1. Hide It in Plain Sight CS 490 Bob Orr
Cryptology 102
Hide It in Plain Sight
CS 490
Bob Orr
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2. Copyright © 2000 Trustees of Indiana University
Transpositions
Also called Permutations
An encryption in which letters are rearranged rather than enciphered
Goal is diffusion rather than confusion
Attempts to break up obvious letter patterns
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3. How the Transposition Works
The Message:
THIS IS A MESSAGE TO SHOW HOW A COLUMNAR TRANSPOSITION WORKS
Create a 5x10 matrix of the letters ~ fill with X’s, J’s & Q’s if necessary
Transmit the message column by column
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4. Copyright © 2000 Trustees of Indiana University
Example T S O H A N I W L R M G U P E K C
TSSOH OANIW
HAASO LRSTO
IMGHW UTPIR
SEEOA MROOK
ISTWC NASNS
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5. Encipherment vs. Transposition
Enciphering takes the same amount of time per character and uses the same amount of storage space
Transposition time is a function of message length; entire message must be stored initially before the message can be transposed; not well-suited for long messages
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6. Digrams and Trigrams Top 10 Digrams EN RE ER NT TH ON IN TF AN OR
Top 10 Trigrams ENT ION AND ING IVE TIO FOR OUR THI ONE
These are just as prevalent as individual characters
and can be subjected to the same kind of relative
frequency analysis ~ some like qp just don’t exist.
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7. Copyright © 2000 Trustees of Indiana University
Digram Analysis
Less algorithmic than analysis of substitution ciphers
More exhaustive and may depend ultimately on “what looks right”
Initially, perform a letter frequency analysis
when frequencies mirror that of English either a simple substitution, Caesar Cipher or transposition has been used
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8. Possible Patterns TSSOH OANIW HAASO LRSTO IMGHW . . .
‘THI’ from THIS ‘SAM’ from [iS A Message]
‘SAG’ from [mesSAGe]
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9. Digram Analysis cont’d
Trick is to determine the start of each column
Process involves an exhaustive comparison of strings of ciphertext
For example, group the first seven letters and then compare them to the 8th-14th letters, 9th-15th letters, and so forth until the digram patterns look right
Called a Moving Window approach
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10. Copyright © 2000 Trustees of Indiana University
Moving Window N I W H A S O R T N I W H A S O R T N I W H A S O R T N I W H A S O R T N I W H A S O R T N I W H A S O R T
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11. Statistical Analysis of Digram Occurrences
Calculate the means and standard deviations of all the digrams within each window
A high mean indicates that the digrams are likely
A low standard deviation suggests that all of the digrams are likely (mean is not distorted by a few popular digrams
In this case, an offset of ten is best
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12. Double Transpositions
Involves two column transpositions in succession with different numbers of columns for each transposition
Technique diffuses characters more and scrambles digrams moreso than a single transposition will
Disadvantage is that these are merely compound functions. Once a small bit is deciphered, the entire message unravels quickly
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13. Double Transposition Example
TH I S I
SAMES
SAGET
OSHOW
HOWAC
OLUMN
ARTRA
NSPOS
I TI ON
WORKS
ORIGINAL
TRANSPOSE
TSSOH OANIW HAASO
LRSTO IMGHW UTPIR
SEEOA MROOK
ISTWC NASNS
THE RED LETTERS
WILL SHOW THE
DIFFUSION.
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14. TNOMI MTSSI LGRRW XSWRH SOCXO HSWEO NXHAT UEKAX
Diffusion at Work
TSSOHOA
NIWHAAS
OLRSTO I
MGHWUTP
I RSE E OA
MROOKI S
TWCNASN
SXXXXXX
TNOMI MTSSI LGRRW XSWRH
SOCXO HSWEO NXHAT UEKAX
OAOTO ISXAS IPASN X
NOTE RED LETTERS ARE MORE
SPREAD OUT - STILL MOSTLY IN
TRIGRAM FORMAT
2nd TRANSPOSE (8 x 7)
WITH X-FILL
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15. Copyright © 2000 Trustees of Indiana University
Stream Ciphers
Convert one plaintext
symbol directly into
a ciphertext symbol.
