1. Lecture 2 Overview

2. Cryptography Secret writing Encryption : encoding (encipher)
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

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

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

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

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

7. Substitution Ciphers
Substitute a character or a symbol for each character of the original message
Caesar Cipher
Ci = pi + 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

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

9. One-Time Pads One-Time Pad Vernam Cipher Book Ciphers
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

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

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

12. fqjcb rwjwj vnjax bnkhj whxcq nawjv nfxdu mbvnu ujbbf nnc
Exercise
Decrypt the following encrypted quotation:
fqjcb rwjwj vnjax bnkhj whxcq
nawjv nfxdu mbvnu ujbbf nnc
CS 450/650 – Lecture 3: Entropy

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

14. Entropy
Shannon demonstrated mathematical methods of treating communication channels, bandwidth, and the effects of random noise on signals
pi 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

15. Example 1 Suppose there is only one possible signal H = -1 x log 1 = 0
i.e., n = 1, and p1 = 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

16. Example 2 There are only two possible, equally probable, messages.
H = -(0.5 log (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

17. Example 3
There are 1024 (= 210) possible signals, all of equal probability (pi = 2-10).
H = -(210 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

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

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

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 x
KBXT LWER ACMF OSJU
CS 450/650 – Lecture 3: Entropy

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

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

23. Shannon Characteristics of ‘Good’ Ciphers
“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
“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
“The implementation of the process should be as simple as possible”
Hand implementation, software bugs
CS 450/650 – Lecture 3: Entropy

24. Shannon Characteristics of ‘Good’ Ciphers
“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
“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

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

26. Stream and Block Ciphers
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

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

28. Confusion and 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