1. Lecture 2 Overview

2. Cryptography Secret writing – Disguised data cannot be read, modified, or fabricated easily – Feasibility of complexity for communicating parties Encryption : encoding (encipher) plaintext  cipher text C = E(c) (E = encryption rule) Decryption : decoding (decipher) Cipher text  plaintext P = D(c) (D = decryption rule) CS 450/650 – Lecture 2 Overview 2

3. Encryption CS 450/650 – Lecture 2 Overview 3 EncryptionDecryption plaintext Original plaintext ciphertextKeyless EncryptionDecryption plaintext Original plaintext ciphertext Symmetric key EncryptionDecryption plaintext Original plaintext ciphertext Asymmetric key

4. Symmetric Encryption System Secret Key Both sender and receiver share one key Encryption and decryptions algorithms are closely related N * (N-1) /2 keys are needed for N users to communicate in pairs Key must be kept secret CS 450/650 – Lecture 2 Overview 4

5. Asymmetric Encryption System Public Key One key must be kept secret, the other can be freely exposed – private key and public key Only the corresponding private key can decrypt what has been encrypted using the private key CS 450/650 – Lecture 2 Overview 5

6. Cryptanalysis How to break an encryption! Cryptanalyst – Deduce the original meaning of the ciphertext – Determine the decryption algorithm that matches the encryption one used Breakable Encryption! CS 450/650 – Lecture 2 Overview 6

7. Substitution Ciphers Substitute a character or a symbol for each character of the original message Caesar Cipher – C i = p i + 3 Permutation – Alphabet is scrambled, each plaintext letter maps to a unique ciphertext letter – Key can be used to control the permutation to be used CS 450/650 – Lecture 2 Overview 7

8. Cryptanalysis of substitution ciphers Clues – Short words, – Words with repeated patterns, – Common initial and final letters, … Knowledge of language may simplify it – English E, T, O, A occur far more than J, Q, X, Z – Digrams, Trigrams, and other patterns – Context CS 450/650 – Lecture 2 Overview 8

9. One-Time Pads One-Time Pad – Set of sheets of paper with keys, glued into a pad – Pre-arranged charts (Vignere Tableau) Vernam Cipher – random numbers Book Ciphers – access to identical objects CS 450/650 – Lecture 2 Overview 9

10. Transposition Ciphers The order of letters is rearranged Columnar transposition cryptanalysis using digrams CS 450/650 – Lecture 2 Overview 10

11. Try breaking – fqjcb rwjwj vnjax bnkhj whxcq nawjv nfxdu mbvnu ujbbf nnc Challenge Letter FrequencyRatioLetterFrequencyRatio E11.1607%56.88M 3.0129%15.36 A 8.4966% 43.31H3.0034%15.31 R7.5809% 38.64G 2.4705%12.59 I7.5448%38.45B2.0720%10.56 O7.1635% 36.51 F1.8121% 9.24 T6.9509%35.43 Y1.7779%9.06 N 6.6544%33.92W1.2899% 6.57 S5.7351%29.23K1.1016% 5.61 L 5.4893%27.98V1.0074% 5.13 C 4.5388%23.13X0.2902%1.48 U3.6308%18.51Z0.2722%1.39 D 3.3844%17.25J0.1965%1.00 P 3.1671%16.14Q 0.1962%(1) CS 450/650 Fundamentals of Integrated Computer Security 11 frequency table of letters in the Concise Oxford Dictionary (9 th ed.,1995)

12. Lecture 3 Entropy CS 450/650 Fundamentals of Integrated Computer Security Slides are modified from David Madison

13. Ciphers The intent of cryptography is to provide secrecy to messages and data Substitutions – ‘hide’ letters of plaintext Transposition – scramble adjacent characters CS 450/650 – Lecture 3: Entropy 13

14. Entropy Shannon demonstrated mathematical methods of treating communication channels, bandwidth, and the effects of random noise on signals – p i is the probability of a given message (or piece of information) – n is the number of possible messages (or pieces of information) CS 450/650 – Lecture 3: Entropy 14

15. Example 1 Suppose there is only one possible signal – i.e., n = 1, and p 1 = 1 H = -1 x log 1 = 0 There is only one possible message that has a probability of 1 – Since there is no uncertainty, the entropy in this case is zero CS 450/650 – Lecture 3: Entropy 15

