CMPE 471

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CMPE 471

• BASIC ENCRYPTION AND DECRYPTION

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TERMINOLOGY BACKGROUND

• Suppose S (Sender) wants to send a message to R
  (Reciever). S entrusts the message to T, who will
  deliver it to R T then becomes the transmission
  medium. If an outsider, O, wants the message and
  tries to access it, we will call O an interceptor
  or intruder.

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TERMINOLOGY BACKGROUND

• Any time after S transmits via T, the message is
  exposed, so O might try to access the message
• Block it, by preventing it to reach to R
  availability
• Intercept it, by reading or listening to the
  message secrecy
• Modify it, by seizing the message and changing
  it integrity
• Fabricate an authentic looking message, arranging
  as if it came from S integrity.

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TERMINOLOGY BACKGROUND

• Encryption (encode/ encipher)
• Process of encoding a message so that its meaning
  is not so obvious.
• Decryption (decode/ decipher)
• Is the reverse process transforming an encrypted
  message back into its normal form.
• Cryptosystem
• A system for encryption and decryption
• Plaintext
• The original form of the message
• Ciphertext
• The encrypted form of the message.

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TERMINOLOGY BACKGROUND

• Encryption Algorithms
• Some encryption algorithms use a key K, so that
  the ciphertext message depends on both the
  original plaintext message and the key value
• C E(K,P)
• E is a set of encryption algorithms, and the key
  K selects one specific algorithm.
• Sometimes the encryption and decryption keys are
  the same P D(K, E(K,P)). This is called
  symmetric encryption since D and E are
  mirror-image processes.
• Other times encryption and decryption keys come
  in pairs. Then a decryption key K inverts the
  encryption of key K so that P D(K , E(K
  ,P)). Encryption algorithms of this form are
  called asymmetric, because converting C back to P
  is not just reversing the steps of E.

D
E
D
E
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ENCRYPTION ALGORITHMS
Original Plaintext
Plaintext
Ciphertext
Decryption
Encryption
ENCRYPTION
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ENCRYPTION ALGORITHMS
Key
Original Plaintext
Plaintext
Ciphertext
Encryption
Decryption
Symmetric Cryptosystem
Encryption Key K
Encryption Key K
E
D
Original Plaintext
Plaintext
Ciphertext
Encryption
Decryption
Asymmetric Cryptosystem
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ENCRYPTION ALGORITHMS

• Cryptograpghy
• Hidden writing, the practice of using encryption
  to conceal text.
• Cryptanalyst
• Studies encryption and encrypted messages, with
  the goal of finding the hidden meanings of the
  messages.
• Cryptology
• Is the research into and study of encryption and
  decryption it includes both cryptography and
  cryptanalysis.

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ENCRYPTION ALGORITHMS

• Substitution
• One letter is exchanged for another
• Transposition
• The order of the letters is rearranged

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MONOALPHABETIC CIPHERS (SUBSTITUTIONS)

• The Caesar Cipher
• Named after Julius Caeser. Each letter is
  translated to the letter a fixed number of
  letters after it in the alphabet. Caesar used to
  shift 3, so that plaintext letter p was
  enciphered as ciphertext letter c by the rule
• c E(p ) p 3
• Plaintext 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
• Chiphertext 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

i
i
i
i
i
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MONOALPHABETIC CIPHERS (SUBSTITUTIONS)

• Using this encryption encode the below message
• TREATY IMPOSSIBLE
• Would be encoded as
• TREATY IMPOSSIBLE
• wu hd wb l p s r vv le o h

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MONOALPHABETIC CIPHERS (SUBSTITUTIONS)

• The pattern p 3 is easy to memorise and it is
  a simple cipher.
• That obvious pattern is also the major weakness
  of the Ceasar cipher.
• A secure encryption should not allow an
  interceptor to use a little piece to predict the
  entire pattern of the encryption.

i
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EXERCISE I

• Please decipher the following
• dh ey vdedk duded wdpluflvlqh jlwwlp vrqud
  eludc jhcphbh jlwwlp zh rnyod jhoglp
  eyudgd ghuvlp zdu

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ANSWER

• ben bu sabah araba tamircisine gittim sonra
  biraz gezmeye gittim ve okula geldim burada
  dersim var

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EXERCISE II

• Please make the cryptanalysis of Caesar chipher.

