgate.edu/faculty/nevison/Core139Web/tools/s
ubstitution.html