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# chapter3-1 - Chapter 3 Block Ciphers and the Advanced...

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1 Chapter 3 Block Ciphers and the Advanced Encryption Standard

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2 Block Cipher - An encryption scheme that plaintext is broken up into blocks of fixed length, and encrypted one block at a time Product Cipher - An encryption scheme that uses multiple ciphers in which the ciphertext of one cipher is used as the plaintext of the next cipher Usually, substitution ciphers and transposition ( permutation) ciphers are used alternatively to construct a product cipher
3 Iterated Block Cipher - A block cipher that iterates a fixed number of times of another block cipher, called round function, with a different key, called round key, for each iteration key schedule- the algorithm for computing the round keys (subkeys) for each round in an iterated cipher from the encryption (or decryption) key Let K be a random binary key of some specified length. K is used to construct N round key (K 1 ,K 2 ,…K N )

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4 round function (g) - taking two inputs: a round key K r and a current state (denoted w r-1 ) The next state is defined as w r =g(w r-1 , K r ) The initial state, w 0 , is defined to be plaintext, x The ciphertext, y, is defined as the state after all N rounds have been performed
5 The encription operation is carried out as: 1 1 0 1 0 1 2 1 ( , ) ( , ) ( , ) N N N N N N N w x w g w K w g w K w g w K y w   

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6 In order for decryption to be possible, g must be injective if the second argument is fixed That is, there exists g -1 such that g -1 (g(w,K),K)=w for all w and K The decryption can be accomplished as 2 1 1 1 1 1 2 0 1 1 0 ( , ) ( , ) ( , ) N N N N w y w g w K w g w K w g w K x w   
7 An SP-network, or substitution-permutation network (SPN), is a series of linked mathematical operations used in block cipher algorithms such as AES These networks consist of S-boxes and P-boxes that transform blocks of input bits into output bits It is common for these transformations to be operations that are efficient to perform in hardware, such as exclusive or (XOR) Substitution-permutation network

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8 S-boxes substitute or transform input bits into output bits A good S-box will have the property that changing one input bit will change about half of the output bits It will also have the property that each output bit will depend on every input bit P-boxes permute or transpose bits across S-box inputs In addition, at each round the key is combined using some group operation, typically XOR Substitution-permutation network
9 Substitution-permutation network Let l,m and Nr be the positive integers let s : {0,1} l {0,1} l be a permutation let P : {0,1,…, lm } {0,1,…, lm } be a permutation Let P=C= {0,1} lm ,and let K ({0,1} lm ) Nr+1 consist of all possible key schedules that could be derived from an initial key K using the key scheduling algorithm For a key schedule (K 1 ,…,K Nr+1 ), we encrypt the plaintext x using Algorithm 3.1

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10 Notation: Let and regard x as the concatenation of m l
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