1 / 29

Lecture 2 Overview

Lecture 2 Overview. 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)

aman
Download Presentation

Lecture 2 Overview

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  3. Encryption Keyless Original plaintext plaintext ciphertext Encryption Decryption Symmetric key Original plaintext plaintext ciphertext Encryption Decryption Asymmetric key Original plaintext plaintext ciphertext Encryption Decryption 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 • 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. Challenge • Try breaking • fqjcb rwjwj vnjax bnkhj whxcq nawjv nfxdu mbvnu ujbbf nnc frequency table of letters in the Concise Oxford Dictionary (9th ed.,1995) CS 450/650 Fundamentals of Integrated Computer Security

  12. Lecture 3Entropy 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

  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 • 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) + 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 lg 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 • 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

  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

  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

  29. CS 450/650 Fundamentals of Integrated Computer Security

More Related