Transformation de-
pends only on the
symbol, the key and
any control informa-
tion needed by the
encryption algorithm.
Key
(Optional)
ISSOPMI
Plaintext
Wdhuw. . .
Ciphertext
Encryption
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16. Stream Cipher Pros & Cons
Advantages
Speed of Transformation
Low error propagation
Relative ease in deciphering of single errors ~ deletion of a single letter often results in recovery
Disadvantages
Low diffusion makes the ciphertext quite vulnerable to decryption efforts
Susceptibility to malicious insertions or modifications - especially after key has been broken
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17. Copyright © 2000 Trustees of Indiana University
Block Ciphers
Plaintext XN OI TP YR CN ES ba qc kd em mc
Ciphertext po
Encrypt a group of plain text symbols into a sin-gle block of ciphertext.
Block sizes need not be related to the number of characters enciphered.
Columnar transpositions
are an example of this
type of cipher.
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18. Block Cipher Pros & Cons
Advantages
Diffusion ~ one ciphertext block may depend on several plaintext characters.
Immunity to Insertions because any such activity would alter block length and be detected.
Disadvantages
Slowness in execution at both ends of the system.
Communication errors will render an entire block indecipherable (no easy method of recovery.
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19. What Constitutes a “Good” Cipher?
Type of application
Longevity of the data
Environmental circumstances
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20. Shannon Characteristics
Amount of secrecy needed should dictate the amount of labor needed to encrypt and decrypt a message.
The set of keys and the enciphering algorithm should be free from complexity ~ don’t tie the algorithm to plaintext characteristics.
Implementation of the process should be as simple as possible.
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21. Copyright © 2000 Trustees of Indiana University
Shannon Continued
Errors in ciphering should not propagate and cause corruption of further information in the message
The size of the enciphered text should be no larger than the size of the plaintext
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22. Confusion ~ Final Thoughts
Relates to the ease with which an interceptor can change one character in the plaintext and predict its impact on the ciphertext.
Caesar ciphers have poor confusion
Polyalphabetic substitutions provide good confusion especially if the key length exceeds message length
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23. Diffusion ~ Final Thoughts
Relates to how well the enciphering algorithm spreads each plaintext character over the entire ciphertext.
Substitution ciphers provide poor diffusion
Transposition ciphers provide good diffusion
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24. Secure Cryptographic Systems
Achieved if an interceptor cannot recover plaintext from ciphertext regardless of the time expended.
One-time pads are perfect transfor- mations unless one assumes bribery, coercion or collusion between the sender and the receiver.
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25. Secure Systems (cont’d)
A good encryption system is one that maps plaintext to zero, one, or many possible ciphertexts
A cryptosystem is basically secure if the probability of applying the encryption function to the ciphertext to determine the plaintext is arbitrarily small.
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26. generate N2 ciphertexts
The Perfect Scheme
Keys P1 P2 . PN C1 C2 CN
Normally, N keys and
N plaintexts will
generate N2 ciphertexts
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27. An Imperfect Scheme Keys C1 More common: a single C2
ciphertext results from
very few plaintext/key
combinations.
For example, knowing
C1 was sent restricts the
possible plaintexts to P2
or P3.
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28. Information Theory ~ Redundancy
All languages are inherently redundant
Consider the set of all 20-character messages:
There are 2620 such messages
Most will not make any sense but some will make perfect language sense.
The difference between these two quantities defines a language’s redundancy
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29. Redundancy Example AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAB * *
* *
AAAAAAAAAAAAAAAAAAAZ
AAAAAAAAAAAAAAAAAABA
ALLGOODTHINGSMUSTEND
ZZZZZZZZZZZZZZZZZZZZ
The set of possible messages of length 20
As you can see, most make no sense at all, but occasionally, one will make perfect sense.
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30. Example Continued AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAB * *
* *
AAAAAAAAAAAAAAAAAAAZ
AAAAAAAAAAAAAAAAAABA
ALLGOODTHINGSMUSTEND
ZZZZZZZZZZZZZZZZZZZZ
By identifying and
numerically coding
all of the sensible
messages, say on the
interval [0,1023], we
could transmit a
message number
rather than the
actual message.
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31. Copyright © 2000 Trustees of Indiana University
“Outta Here”
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