Chapter 2 Basic Encryption and Decryption

1. Chapter 2Basic Encryption and Decryption

2. A B plaintext plaintext encryption encrypted transmission ciphertext decryption Encryption / Decryption • A: sender; B: receiver • Transmission medium • An interceptor (or intruder) may block, intercept, modify, or fabricate the transmission. csci5233 computer security & integrity

3. Encryption / Decryption • Encryption: A process of encoding a message, so that its meaning is not obvious. (= encoding, enciphering) • Decryption: A process of decoding an encrypted message back into its original form. (= decoding, deciphering) • A cryptosystem is a system for encryption and decryption. csci5233 computer security & integrity

4. Plaintext / ciphertext • P: plaintext • C: ciphertext • E: encryption • D: decryption • C = E (P) • P = D (C) • P = D ( E(P) ) csci5233 computer security & integrity

5. Cryptosystems • Symmetric encryption: P = D (Key, E(Key,P) ) • Asymmetric encryption: P = D (KeyD, E(KeyE,P) ) • Symmetric cryptosystem: A cryptosystem that uses symmetric encryption. • Asymmetric cryptosystem • See Fig. 2-2 (p.23) csci5233 computer security & integrity

6. Keys • Use of a key provides additional security. • Exposure of the encryption algorithm does not expose the future messages< as long as the key(s) are kept secret. • c.f., keyless cipher csci5233 computer security & integrity

7. Terminology • Cryptography: The practice of using encryption to conceal text. (cryptographer) • Cryptanalysis: The study of encryption and encrypted messages, with the goal of finding the hidden meanings of the messages. (cryptanalyst) • Cryptology = cryptography + cryptanalysis csci5233 computer security & integrity

8. Cryptanalysis • A cryptanalyst may work with various data (intercepted messages, data items known or suspected to be in a ciphertext message), known encryption algorithms, mathematical or statistical tools and techniques, properties of languages, computers, and plenty of ingenuity and luck. • Attempt to break a single message • Attempt to recognize patterns in encrypted messages • Attempt to find general weakness in an encryption algorithm csci5233 computer security & integrity

9. Breakability of an encryption • An encryption algorithm may be breakable, meaning that given enough time and data, an analyst could determine the algorithm. • Suppose there exists 1030 possible decipherments for a given cipher scheme. A computer performs 1010 operations per second. Finding the decipherment would require 1020 seconds (or roughly 1012 years). csci5233 computer security & integrity

10. Modular arithmetic • A .. Z: 0 .. 25 • Example: p.24 C = P mod 26 csci5233 computer security & integrity

11. Two forms of encryption • Substitutions One letter is exchanged for another Examples: monoalphabetic substitution ciphers, polyalphabetic substitution ciphers • Transpositions (= permutations) The order of the letters is rearranged Examples: columnar transpositions csci5233 computer security & integrity

12. Substitutions • Caesar cipher: Each letter is translated to the letter a fixed number of letters after it in the alphabet. Ci = E(Pi) = Pi + 3 • Advantage: simple • Weakness csci5233 computer security & integrity

13. Cryptanalysis of the Caesar Cipher • Exercise (p.26): Decrypt the encrypted message. • Deduction based on guesses versus frequency distribution (p.28) csci5233 computer security & integrity

14. Other monoalphabetic substitutions • Using permutation Pi (lambda) = 25 – lambda • Weakness: Double correspondence E(F) = u and D(u) = F • Using a key A key is a word that controls the ciphering. p.27 csci5233 computer security & integrity

15. Complexity of monoalphabetic substitutions • Monoalphabetic substitutions amount to table lookups. • The time to encrypt a message of n characters is proportional to n. csci5233 computer security & integrity

16. Frequency distribution • Table 2-1 (p.29) shows the counts and relative frequencies of letters in English. • Frequencies in a sample cipher: Table 2-2 (p.30) • Compare the sample cipher against the normal frequency distribution: Fig. 2-4 csci5233 computer security & integrity

17. Polyalphabetic substitutions • By combining distributions that are high with the ones that are low • Using multiple substitution tables • Example (p.32): table for odd positions, table for even positions csci5233 computer security & integrity

18. Vigenère Tableaux • Table 2-5: p.34 • Example: p.35 • Exercise: Complete the encryption of the original message. • Exercise: Decipher the encrypted message using the key (‘juliet’) csci5233 computer security & integrity

19. Cryptanalysis of Polyalphabetic substitutions • The Kasiski method: a method to find the number of alphabets used for encryption • Works on duplicate fragments in the ciphertext • The distance between the repeated patterns must be a multiple of the keyword length csci5233 computer security & integrity

20. Steps for the Kasiski method • p.36 • Initial find + verification using frequency distribution csci5233 computer security & integrity

21. Index of coincidence • A measure of the variation between frequencies in a distribution • To measure the nonuniformity of a distribution • To rate how well a particular distribution matches the distribution of letters in English • RFreq versus Prob (p.38) • Example: • In the English language, RFreqa = Proba = 7.49 (from Table 2.1) • In the sample cipher in Table 2-2 (p.30): RFreqa = 0 Proba csci5233 computer security & integrity

22. Index of Coincidence • Measure of roughness (or the variance): a measure of the size of the peaks and valleys (See Fig. 2-6, p.38) • The var of a perfectly flat distribution = 0. • The variance can be estimated by counting the number of pairs of identical letters and dividing by the total number of pairs possible • Example (Given 200 letters): 60 / 100 csci5233 computer security & integrity

23. Index of Coincidence • IC (index of coincidence): a way to approximate variance from observed data (p.39) • 0.0384 (perfect)  IC  0.068 (English) csci5233 computer security & integrity

24. Combined use of IC with Kasiski method • Bottom of p.39 • All the subsets from the Kasiski method, if the key length was correct, should have distributions close to 0.068. csci5233 computer security & integrity

25. Analyzing a polyalphabetic cipher • Use the Kasiski method to predict the likely numbers of enciphering alphabets. • Compute the IC to validate the predictions • (When 1 and 2 show promises) Generate subsets and calculate IC’s for the subsets csci5233 computer security & integrity

26. The “Perfect” Substitution Cipher • Use an infinite nonrepeating sequence of alphabets • A key with an infinite number of nonrepeating digits • Examples: one-time pads, the Vernam cipher, … csci5233 computer security & integrity

27. Vernam Cipher • Sample function: c = ( p + random( ) ) mod 26 • Example: p.42 • Binary Vernam Cipher p.43: How would you decipher a ciphertext encrypted by Binary Vernam Cipher? Ans.: p = (c – random( ) ) mod 26 Example (p.42): c = 19 (‘t’), random( ) = 76 p = (19-76) mod 26 = 21 csci5233 computer security & integrity

28. Random Number Generators • A pseudo-random number generator is a computer program that generates numbers from a predictable, repeating sequence. • Example: The linear congruential random number generator ri+1 = (a * ri + b) mod n Note: 12 is congruent to 2 (modulo 5), since (12-2) mod 5 = 0 • Problem? Its dependability; probable word attack csci5233 computer security & integrity

29. The six frequent letters • P.45 • A correction: (E, e)  i • How to use the table ‘inside out’? csci5233 computer security & integrity

30. Dual-Message Entrapment • P.46 • Encipher two messages at once • One message is real; the other is the dummy. • Both the sender and the receiver know the dummy message (the key). • The key cannot be distinguished from the real message. csci5233 computer security & integrity

31. Summary • Substitutions and permutations together form a basis for the most widely used encryption algorithms  Chap. 3. • Next: Pf, Ch 2 (part b) csci5233 computer security & integrity