ITTChapter_08_Slides

ITTChapter_08_Slides - Chapter 8 Basic Cryptography...

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9/13/2010 1 Chapter 8: Basic Cryptography • Classical Cryptography Classical Cryptography Public Key Cryptography Cryptographic Checksums Slide #8-1 Overview • Classical Cryptography Classical Cryptography Cæsar cipher Vigènere cipher – DES Public Key Cryptography – Diffie-Hellman Slide #8-2 – RSA Cryptographic Checksums – HMAC
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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 #8-3 – D set of decryption functions : Example • Example: Cæsar cipher Example: Cæsar 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 #8-4 D k ( c ) = (26 + c k ) mod 26 } – C = M
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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 t d h i h t t Slide #8-5 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 attacks 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 #8-6 letters (trigrams), etc. • Called models of the language – Examine ciphertext, correlate properties with the assumptions.
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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 ciphers Slide #8-7 – 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 (Rail-Fence Cipher) – Plaintext is HELLO WORLD – Rearrange as HLOOL Slide #8-8 ELWRD – Ciphertext is HLOOL ELWRD
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9/13/2010 5 Attacking the Cipher • Anagramming – If 1-gram frequencies match English frequencies, but other n -gram frequencies do not, probably transposition – Rearrange letters to form n -grams with highest freq encies Slide #8-9 frequencies Example • Ciphertext: HLOOLELWRD Ciphertext: Frequencies of 2-grams beginning with H – HE 0.0305 – HO 0.0043 HL, HW, HR, HD < 0.0010 Frequencies of 2-grams ending in H Slide #8-10 – WH 0.0026 EH, LH, OH, RH, DH 0.0002 Implies E follows H
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9/13/2010 6 Example • Arrange so the H and E are adjacent Arrange so the H and E are adjacent HE
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