Lecture 2 Overview

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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