# 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 10 12 1 ( , ) ( , ) ( , ) N N NN N wx w g w K w g w K w g w K yw  

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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 11 1 1 2 0 1 1 0 ( , ) ( , ) ( , ) N N NN wy w g w K w g w K w g w K xw  
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 -bit substrings, denoted as And we have   1 ,.... , , lm x x x ) ( ) 1 ( ...
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## chapter3-1 - Chapter 3 Block Ciphers and the Advanced...

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