Chapter 2 Basic Encryption and Decryption

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Chapter 2Basic Encryption and Decryption
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Encryption / Decryption

• A sender B receiver
• Transmission medium
• An interceptor (or intruder) may block,
  intercept, modify, or fabricate the transmission.

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Encryption / Decryption

• Encryption A process of encoding a message, so
  that its meaning is not obvious. ( encoding,
  enciphering)
• Decryption A process of decoding an encrypted
  message back into its original form. ( decoding,
  deciphering)
• A cryptosystem is a system for encryption and
  decryption.

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Plaintext / ciphertext

• P plaintext
• C ciphertext
• E encryption
• D decryption
• C E (P)
• P D (C)
• P D ( E(P) )

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Cryptosystems

• Symmetric encryption
• P D (Key, E(Key,P) )
• Asymmetric encryption
• P D (KeyD, E(KeyE,P) )
• Symmetric cryptosystem A cryptosystem that uses
  symmetric encryption.
• Asymmetric cryptosystem
• See Fig. 2-2 (p.23)

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Keys

• Use of a key provides additional security.
• Exposure of the encryption algorithm does not
  expose the future messageslt as long as the key(s)
  are kept secret.
• c.f., keyless cipher

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Terminology

• Cryptography The practice of using encryption to
  conceal text. (cryptographer)
• Cryptanalysis The study of encryption and
  encrypted messages, with the goal of finding the
  hidden meanings of the messages. (cryptanalyst)
• Cryptology cryptography cryptanalysis

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Cryptanalysis

• A cryptanalyst may work with various data
  (intercepted messages, data items known or
  suspected to be in a ciphertext message), known
  encryption algorithms, mathematical or
  statistical tools and techniques, properties of
  languages, computers, and plenty of ingenuity and
  luck.
• Attempt to break a single message
• Attempt to recognize patterns in encrypted
  messages
• Attempt to find general weakness in an encryption
  algorithm

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Breakability of an encryption

• An encryption algorithm may be breakable, meaning
  that given enough time and data, an analyst could
  determine the algorithm.
• Suppose there exists 1030 possible decipherments
  for a given cipher scheme. A computer performs
  1010 operations per second. Finding the
  decipherment would require 1020 seconds (or
  roughly 1012 years).

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Modular arithmetic

• A .. Z 0 .. 25
• Example p.24
• C P mod 26

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Two forms of encryption

• Substitutions
• One letter is exchanged for another
• Examples monoalphabetic substitution ciphers,
  polyalphabetic substitution ciphers
• Transpositions ( permutations)
• The order of the letters is rearranged
• Examples columnar transpositions

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Substitutions

• Caesar cipher Each letter is translated to the
  letter a fixed number of letters after it in the
  alphabet.
• Ci E(Pi) Pi 3
• Advantage simple
• Weakness

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Cryptanalysis of the Caesar Cipher

• Exercise (p.26) Decrypt the encrypted message.
• Deduction based on guesses versus frequency
  distribution (p.28)

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Other monoalphabetic substitutions

• Using permutation
• Pi (lambda) 25 lambda
• Weakness Double correspondence
• E(F) u and D(u) F
• Using a key
• A key is a word that controls the ciphering.
• p.27

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Complexity of monoalphabetic substitutions

• Monoalphabetic substitutions amount to table
  lookups.
• The time to encrypt a message of n characters is
  proportional to n.

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Frequency distribution

• Table 2-1 (p.29) shows the counts and relative
  frequencies of letters in English.
• Frequencies in a sample cipher Table 2-2 (p.30)
• Compare the sample cipher against the normal
  frequency distribution Fig. 2-4

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Polyalphabetic substitutions

• By combining distributions that are high with the
  ones that are low
• Using multiple substitution tables
• Example (p.32) table for odd positions, table
  for even positions

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Vigenère Tableaux

• Table 2-5 p.34
• Example p.35
• Exercise Complete the encryption of the original
  message.
• Exercise Decipher the encrypted message using
  the key (juliet)

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Cryptanalysis of Polyalphabetic substitutions

• The Kasiski method a method to find the number
  of alphabets used for encryption
• Works on duplicate fragments in the ciphertext
• The distance between the repeated patterns must
  be a multiple of the keyword length

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Steps for the Kasiski method

• p.36
• Initial find verification using frequency
  distribution

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Index of coincidence

• A measure of the variation between frequencies in
  a distribution
• To measure the nonuniformity of a distribution
• To rate how well a particular distribution
  matches the distribution of letters in English
• RFreq versus Prob (p.38)
• Example
• In the English language, RFreqa Proba 7.49
  (from Table 2.1)
• In the sample cipher in Table 2-2 (p.30) RFreqa
  0 ? Proba

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Index of Coincidence

• Measure of roughness (or the variance) a measure
  of the size of the peaks and valleys (See Fig.
  2-6, p.38)
• The var of a perfectly flat distribution 0.
• The variance can be estimated by counting the
  number of pairs of identical letters and dividing
  by the total number of pairs possible
• Example (Given 200 letters) 60 / 100

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Index of Coincidence

• IC (index of coincidence) a way to approximate
  variance from observed data (p.39)
• 0.0384 (perfect) ? IC ? 0.068 (English)

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Combined use of IC with Kasiski method

• Bottom of p.39
• All the subsets from the Kasiski method, if the
  key length was correct, should have distributions
  close to 0.068.

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Analyzing a polyalphabetic cipher

1. Use the Kasiski method to predict the likely
   numbers of enciphering alphabets.
2. Compute the IC to validate the predictions
3. (When 1 and 2 show promises) Generate subsets and
   calculate ICs for the subsets

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The Perfect Substitution Cipher

• Use an infinite nonrepeating sequence of
  alphabets
• A key with an infinite number of nonrepeating
  digits
• Examples one-time pads, the Vernam cipher,

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Vernam Cipher

• Sample function
• c ( p random( ) ) mod 26
• Example p.42
• Binary Vernam Cipher
• p.43 How would you decipher a ciphertext
  encrypted by Binary Vernam Cipher?
• Ans. p (c random( ) ) mod 26
• Example (p.42) c 19 (t), random( ) 76
• p (19-76) mod 26 21

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Random Number Generators

• A pseudo-random number generator is a computer
  program that generates numbers from a
  predictable, repeating sequence.
• Example The linear congruential random number
  generator
• ri1 (a ri b) mod n
• Note 12 is congruent to 2 (modulo 5), since
  (12-2) mod 5 0
• Problem? Its dependability probable word attack

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The six frequent letters

• P.45
• A correction (E, e) ? i
• How to use the table inside out?

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Dual-Message Entrapment

• P.46
• Encipher two messages at once
• One message is real the other is the dummy.
• Both the sender and the receiver know the dummy
  message (the key).
• The key cannot be distinguished from the real
  message.

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Summary

• Substitutions and permutations together form a
  basis for the most widely used encryption
  algorithms ? Chap. 3.
• Next Pf, Ch 2 (part b)