Chapter 2 basic encryption and decryption part b
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Chapter 2 Basic Encryption and Decryption (part B). 2.4 Transpositions (Permutations). P.47 Transposition: an encryption in which the letters of the message are rearranged Also known as permutations Compare the goals: Substitution  confusion Transposition  diffusion.

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Chapter 2 Basic Encryption and Decryption (part B)

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Chapter 2 basic encryption and decryption part b

Chapter 2Basic Encryption and Decryption (part B)


2 4 transpositions permutations

2.4 Transpositions (Permutations)

  • P.47

  • Transposition: an encryption in which the letters of the message are rearranged

  • Also known as permutations

  • Compare the goals:

    • Substitution  confusion

    • Transposition  diffusion

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Confusion vs diffusion

Confusion vs Diffusion

  • Confusion: making it difficult to determine how a message and key were transformed into ciphertext.

  • Diffusion: spreading the information from the message or the key out widely across the ciphertext

  • See p.59 for more discussions.

  • Note: The definition of diffusion in the book seems to change depending on the context of discussion, leading to contradictory statements regarding whether ‘transposition’ methods have diffusion or not. See p.47 (1st paragraph) and p.59 (last 2nd paragraph).

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Columnar transpositions

Columnar Transpositions

  • A rearrangement of the plaintext characters into columns.

  • The ciphertext is generated from the columns.

  • Example: p.47

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Complexity of columnar transpositions

Complexity of Columnar Transpositions

  • Time: proportional to the length of the message, that is, O(n) or at the order of function n.

  • Space: depends on the length of the message.

  • Output cannot be produced until all characters of the message have been read.

  • Initial delay varies, depending on the length of the message. C.f., constant initial delay in the previous (substitution) algorithms.

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Digrams trigrams other patterns

Digrams, Trigrams, & Other Patterns

  • Digrams: groups of two letters

  • Trigrams: groups of three letters

  • Table 2-8 (p.49): Frequencies of digrams

    Note: not counting digrams that consist of the last letter of one word and the first letter of the next word

  • Exercise: What’s the frequency of digrams BE, RF, and WY?

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Cryptanalysis by digram analysis

Cryptanalysis by Digram Analysis

  • To compute the letter frequencies

    • Clue: The fact that all letters appear with their normal frequencies implies that a transposition has been performed.

  • To find where in the ciphertext a pair of adjacent columns lies (that is, to determine the width of a row in the original table used for encryption)

    • The ‘moving window’ method: Fig. 2-9 (p.50)

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The moving window method

The ‘moving window’ method

  • Pick a window size, say n.

  • Compare every Ci, 1  i  n,in the window to Ci+n and determine if the two form a common digram by checking their frequency (table 2-8, p.49)

  • Do most of the digrams look reasonable? Compute their mean and std. deviation

  • Example: Table 2-9, p.51

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Double transposition p 51

Double transposition (P.51)

  • Involves two columnar transpositions

  • An example of product ciphers, in which one encryption is applied to the result of another

    C = E2 (E1 (P) )

  • Example: Table 2-10 and 2-11

  • Cryptanalysis

    Pi C column * ( (i-1) mod row ) + (i-1) div row + 1

    Note: correction of the formula!

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Double transposition

Double transposition

  • Example: p.52

    1st transposition: # of rows = 10, # of columns = 5

    example 1: P8 C10*((8-1) mod 5) + (8-1) div 5 + 1 = C22

    example 2: P14 C10*((14-1) mod 5) + (14-1) div 5 + 1 = C33

    2nd transposition: # of rows = 8, # of columns = 7

    example 1: C22 C’8*((22-1) mod 7) + (22-1) div 7 + 1 = C’4

    example 2: C33 C’8*((33-1) mod 7) + (33-1) div 7 + 1 = C’37

    So, P8 C’4 and P14 C’37

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Analysis of double transposition ciphers

Analysis of double transposition ciphers

  • Locating pairs of ciphertext letters that probably appear together in the plaintext (chosen plaintext attack, probable plaintext attack)  p. 64.

  • Inferring a mathematical relationship from those pairs of letters

  • Verifying the relationship on other ciphertext letters to see if they produce probable digrams

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Fractionated morse

Fractionated Morse

  • A keyed monoalphabetic cipher

  • Uses Morse code (Table 2-12, p.53) as its base

  • Double encodings (P  Morse code  P’)

  • 3 steps:

    • Convert P to Morse code, using separator(s) between letters and words.

    • Divide the Morse code messages into blocks of 3 symbols.

    • Each block of symbols is encoded as the letter corresponding to that 3-symbol pattern (see Table 2-13, p.55).

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Stream versus block ciphers

Stream versus Block Ciphers

  • Stream ciphers: The plaintext characters are encoded by the sender letter-by-letter as sent to the receiver.

    • Example: substitution ciphers

  • Block ciphers: Blocks of plaintext are encoded into ciphertext before being sent.

    • Example: columnar transposition

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Stream ciphers

Stream Ciphers

+ Fast

+ Little storage space

+ Low error propagation, meaning that encoding errors affect just one character in the ciphertext

  • low diffusion, meaning that individual characters in the ciphertext can be analyzed using frequency distribution, digram analysis, IC and the Kasiski method

  • Susceptibility to malicious insertions and modifications

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Block ciphers

Block Ciphers

- Slow

- Require more storage space

- Error propagation

+ High diffusion

+ High immunity to insertions

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4 cryptanalysis cases 5 approaches

4 cryptanalysis cases & 5 approaches

  • Ciphertext only

    • Ciphertext-only attack

  • Full or partial plaintext

    • Known plaintext attack

    • Probable plaintext analysis

  • Ciphertext of any plaintext

    • Chosen plaintext attack

  • Algorithm + Ciphertext

    • Chosen ciphertext attack

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Summary

Summary

  • Two basic methods of encryption: substitutions and transposition

  • Common cryptanalytic tools:

    • Frequency distribution, Digram/trigram study, IC, Repeated patterns, Probable letters

  • Four cryptanalysis cases & 5 approaches:

  • Next: Pf, Ch 3 (Cryptosystems)

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