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Introduction to Cryptography
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  1. Introduction to Cryptography --- Foundations of computer/network security ---

  2. Outline • Why study cryptology? • basic terms in cryptology • classic secret key ciphers • modern secret key ciphers • DES (Data Encryption Standard) • how does it work • how to use DES in practice • 4 modes of operations CPE3001 Information and Network Security

  3. Why Study cryptology(1) A B Intruder Communications security CPE3001 Information and Network Security

  4. Why Study cryptology(2) Customer Merchant TTP Electronic Commerce Security CPE3001 Information and Network Security

  5. Why Study cryptology(3) A B LEA Law enforcement CPE3001 Information and Network Security

  6. The Basic Problem • We consider the confidentiality goal: • Alice and Bob are Friends • Marvin is a rival • Alice wants to send secret messages (M1,M2,…) to Bob over a network such as Internet • Rival Marvin wants to read the messages (M1,M2,…) - Alice and Bob want to prevent this! • Assumption: The network is OPEN: Marvin is able to eavesdrop and read all data sent from Alice to Bob. • Consequence: Alice must not send messages (M1,M2,…) directly – they must be “scrambled” or encrypted using a ‘secret code’ unknown to Marvin but known to Bob. CPE3001 Information and Network Security

  7. Basic terms • cryptology (to be very precise) • cryptography --- designing • cryptanalysis --- code breaking • cryptologist • cryptographer • cryptanalyst • encryption/encipherment • scrambling data into unintelligible to unauthorised parties CPE3001 Information and Network Security

  8. Basic terms (2) • decryption/decipherment • un-scrambling • cipher/cryptosystem CPE3001 Information and Network Security

  9. A short history • dividing line is 1976/77 • classic ~1976/77 • 1976: Diffie & Hellman discovered public key cryptography • 1977: National Bureau of Standards published DES (Data Encryption Standard) • modern 1976/77 ~ today CPE3001 Information and Network Security

  10. History (2) • the word of “cipher”--- from Greek (secret writing) • ancient Egypt, Julius Caesar, ... • WWII • Enigma cipher machine • broken by British team including Alan Turing • Purple cipher • broken by US, led to the death of Yamamoto • Mainly for war, diplomacy & politics CPE3001 Information and Network Security

  11. Best book on history of crypto • David Kahn, The Codebreakers, Macmillan, New York, 1972. • PS: a revised edition has been published in 1996. CPE3001 Information and Network Security

  12. Types of ciphers • private key cryptosystems/ciphers • public key cryptosystems/ciphers CPE3001 Information and Network Security

  13. Examples of “Messages” • Types of secret “Messages” Alice might want to send Bob (in increasing length): • Decision (yes/no), eg as answer to the question “Are we meeting tomorrow?” • Numerical Value, eg as answer to the question “at what hour are we meeting?” • Document • Software, • Images etc. CPE3001 Information and Network Security

  14. Representation of Data (1) • Before encryption, messages must be represented in a standard way. • A representation code for a set of messages is: • A code which associates each possible message to a unique representing string of symbols • The symbols are elements of an “alphabet” • English Letter alphabet = {A,B,C,…,X,Y,Z} (26 elements) • Decimal digit alphabet = {0,1,…,9} (10 elements) • Binary digit (bit) alphabet = {0,1} (2 elements) • Assumption: The message representation code is NOT secret and is known to everyone, including Marvin! CPE3001 Information and Network Security

  15. Representation of Data (2) • Example 1: • Set of Messages = {yes, no} (Decisions) • Symbol Alphabet = {0,1} (bit alphabet) • Representation Code: • 0 = yes, 1 = no • Example 2: • Set of messages = {English text} • Symbol alphabet = {A,B,…,Y,Z} (letters) • Representation code: Leave as is. CPE3001 Information and Network Security

  16. Representation of Data (3) • Example 3: • Set of Messages = {English text} • Symbol Alphabet = {0,1} (bits) • Representation Code: • Convert each English letter in text to an 8-bit ASCII code, and concatenate the 8-bit codes. • Example 4: • Set of Messages = {0,1,…,1000} • Symbol Alphabet = {0,1} (bits) • Representation code: binary base system • Represent number x as string of 10 bits where: • Eg x = 734 is encoded as 1011011110 CPE3001 Information and Network Security

  17. Private key cipher Original Plain Text Cipher Text Plain Text Cipher Text D Network or Storage E Secret Key Secret Key Bob Alice CPE3001 Information and Network Security

  18. Concepts • a private key cipher is composed of two algorithms • encryption algorithm E • decryption algorithm D • the same key K is used for encryption & decryption • K has to be distributed beforehand CPE3001 Information and Network Security

  19. Notations • encrypt a plaintext P using a key K & an encryption algorithm E C = E(K,P) • decrypt a ciphertext C using the same key K and the matching decryption algorithm D P = D(K,C) • Note: P = D(K,C) = D(K, E(K,P)) CPE3001 Information and Network Security

  20. Classic ciphers • substitution ciphers • monoalphabetic ciphers • polyalphabetic ciphers • transposition (permutation) ciphers • product ciphers • using both • substitution, and • transposition CPE3001 Information and Network Security

  21. The Caesar cipher • The Caesar cipher is a substitution cipher, named after Julius Caesar. • Operation principle:each letter is translated into the letter a fixed number of positions after it in the alphabet table. • the fixed number of positions is a key both for encryption and decryption. CPE3001 Information and Network Security

