CIS 628 Intro to Crypto

1. CIS 628 Intro to Crypto Dr. Leonard Popyack Fall 2007

2. 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)

3. Frequencies of Chars in Text

4. Vigenère Tableaux

5. Example

6. Methods to Crack Polyalphabetic Ciphers • Kasiski Method • Developed by Prussian Military Officer • Index of Coincidence • Developed by Sinkov

7. Kasiski Method Exploits 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 dicke ITWAS THEBE STOFT IMESI TWAST HEWOR STOFT IMESI nsdic kensd icken sdick ensdi ckens dicke nsdic TWAST HEAGE OFWIS DOMIT WASTH EAGEO FFOOL ISHNE kensd icken sdick ensdi ckens dicke nsdic kensd SSITW ASTHE EPOCH OFBEL IEFIT WASTH EEPOC HOFIN

8. 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.

9. Index of Coinidence • Sinkov [1966] • Exploits the variance of the ciphertext distribution to attempt to identify the keysize.

10. 1/26 = 0.0384 or 3.84%

11. 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

12. 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 IC0.038) • Use in combination with the sets generated by Kasiski method (as a test for likely key size)

13. 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.

14. Perfect substitution Ciphers • IC0.038 • One-Time Pad • Problems: synchronization, materials & control (printing, storing) • Long random number sequences • Gilbert Vernam cipher (AT&T) (phone book) • Binary Vernam

15. Vernam Cipher

16. Random Number Generators • GOALS: • Reproducible Random Number Generator • Not Predictable • WHERE?: • Seeded from Phone Books • Generators • Irrational numbers and functions

17. Transpositions (Permutations) • Letters of plaintext message are re-arranged

18. Transpositions (Permutations)

19. Transpositions - Concerns 1. Need for storage 2. Wait for complete message to begin encoding or sending

20. Cracking Transpositions • Knowledge of Digrams and Trigrams • Computer methods • sliding windows, etc