crypto7_new

crypto7_new - CIS CIS 5371 Cryptography 7. Symmetric...

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CIS 5371 Cryptography 7. Symmetric encryption symmetric cryptography 1
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Cryptographic systems Cryptosystem: ( M,C,K,K’,G,E,D ) M, plaintext message space C, ciphertext message space K, K’, encryption and decryption key spaces G : N K K’, key generation algorithm E : M K C, encryption algorithm : C ecryption algorithm D : C K M, decryption algorithm G,E,D must be efficient symmetric cryptography 2
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Examples Cryptosystem: ( M,C,K,K’,G,E,D ) Substitution Cipher : M = C = Z 26 , with K=K’ he encryption algorithm is a mapping E The encryption algorithm k :M C -- E k (x) = (x), where k K is the key. The dencryption algorithm is a mapping D k :M C -- D k (y) = -1 (y). Shift Cipher : M = C = K = K’ = Z 26 , with -- E k (x) = x + k mod26 -- ) = y mod 6 symmetric cryptography 3 D k (y) y k mod26 where x,y Z 26
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xamples Examples Polyalphabetic ciphers: a plaintext message can be encrypted into any ciphertext Vigenere cipher -- 0 2 e 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 u t s r q p o n m l k j i h g f e d c b a z y x w v 4 5 7 4 9 5 4 7 24 7 15 0 17 6 14 19 15 24 17 2 y h p a r g o t p y r Plaintext 4 10 8 12 e k i m Key c 2 17 23 12 21 16 22 5 19 8 25 14 4 10 8 12 4 10 8 12 4 10 8 12 24 7 15 0 17 6 14 19 15 24 17 2 t x e t r e h p i c y e k t x e t n i a l p symmetric cryptography 4 c r x m v q w f t i z o t x Cipherte
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Vernam cipher –the one-time pad = C = K = K’ = 0 1} n 1 M = C = K = K = {0,1} , n > 1 . The keys k = k 1 ,k 2 ,…, k n are selected at random in K with niform distribution. uniform distribution. Encryption is bit by bit at a time, with each ciphertext bit obtained by XORing each message bit with the corresponding key bit. Decryption is the same as encryption since the XOR operation i t i is its own inverse. The special case when M = C = K = K’ = {0,1}*, and the key only used once (one- me key) gives us a cipher with a symmetric cryptography 5 is only used once (one time key) gives us a cipher with a strong security property: perfect secrecy .
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Transposition (permutation) cipher xample Example M = C = (Z 26 ) m , m > 1, K=K’ is the set of all permutations of {1,…, m }. For a key (permutation) -- e ( x 1 , …, x m ) = ( x (1) , …, x  m) ) -- d (y , …, y ) = (y ) , …, y ) ) (y 1 ,, m )( y (1) y (1) ) where  (1) is the inverse of  symmetric cryptography 6
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Structure of classical ciphers Classical ciphers are based on: ubstitution and Substitution and Transposition . This is also the basis for modern ciphers symmetric cryptography 7
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Cryptanalysis: attacks on cryptosystems Ciphertext only attacks: the opponent possesses a string of ciphertexts: y 1 ,y 2 , … Known plaintext attack: the opponent possesses a string of plaintexts x 1 ,x 2 , … nd the corresponding string of ciphertexts: and the corresponding string of ciphertexts: y 1 2 , … symmetric cryptography 8
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Usefulness of classical ciphers Cryptanalysis of substitution ciphers: Known plaintext attack –- easy to get the keys iphertext only attack se statistical properties Ciphertext only attack -- use statistical properties of the language.
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This note was uploaded on 12/11/2011 for the course CIS 5371 taught by Professor Mascagni during the Fall '11 term at FSU.

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crypto7_new - CIS CIS 5371 Cryptography 7. Symmetric...

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