# chapter1-2 - Cryptanalysis Study(methods of breaking system...

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1 Study (methods) of breaking system, that is, deciphering without the key The objective: determine the key (Herckhoff principle: know the cryptosystem used) Cryptanalysis 2.5 hour

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2 Four kinds of attacks 1. Ciphertext only attack The opponent possesses a string of ciphertext, Y Most difficult to break Using the necessary statistics and analyzing apparent patterns to decipher the hidden message or key Cases: analyzing enciphered speech, tapping car telephones Cryptanalysis
3 2. Known plaintext attack The opponent possesses a string of plaintext, X , and the corresponding ciphertext, Y Finding the relation between a certain part of the ciphertext and the plaintext Using the knowledge to decrypt other section of ciphertext or find the key Case: every financial transaction contains information on the payer and the payee, if a cryptanalysist has inside information on how the information on the parties involved is enciphered in the message, he can attempt to decipher the remaining

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4 3. Chosen plaintext attack The opponent has obtained temporary access to the encryption machinery. He can choose a plaintext, X , and construct the corresponding ciphertext, Y Case: a word processor which stores files in an encrypted form
5 4. Chosen ciphertext attack The opponent has obtained temporary access to the decryption machinery. He can choose a ciphertext, Y , and construct the corresponding plaintext, X

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6 Cryptanalysis Assumption: English plaintext text Basic techniques: frequency analysis based on: Probabilities of occurrences of 26 letters Common digrams (two consecutive letters) and trigrams (three consecutive letters)
7 Cryptanalysis -- statistical analysis Probabilities of occurrences of 26 letters (see Table 1.1 , page 26) E, having probability about 0.127 (13%) T,A,O,I,N,S,H,R, each between 0.06 and 0.09 D,L, each around 0.04 C,U,M,W,F,G,Y,P,B, each between 0.015 and 0.028 V,K,J,X,Q,Z, each less than 0.01 30 most common digrams (in decreasing order): TH, HE, IN, ER, AN, RE,… 12 most common trigrams (in decreasing order): THE, ING,AND,HER,ERE,…

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8 Cryptanalysis of Affine Cipher Suppose an attacker got the following Affine cipher FMXVEDKAPHFERBNDKRXRSREFNORUD SDKDVSHVUFEDKAPRKDLYEVLRHHRH Cryptanalysis steps: Compute the frequency of occurrences of letters R: 8, D:7, E,H,K:5, F,S,V: 4 (see table 1.2, page 27)
9 Cryptanalysis of Affine Cipher Guess the letters, solve the equations, decrypt the cipher, judge correct or not. First guess: R e, D t, i.e., e K (4)=17, e K (19)=3 4a+b=17 19a+b=3 a=6, b=19, since gcd (6,26)=2, so incorrect. Next guess: R e, E t, the result will be a=13, not correct

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10 Cryptanalysis of Affine Cipher Guess again: R e, H t, the result will be a=3, b=5. Decrypt the cipher: algorithmsarequitegeneraldefinitionsofarithmeticprocesses Algorithms are quite general definitions of arithmetic processes If the decrypted text is not meaningful, try another guess.
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