1. Chapter 2 Basic Encryption and Decryption

2. Encryption / Decryption
A: sender; B: receiver
Transmission medium
An interceptor (or intruder) may block, intercept, modify, or fabricate the transmission.
encrypted transmission A B
plaintext
ciphertext
encryption
decryption
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3. 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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4. Plaintext / ciphertext
P: plaintext
C: ciphertext
E: encryption
D: decryption
C = E (P)
P = D (C)
P = D ( E(P) )
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5. csci5233 computer security & integrity
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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6. csci5233 computer security & integrity
Keys
Use of a key provides additional security.
Exposure of the encryption algorithm does not expose the future messages< 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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8. csci5233 computer security & integrity
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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9. 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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10. csci5233 computer security & integrity
Modular arithmetic
A .. Z:
Example: p.24
C = P mod 26
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11. 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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12. csci5233 computer security & integrity
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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13. 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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14. 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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15. 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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16. 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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17. 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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18. csci5233 computer security & integrity
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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19. 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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20. Steps for the Kasiski method
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)
(perfect)  IC  (English)
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24. 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
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25. Analyzing a polyalphabetic cipher
Use the Kasiski method to predict the likely numbers of enciphering alphabets.
Compute the IC to validate the predictions
(When 1 and 2 show promises) Generate subsets and calculate IC’s for the subsets
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26. 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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27. csci5233 computer security & integrity
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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28. 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
ri+1 = (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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29. The six frequent letters
P.45
A correction: (E, e)  i
How to use the table ‘inside out’?
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30. Dual-Message Entrapment
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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31. csci5233 computer security & integrity
Summary
Substitutions and permutations together form a basis for the most widely used encryption algorithms  Chap. 3.
Next: Pf, Ch 2 (part b)
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