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ANSWER

• Suppose you were trying to break the following
  ciphertext message
• Wklv phvvdjh lv qrw wrr kdug wr euhdn
• The message has been enciphered with a 27-symbol
  alphabet
• Worst of all the blank has been translated to
  itself
• It shows which are the small words
• In encryption spaces between words often are
  deleted under the assumption that a legitimate
  reciever can breakmostmessagesintowordsfairlyeasil
  y.

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ANSWER

• English has relatively few small words such as
  am, is, to, be, he, we, and, are, you, she...
• One attack is to substitute known short words at
  appropriate places in the ciphertext and try to
  substituting for matching characters other places
  in the ciphertext.
• A stronger clue is the repeated R in the word
  wrr see, too, add, odd, off

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ANSWER

• The cryptanalysis here is ad hoc
• Uses deduction based on guesses instead of solid
  principles.
• Another approach is to consider which letters
  commonly start words, which letters commonly end
  words, and which prefixes and suffixes are common.

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Polyalphabetic Substitution Ciphers

• The weakness of monoalphabetic ciphers is that
  their frequency distribution reflects the
  distribution of the underlying alphabet.
• A cipher that is more cryptographicaly secure
  would display a rather flat distribution, which
  gives no information to cryptanalyst.
• One way to flatten the distribution is to combine
  distributions that are high with ones that are
  low
• If T is enciphered as a and b, and if X is also
  enciphered as a and b, the high frequency of T
  mixes with the low frequency of X to produce a
  more moderate distribution for a and b.

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Polyalphabetic Substitution Ciphers

• We can combine two distributions by using two
  separate encryption alphabets
• All charaters in odd positions of the plaintext
  message
• All characters in even positions
• 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
• a d g j m p s v y b e h k n q t w z
  c f i l o r u x
• 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
• n s x c h m r w b g l q v a f k p u z
  e j o t y d i

Table for odd positions
Table for even positions
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Polyalphabetic Substitution Ciphers

• The first table uses the permutation
• ?i(?) (3?) mod 26
• The second uses the permutation
• ?2(?) ((5?) 13) mod 26
• Encryption with these tables would be
• TREATY IMPOSSIBLE
• TREAT YIMPO SSIBL E
• f u m nf dyvtf czysh h

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Polyalphabetic Substitution Ciphers

• Notice that the double S becomes cz and that the
  two Es are enciphered as m and h
• Polyalphabetic encryption flattens the frequency
  distribution of the plaintext considerably.

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EXERCISE 3

• Please make the cryptanalysis of polyalphabetic
  substitutions

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ANSWER

• With a little help from frequency distributions
  and letter patterns you can break monoalphabetic
  substitution by hand
• With the aid of computer programs and with an
  adequate amount of ciphertext, a good
  cryptanalyst can break such a cipher in an hour.
• In some applications the prospect of one days
  effort may not make sense and it may be enough to
  protect the message.
• There are two tools that can decrypt messages
  written even with a large number of alphabets
• The Kasiski method for repeated patterns the
  method relies on the regularity of English. If a
  message is encoded with n alphabets in cyclic
  rotation, and if a particular word or letter
  group apperas k times in a plaintext message, it
  should be encoded approximately k/n times from
  the same alphabet.
• Index of Coincidence to rate how well a
  particular distribution matches the distribution
  of letters in English. The index of coincidence
  is a measure of the variation between frequencies
  in a distribution.

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Summary of Substitutions

• Substitutions are effective cryptographic devices
  used in diplomatic communications and appeared in
  the mysteries of
• Arthur Conan Doyle, Allan Poe, Agatha Cristie...
• The presentation of substitution ciphers has also
  introduced several cryptoanalytic tools
• Frequency distribution
• Index of coincidence
• Consideration of highly likely letters and
  probable words
• Repeated pattern analysis and the Kasiski
  approach
• Persistence, organisation, ingenuity, and luck

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Transpositions (Permutations)

• The goal of substitution is confusion, an attempt
  to make it difficult to determine how a message
  and key were transformed into ciphertext.
• A transposition is an encryption in which the
  letters of the message are rearranged.
• The goal is diffusion, spreading the information
  from the message or the key out widely across the
  ciphertext permutation.

