cis 628 intro to crypto
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CIS 628 Intro to Crypto . Dr. Leonard Popyack Fall 2007. Polyalphabetic Substitution Ciphers. Flattens the frequency distribution of the ciphertext. Many ways to do this: Map high distribution plain text to multiple low distribution ciphertext. - PowerPoint PPT PresentationTRANSCRIPT
CIS 628 Intro to Crypto
Dr. Leonard PopyackDr. Leonard PopyackFall 2007Fall 2007
Polyalphabetic Substitution Ciphers
• Flattens the frequency distribution of the ciphertext.
• Many ways to do this:– Map high distribution plain text to multiple low
distribution ciphertext.– Use multiple monoalphabetic substitutions
(with different permutations) (even/odd)– Use Vigenère Tableaux (26 permutations)
Frequencies of Chars in Text
Vigenère Tableaux
Exam
ple
Methods to Crack Polyalphabetic Ciphers
• Kasiski Method– Developed by Prussian Military Officer
• Index of Coincidence– Developed by Sinkov
Kasiski MethodExploits the fact that many English words have common plaintext forms in them, particularly parts equal or greater than 3 letters. (-ing, -tion, -ation, with, the, them, that).
Method tries to factor the key length.
dicke nsdic kensd icken sdick ensdi ckens dickeITWAS THEBE STOFT IMESI TWAST HEWOR STOFT IMESI
nsdic kensd icken sdick ensdi ckens dicke nsdicTWAST HEAGE OFWIS DOMIT WASTH EAGEO FFOOL ISHNE
kensd icken sdick ensdi ckens dicke nsdic kensdSSITW ASTHE EPOCH OFBEL IEFIT WASTH EEPOC HOFIN
Kasiski Steps• 1. Identify repeated patterns of three
or more characters.• 2. For each pattern write down the
position at which each instance of the pattern begins.
• 3. Compute the difference between the starting points of successive instances.
• 4. Determine all factors of each difference.
• 5. If a polyalphabetic substitution cipher was used, the key length will be one of the factors that appears often in step 4.
Finally, create sets, then use mono-alphabetic cracking methods.
Index of Coinidence
• Sinkov [1966]• Exploits the variance of the ciphertext
distribution to attempt to identify the keysize.
1/26 = 0.0384 or 3.84%
Index of Coincidence
n number of observed sample ciphertext letters
Freq is instances of the character
IC can range from 0.0384 for perfect flat polysubstitution. To 0.0680 for mono substitution from common English
What IC tells us
• If the key size is small or large.• Small number of enciphering alphabets can be
readily discerned• Larger key sizes approach the “perfect”
distribution (With IC0.038)• Use in combination with the sets generated by
Kasiski method (as a test for likely key size)
Steps in analyzing a polyalphabetic cipher
• 1. Use the Kasiski method to predict likely numbers of enciphering alphabets. If no numbers emerge fairly regularly, the encryption is probably not simply a polyalphabetic substitution.
• 2. Compute the index of coincidence to validate the predictions from step 1.
• 3. Where steps 1 and 2 indicate a promising value, separate the ciphertext into appropriate subsets and independently compute the index of coincidence of each subset.
Perfect substitution Ciphers
• IC0.038• One-Time Pad
– Problems: synchronization, materials & control (printing, storing)
• Long random number sequences• Gilbert Vernam cipher (AT&T) (phone book)
• Binary Vernam
Vernam Cipher
Random Number Generators
• GOALS: – Reproducible Random Number Generator– Not Predictable
• WHERE?:– Seeded from Phone Books– Generators– Irrational numbers and functions
Transpositions (Permutations)
• Letters of plaintext message are re-arranged
Transpositions (Permutations)
Transpositions - Concerns
1. Need for storage
2. Wait for complete message to begin encoding or sending
Cracking Transpositions
• Knowledge of Digrams and Trigrams
• Computer methods– sliding windows, etc