Cryptographyy

# Cryptographyy - ComputerSecurity 1 Encryption key KE x...

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11/07/11 1 Computer Security Cryptography –an introduction

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11/07/11 2 Encryption key K E key K D x plaintext y ciphertext original plaintext x . encryption decryption Eavesdropper
11/07/11 3 Encryption A cryptosystem involves an encryption algorithm E , and a a decryption algorithm D Both algorithms make use of a key. Let K E be the encryption key and K D the decryption key. For symmetric cryptosystems the same key is used both encryption and decryption: K E = K D .

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11/07/11 4 Encryption If P is the plaintext message, C the ciphertext, then for symmetric cryptosystems: C = E ( K,P ) and P = D ( K,E ( K,P )) = D ( K,C ) For an asymmetric cryptosystem C = E ( K E ,P ) and P = D ( K D ,E ( K E ,P )) = D ( K D ,C )
11/07/11 5 Kerchoffs’ assumption The adversary knows all details of the encrypting function except the secret key

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11/07/11 6 Symmetric key encryption There are two types of cipher systems: Stream ciphers, Block ciphers.
11/07/11 7 Stream ciphers Encryption x = ISSOPMI y = wdhuvad Key K E

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11/07/11 8 Block ciphers Encryption x = XNE OIG TPH YRK … y = . Key K E wdm . hut vap dgd …
11/07/11 9 Block ciphers An overview of the DES Algorithm DES is an iterated block cipher with 16 rounds, block length 64 bits and key length 56 bits

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11/07/11 10 Iterating Block ciphers 1. Iterated block cipher Random (binary) key K round keys : K 1 ,..., K Nr , 2. Round function g            w r = g(w r-1 , K r ), where w r-1 is the previous state
11/07/11 11 Iterated cipher … Encryption operation: w 0 x ( x = plaintext ) w 1 = g(w 0 , K 1 ), w 2 = g(w 1 , K 2 ), w Nr = g(w Nr-1 , K Nr ), y w Nr ( y = ciphertext )

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11/07/11 12 Iterated cipher … For decryption we must have: g ( . , K ) must be invertible for all K Then decryption is the reverse of encryption (bottom-up)
11/07/11 13 Data Encryption Standard DES is a special type of iterated cipher called a Feistel cipher . Block length 64 bits Key length 56 bits Ciphertext length 64 bits

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11/07/11 14 DES The round function is: g([L i-1 ,R i-1 ]),K i ) = (L i ,R i ), where L i = R i-1 and R i = L i-1 XOR f (R i-1 , K i ).
11/07/11 15 DES round encryption

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11/07/11 16 DES inner function
11/07/11 17 DES computation path

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11/07/11 18 Inner function f Combine 32 bit input and 48 bit key into 32 bit output Expand 32 bit input to 48 bits XOR the 48 bit key with the expanded 48 bit input Apply the S-boxes to the 48 bit input to produce 32 bit output Permute the resulting 32 bits
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