cryptoanal

cryptoanal - CS177 Computer Security October 13th, 2011...

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CS177 – Computer Security October 13 th , 2011 Adam Doupé [email protected]

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Overview Cryptoanalysis Overview Attacking Substitution Ciphers C±sar Cipher Vigenère Cipher Attacking Transposition Ciphers Simple Transposition Cipher Rails-Fence Cipher Columnar Transposition Cipher Real-World Examples Questions
Cryptosystem • 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

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Example • 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 , D k ( c ) = (26 + c k ) mod 26 } –C = M
Attacks 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 Fnd plaintext, possibly key known plaintext : adversary has ciphertext, corresponding plaintext; goal is to Fnd key chosen plaintext : adversary may supply plaintexts and obtain corresponding ciphertext; goal is to Fnd key

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Basis for Attacks Mathematical attacks – Based on analysis of underlying mathematics Statistical attacks – Make assumptions about the distribution of letters, pairs of letters (digrams or bigrams), triplets of letters (trigrams), etc. • Called models of the language – Examine ciphertext, correlate properties with the assumptions.
Classical Cryptography • Sender, receiver share common key – Keys may be the same, or trivial to derive from one another – Sometimes called symmetric cryptography • Two basic types – Substitution ciphers – Transposition ciphers – Combinations are called product ciphers

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Substitution Ciphers • Change characters in plaintext to produce ciphertext • Example (CAsar cipher) – Plaintext is HELLO WORLD – Change each letter to the third letter following it (X goes to ±, Y to B, Z to C) • Key is 3, usually written as letter ‘D’ – Ciphertext is KHOOR ZRUOG
Attacking the Caeser Cipher • Exhaustive search – If the key space is small enough, try all possible keys until you Fnd the right one – C±sar cipher has 26 possible keys • Statistical analysis – Compare to 1-gram model of English

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Statistical Attack • Compute frequency of each letter in ciphertext: G 0.1 H 0.1 K 0.1 O 0.3 R 0.2 U 0.1 Z 0.1 • Apply 1-gram model of English – Frequency of characters (1-grams) in English is on next slide (Can also ±nd on web)
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This note was uploaded on 12/27/2011 for the course CMPSC 117 taught by Professor Kemm during the Fall '09 term at UCSB.

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cryptoanal - CS177 Computer Security October 13th, 2011...

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