16. Example 2 There are only two possible, equally probable, messages. H = -(0.5 log (0.5) + 0.5 log(0.5)) = - ( 0.5(-1)+0.5 (-1)) = 1 There are two possible equally probable messages, and the uncertainty (entropy) is 1 – one bit can specify two possible conditions, i.e., 0 or 1 CS 450/650 – Lecture 3: Entropy 16

17. Example 3 There are 1024 (= 2 10 ) possible signals, all of equal probability (p i = 2 -10 ). H = -(2 10 x 2 -10 log(2 -10 )) = 10 There are 1024 equally probably possible messages, and the uncertainty (entropy) is 10 bits. CS 450/650 – Lecture 3: Entropy 17

18. Entropy Entropy gives an indication of the complexity, or randomness, of a message or a data set. Generally, signals or data sets with high entropy, – Have a greater chance of a data transmission error – Require greater bandwidth to transmit – Have smaller capacity for compression – Appear to have a greater degree of "disorder” CS 450/650 – Lecture 3: Entropy 18

19. Entropy English language (and most other human languages) have a relatively low entropy due to the frequency of certain characters – the letters 'e' and 't‘ Information can be compressed using algorithms that "squeeze out" the redundancies in a message – making the compressed version much smaller, and much more random Compressing a file twice doesn't reduce the size ! CS 450/650 – Lecture 3: Entropy 19

20. Entropy and Cryptography Through cryptography, we increase the uncertainty in the message for those who do not know the key Plaintext has an entropy of zero as there is no uncertainty about it. – This class is CS 450 Encryption using one of x equally probable keys increases the entropy to lg x – KBXT LWER ACMF OSJU CS 450/650 – Lecture 3: Entropy 20

21. Entropy and Cryptography With a perfect cipher “all keys are essentially equivalent” – having an encrypted sample won't help the cryptanalyst do his or her job – an encrypted message is similar to a signal that is buried in noise; the higher the noise level, the more difficult it is to extract the message A good cipher will make a message look like noise CS 450/650 – Lecture 3: Entropy 21

22. Entropy and Cryptography Encryption should "scramble" the original message to the maximum possible extent Algorithms should take a message through a sequence of substitutions and transpositions Shannon: – “Encrypting a message will intentionally increase the message's entropy” CS 450/650 – Lecture 3: Entropy 22

23. Shannon Characteristics of ‘Good’ Ciphers 1.“The amount of secrecy needed should determine the amount of labor appropriate for the encryption and decryption” – Hold off the interceptor for required time duration 2.“The set of keys and enciphering algorithm should be free from complexity” – There should not be restriction on choice of keys or types of plaintext 3.“The implementation of the process should be as simple as possible” – Hand implementation, software bugs CS 450/650 – Lecture 3: Entropy 23

24. Shannon Characteristics of ‘Good’ Ciphers 4.“Errors in ciphering should not propagate and cause corruption of further information in the message” – An error early in the process should not throw off the entire remaining cipher text 5.“The size of the enciphered text should be no larger than the text of original message” – A ciphertext that expands in size cannot possibly carry more information than the plaintext CS 450/650 – Lecture 3: Entropy 24

25. Trustworthy Encryption Systems Commercial grade encryption 1.Based on sound mathematics 2.Analyzed by competent experts 3.Test of time DES: Data Encryption Standard RSA: River-Shamir-Adelman AES: Advanced Encryption Standard CS 450/650 – Lecture 3: Entropy 25

26. Stream and Block Ciphers Stream – Converts one symbol of plaintext into a symbol of ciphertex Block – Encrypts a group of plaintext symbols as one block CS 450/650 – Lecture 3: Entropy 26

27. Confusion and Diffusion Confusion – Has complex relation between plaintext, key, and ciphertext – The interceptor should not be able to predict what will happen to ciphertext by changing one character in plaintext – Example Caesar Cipher One time pad CS 450/650 – Lecture 3: Entropy 27

28. Confusion and Diffusion Diffusion – Cipher should spread information from plaintext over entire ciphertext – The interceptor should require access to much of ciphertext to infer algorithm – Example Caesar Cipher One time pad CS 450/650 – Lecture 3: Entropy 28

29. Stream Encryption Algorithms Block Encryption Algorithms Advantages Speed of transformation Low error propagation High diffusion Immunity to insertion of symbols Disadvantages Low diffusion Susceptibility to malicious insertions and modifications Slowness of encryption Error propagation CS 450/650 Fundamentals of Integrated Computer Security 29