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Transpositions (Permutations)
Plaintext message
five-column transposition
Ciphertext is formed by traversing the columns
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Transpositions (Permutations)

• The resulting ciphertext would then be read as
• tssoh oaniw haaso lrsto imghw
• utpir seeoa mrook istwc nasns
• The length of this message happened to be a
  multiple of five, so all columns came out the
  same length
• If the message length is not a multiple of the
  length of a row, the last columns will be a
  letter short.

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Transpositions (Permutations)

• Encipherment/ Decipherment Complexity
• Involves no additional work beyond arranging the
  letters and reading them off again.
• The algorithm is constant in the amount of work
  per character, and the time for the algorithm is
  proportional to the length of the message
• This algorithm requires storage for all
  characters of the message, so the space required
  is not constant but depends directly on the
  length of the message.
• Because of the storage space and the delay
  involved, it is not appropriate for long messages.

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Transpositions (Permutations)

• Diagrams
• Characteristic patterns of pairs of adjacent
  letters.
• Such as re, -th, -en, -ed, -on, -in, -an...
• Trigrams
• Groups of three letters in English
• Such as ent, -ion, -ing, -ive, -for, -one...

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EXERCISE 4

• Please make the cryptanalysis of transpositions

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ANSWER

• The basic attack on columnar transpositions is
  not as precise as the attack on substitution
  ciphers.
• Transpositions look less secure since they leave
  the plaintext letters intact, the work for
  cryptanalyst is more exhausting, because it
  relies on a human judgement of what looks
  right.
• The process involves exhaustive comparison of
  strings of ciphertext.
• Compares a block of ciphertext characters against
  characters successively farther away in the
  ciphertext.

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Fractionated Morse

• Morse Code
• Means of representing letters as sequences of
  dots and dashes, used with telegraphs, and
  flashing lights.

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Stream Ciphers

• They convert one symbol of plaintext immediately
  into a symbol of ciphertext (columnar
  transposition is the exception).
• The transformation depends only on the symbol,
  the key, and control information of the
  encipherment algorithm.

Key (Optional)
Stream Encryption
Y
wdhuw...
ISSOPMI
Plaintext
Ciphertext
Encryption
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Stream Ciphers

• Advantages
• Speed of transformation each symbol is encrypted
  without regard for any other plaintext symbols,
  each symbol can be encrypted as soon as it is
  read. Thus the time to encrypt each symbol
  depends only on the encryption algorithm itself,
  not on the time it takes to receive more
  plaintext.
• Low error propogation since each symbol is
  separately encoded, an error in the encryption
  process affects only that character.

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Stream Ciphers

• Disadvantages
• Low diffusioneach symbol is separately
  enciphered. Therefore, all the information of
  that symbol is contained in one symbol of the
  ciphertext. A cryptanalyst can attempt to break
  it by analaysing the characteristics of all
  individual symbols of the ciphertext, using tools
  such as frequency distribution counts, Kasiski
  method, etc.
• Susceptibility to malicious insertions and
  modifications because each symbol is separately
  encipherde, an active interceptor who has broken
  the code can splice together pieces of previous
  messages and transmit a spurious new message that
  may look authentic.

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Block Ciphers

• Encrypt a group of plaintext symbols as one
  block.
• Columnar transpositions and other transpositions
  are examples of block ciphers.

Key (Optional)
XN OI TP YR CN ES
Block Cipher Systems
IH
po
Plaintext
Ciphertext
ba qc kd em mc
Encryption
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Block Ciphers

• Advantages
• Diffusion information from plaintext is diffused
  into several ciphertext symbols. One ciphertext
  block may depend on several plaintext letters.
• Immunity to insertions because blocks of symbols
  are enciphered, it is impossible to insert a
  single symbol into one block. The length of the
  block would then be incorrect, and the
  decipherment would quickly reveal the insertion.

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Block Ciphers

• Disadvantages
• Slowness of encryption block ciphers must wait
  until an entire block of plaintext symbols has
  been received before starting the encryption
  process.
• Error propagation an error will affect the
  transformation of all characters in the same
  block.

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Good Ciphers

• Shannon Characteristics
• The amount of secrecy needed should determine the
  amount of labour appropriate for the encryption
  and decryption
• The set of keys and the enciphering algorithm
  should be free from complexity
• The implementation of the process should be as
  simple as possible
• Errors in ciphering should not propogate and
  cause corruption of further information in the
  message
• The size of the enciphered text should be no
  longer than the text of the original message.