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Unformatted text preview: 9/13/2010 1 Chapter 8: Basic Cryptography Classical Cryptography • Classical Cryptography • Public Key Cryptography • Cryptographic Checksums Slide #81 Overview • Classical Cryptography Classical Cryptography – CAsar cipher – Vigènere cipher – DES • Public Key Cryptography – DiffieHellman Slide #82 – RS¡ • Cryptographic Checksums – HM¡C 9/13/2010 2 Cryptosystem • Quintuple E D M K C Quintuple ( E , D , M , K , C ) – M set of plaintexts – K set of keys – C set of ciphertexts – E set of encryption functions e : M K C D set of decryption functions d : C K M Slide #83 – D set of decryption functions d : C K M Example Example: CAsar ciphe • Example: CAsar cipher – M = { sequences of letters } – K = { i  i is an integer and 0 ≤ i ≤ 25 } – E = { E k  k K and for all letters m , E k ( m ) = ( m + k ) mod 26 } – D = { D k  k K and for all letters c , Slide #84 k D k ( c ) = (26 + c – k ) mod 26 } – C = M 9/13/2010 3 Attacks • Opponent whose goal is to break cryptosystem is Opponent whose goal is to break cryptosystem is the adversary – Assume adversary knows algorithm used, but not key • Three types of attacks: – ciphertext only : adversary has only ciphertext; goal is to find plaintext, possibly key k l i t d h i h t t Slide #85 – known plaintext : adversary has ciphertext, corresponding plaintext; goal is to find key – chosen plaintext : adversary may supply plaintexts and obtain corresponding ciphertext; goal is to find key Basis for Attacks Mathematical attack • Mathematical attacks – Based on analysis of underlying mathematics • Statistical attacks – Make assumptions about the distribution of letters, pairs of letters (digrams), triplets of letters (trigrams) etc Slide #86 letters (trigrams), etc. • Called models of the language – Examine ciphertext, correlate properties with the assumptions. 9/13/2010 4 Classical Cryptography Sender receiver share common key • Sender, receiver share common key – Keys may be the same, or trivial to derive from one another – Sometimes called symmetric cryptography • Two basic types Transposition cipher Slide #87 – Transposition ciphers – Substitution ciphers – Combinations are called product ciphers Transposition Cipher Rearrange letters in plaintext to produce • Rearrange letters in plaintext to produce ciphertext • Example (RailFence Cipher) – Plaintext is HELLO WORLD – Rearrange as Slide #88 HLOOL ELWRD – Ciphertext is HLOOL ELWRD 9/13/2010 5 Attacking the Cipher Anagramming • Anagramming – If 1gram frequencies match English frequencies, but other ngram frequencies do not, probably transposition – Rearrange letters to form ngrams with highest freq encie Slide #89 frequencies Example • Ciphertext: HLOOLELWRD Ciphertext: HLOOLELWRD • Frequencies of 2grams beginning with H – HE 0.0305 – HO 0.0043 – HL, HW, HR, HD < 0.0010 • Frequencies of 2grams ending in H Slide #810 – WH 0.0026 – EH, LH, OH, RH, DH ≤ 0.0002 • Implies E follows H 9/13/2010...
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This note was uploaded on 02/08/2012 for the course ITT 650 taught by Professor Dewey during the Spring '11 term at UNC Asheville.
 Spring '11
 Dewey

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