Chapter%202%20Basic%20Encryption%20and%20Decryption%20(part%20B) - PowerPoint PPT Presentation
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Chapter%202%20Basic%20Encryption%20and%20Decryption%20(part%20B)
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Title: Chapter%202%20Basic%20Encryption%20and%20Decryption%20(part%20B)
1
Chapter 2Basic Encryption and Decryption (part
B)
2
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
3
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).
4
Columnar Transpositions
- A rearrangement of the plaintext characters into
columns. - The ciphertext is generated from the columns.
- Example p.47
5
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.
6
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 Whats the frequency of digrams BE, RF,
and WY?
7
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)
8
The moving window method
- Pick a window size, say n.
- Compare every Ci, 1 ? i ? n ,in the window to
Cin 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
9
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!
10
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 ? C8((22-1) mod 7) (22-1) div
7 1 C4 - example 2 C33 ? C8((33-1) mod 7) (33-1) div
7 1 C37 - So, P8 ? C4 and P14 ? C37
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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
12
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).
13
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
14
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
15
Block Ciphers
- - Slow
- - Require more storage space
- - Error propagation
- High diffusion
- High immunity to insertions
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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
- 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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