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