Example 1.11: Ciphertext obtained from a Substitution Cipher

1
Example 1.11 Ciphertext obtained from a
Substitution Cipher

• YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ
• NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ
• NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ
• XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR

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Table 1.3 Frequency of Occurrence of 26
Ciphertext Letters
3
Guess Ze, ZW ed, R n

• ------end---------e----ned---e------------
• YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ
• --------e----e---------n--d---en----e----e
• NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ
• -e---n------n------ed---e---e--ne-nd-e-e--
• NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ
• -ed-----n-----------e----ed-------d---e--n
• XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR

4
Guess Nh, Ca

• ------end-----a---e-a--nedh--e------a-----
• YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ
• h-------ea---e-a---a---nhad-a-en--a-e-h--e
• NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ
• he-a-n------n------ed---e---e--neandhe-e--
• NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ
• -ed-a---nh---ha---a-e----ed-----a-d--he--n
• XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR

5
Guess Mi

• -----iend-----a-i-e-a-inedhi-e------a---i-
• YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ
• h-----i-ea-i-e-a---a-i-nhad-a-en--a-e-hi-e
• NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ
• he-a-n-----in-i----ed---e---e-ineandhe-e--
• NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ
• -ed-a--inhi--hai--a-e-i--ed-----a-d--he--n
• XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR

6
Guess Yo, Ds, Fr, Hc, Jt

• o-r-riend-ro--arise-a-inedhise--t---ass-it
• YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ
• hs-r-riseasi-e-a-orationhadta-en--ace-hi-e
• NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ
• he-asnt-oo-in-i-o-redso-e-ore-ineandhesett
• NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ
• -ed-ac-inhischair-aceti-ted--to-ardsthes-n
• XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR

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Subsitution Cipher Plaintext

• Our friend from Paris examined his empty glass
  with surprise, as if evaporation had taken place
  while he wasnt looking. I poured some more wine
  and he settled back in his chair, face tilted up
  towards the sun

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Example 1.11 Ciphertext obtained from a Vigenere
Cipher

• CHREEVOAHMAERATBIAXXWTNXBEEOPHBSBQMQEQERBW
• RVXUOAKXAOSXXWEAHBWGJMMQMNKGRFVGXWTRZXWIAK
• LXFPSKAUTEMNDCMGTSXMXBTUIADNGMGPSRELXNJELX
• VRVPRTULHDNQWTWDTYGBPHXTFALJHASVBFXNGLLCHR
• ZBWELEKMSJIKNBHWRJGNMGJSGLXFEYPHAGNRBIEQJT
• AMRVLCRREMNDGLXRRIMGNSNRWCHRQHAEYEVTAQEBBI
• PEEWEVKAKOEWADREMXMTBHHCHRTKDNVRZCHRCLQOHP
• WQAIIWXNRMGWOIIFKEE

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Index of Coincidence

• m1 0.045
• m2 0.046, 0.041
• CREOHART
• HEVAMEAB
• m3 0.043, 0.050, 0.047
• CEOMRBX
• HEAAAIX
• RVHETAW
• m4 0.042, 0.039, 0.046, 0.040
• CEHRIW
• HVMAAT
• ROATXN
• EAEBXX
• m5 0.063, 0.068, 0.069, 0.061, 0.072
• CVABW
• HOEIT
• RARAN
• EHAXX
• EMTXB

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Table 1.4 Values of Mg
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Vigenere Cipher Plaintext

• The almond tree was in tentative blossom. The
  days were longer, often ending with magnificent
  evenings of corrugated pink skies. The hunting
  season was over, with hounds and guns put away
  for six months. The vineyards were busy again as
  the well-organized farmers treated their vines
  and the more lackadaisical neighbors hurried to
  do the pruning they should have done in November.

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LFSR Stream Cipher

• Recall
• ciphertext element yi (xi zi) mod 2, where
• xi corresponding plaintext element
• zi corresponding keystream element
• keystream produced from (z1, , zm) by
• zmi mod 2 for constants c0,
  , cm-1
• For n 2m, there are m linear equations in m
  unknowns

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Cryptanalysis of LFSR Stream Cipher
Plaintext x1 x2 xn Ciphertext y1 y2 yn zmi
Sj0 to m-1 cj zij
(zm1, zm2, , z2m) (c0, c1, , cm-1)
-1
(c0, c1, , cm-1) (zm1, zm2, , z2m)
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LFSR Stream Cipher Example

• Ciphertext 011001111111000
• Plaintext 101101011110010
• So keystream is 110100100001010
• Suppose Oscar knows m5

(0,1,0,0,0) (c0, c1, , cm-1)
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LFSR Example Continued
Then (c0, c1, , c4) (0, 1, 0, 0, 0)
(1,0,0,1,0)

• So the recurrence used to generate the keystream
  is zi5 (zi zi3 mod 2)

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Information Theory

• Probability a given plaintext x was sent p(Xx)
• Sall possible plaintexts x(p(Xx)) 1
• Probability a given key k was used p(Kk)
• Sall possible keys k(p(Kk)) 1
• Probability a given ciphertext y was received
  p(Yy)
• For each possible y, p(Yy) S(p(Kk)p(XdK(y)))
  
• for all keys k such that y is a ciphertext from
  key k
• Probability x was sent, assuming we know y was
  received p(XxYy) or p(xy)
• Perfect secrecy p(xy) p(Xx)
• intercepting ciphertext gives cryptanalyst no
  additional information.

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Perfect Secrecy (see section 2.3) - example for
Shift Cipher

• 31-character ciphertext from a shift cipher
• y LZWJWAKFGGLZWJDSFYMSYWTMLXJWFUZ
• Number of possible keys lt number of possible
  English sentences of length 31 ? perfect secrecy
  not achieved.
• Just try all 26 keys. Only one (K18) produces a
  meaningful message
• y LZWJWAKFGGLZWJDSFYMSYWTMLXJWFUZ
• x Thereisnootherlanguagebutfrench