  22. The Caesar cipher (cnt’d) Outer: plaintext Inner: ciphertext CPE3001 Information and Network Security

  23. The Caesar cipher (cnt’d) K=3 CPE3001 Information and Network Security

  24. An example • for a key K=3,plaintext letter: ABCDEF...UVWXYZciphtertext letter: DEF...UVWXYZABC • HenceTREATY IMPOSSIBLEis translated intoWUHDWB LPSRVVLEOH CPE3001 Information and Network Security

  25. An exercise • Using the Caesar cipher to encode the following message under a key K=5WAR STARTS TOMORROW CPE3001 Information and Network Security

  26. Breaking the Caesar cipher • by trial-and error • by using statistics on letters • frequency distributions of lettersletter percentA 7.49%B 1.29%C 3.54%D 3.62%E 14.00%.................................. CPE3001 Information and Network Security

  27. 4 types of cryptanalysis • depending on what a cryptanalyst has to work with, attacks can be classified into • ciphertext only attack • known plaintext attack • chosen plaintext attack • chosen ciphertext attack (most severe) CPE3001 Information and Network Security

  28. 4 types of attacks (2) • ciphertext only attack • the only data available is a target ciphertext • known plaintext attack • a target ciphertext • pairs of other ciphertext and plaintext (say, previously broken) CPE3001 Information and Network Security

  29. 4 types of attacks (3) • chosen plaintext attacks • a target ciphertext • can feed encryption algorithm with plaintexts and obtain the matching ciphertexts • chosen ciphertext attack • a target ciphertext • can feed decryption algorithm with ciphertexts and obtain the matching plaintexts CPE3001 Information and Network Security

  30. Two Main Types of Secrecy • Types of secrecy a cipher can offer: • Perfect Secrecy: For these ciphers Marvin cannot determine the message M even with unlimited computation time • Decrypting C with all possible keys K gives many possible messages, all reasonable candidates for the actual message M • One of the decrypted messages is M, but Marvin has no way to tell which one is the actual message encrypted by Alice! • Example: Caesar cipher with all 26 possible keys equally likely and message being just ONE letter (26 possible messages). • Eg Given ciphertext A, corresponding plaintexts under keys {0,1,2,…,25} are {A,B,C,…,X,Y,Z}. CPE3001 Information and Network Security

  31. Two Main Types of Secrecy (2) • Unfortunately, ciphers achieving perfect secrecy are not practical in most cases: • May require very long keys (eg as long as message) • Cannot withstand known plaintext attacks (or stronger) • Instead, most common are ciphers aiming to achieve: • Computational Secrecy: Marvin cannot determine the message M unless he performs an unfeasible amount of computation (eg it would take 10,000 years for Marvin to determine M using the fastest supercomputer!) • This can be achieved under all 4 possible attack scenarios, and using quite short keys! CPE3001 Information and Network Security

  32. Breaking classic ciphers • with the help of fast computers, 99.99% ciphers used before 1976 are breakable by using one of the 4 types of attacks. • The first computer designed by Alan Turing was used to break the Enigma cipher in WWII. CPE3001 Information and Network Security

  33. Modern private key ciphers • DES (US, 1977) • key -- 56 bits, plaint/ciphertext -- 64 bits • IDEA (Lai & Massey, Swiss, 1991) • key -- 128 bits, plaint/ciphertext -- 64 bits • LOKI (ADFA, Australia, 1989) • key, plaint/ciphertext -- 64 bits • FEAL (NTT, Japan, 1990) • key -- 128 bits, plaint/ciphertext -- 64 bits CPE3001 Information and Network Security

  34. The SPEED Cipher • designed by Y Zheng in 1996 • SPEED stands for “Secure Package for Encrypting Electronic Data” • length of a Key • 48,64,80,…,256 bits • length of a plaintext/ciphertext • 64 bits, or • 128 bits, or • 256 bits CPE3001 Information and Network Security

  35. DES Encryption (Pfleeger, P.114) CPE3001 Information and Network Security

  36. 0 0 = 0 1 1 = 0 0 1 = 1 1 0 = 1 Bit-wise exclusive-or (XOR) 101010111 110000010 011010101 CPE3001 Information and Network Security

  37. Encryption using DES • a 56-bit key K is expanded into 16 subkeys, each 48 bits (K1, K2, ..., K16) • Encryption consists of 16 rounds, each using a different 48-bit subkey • Both a plaintext & a ciphertext are 64 bits long CPE3001 Information and Network Security

  38. DES as an iterative cipher plaintext 0101101010111011 0101101010111011 after round 1 0101101010111011 after round 2 after round 3 0101101010111011 after round 4 0101101010111011 after round 16 0101101010111011 ciphertext 0101101010111011 CPE3001 Information and Network Security

  39. Decryption using DES • Similar to encryption, except that the order in which the subkeys are used is reversed, namely, (K16, K15, ..., K2, K1) CPE3001 Information and Network Security

  40. DES Decryption CPE3001 Information and Network Security

  41. DES decryption illustrated plaintext 0101101010111011 0101101010111011 after round 16 0101101010111011 after round 15 0101101010111011 after round 14 0101101010111011 after round 13 after round 1 0101101010111011 ciphertext 0101101010111011 CPE3001 Information and Network Security