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Block Ciphers Block Ciphers and Stream Ciphers Block Ciphers and Stream Ciphers In practical ciphers the plaintext M is divided into fixed-length blocks M = M1M2 : : : MN . Then, each block Mi is encrypted to the ciphertext block Ci = EK(Mi), and the results are concatenated to the ciphertext C = C1C2 : : : CN . There are two major kind of ciphers, which differ in the way the plaintexts are encrypted: Block Ciphers c Eli Biham - May 3, 2005 83 Block Ciphers (4) c Eli Biham - May 3, 2005 84 Block Ciphers (4) y Stream Ciphers Block Ciphers The blocks are encrypted sequentially, each block is encrypted by a distinct All the blocks are encrypted in the same way, under exactly the same transfor- transformation, which might depend on mation (no memory): C1 = E(M1), C2 = E(M2), etc. Encryption transformation should not be vulnerable to known plaintext attacks. 1. the previous encrypted blocks, Attacker should not be able to collect (almost) all the plaintext/ciphertext blocks pairs, keep the transformation table T (M) = C, and use it to en- 2. the previous transformation, crypt/decrypt if they do not know the mathematical formulation of the trans- 3. the block number, formation (and in particular the key). Thus, the block size should be large, and the number of distinct possible 4. the key. values in a plaintext block should be larger than the minimal allowed complexity of an attack. This information from one block is kept in memory between the encryption In the past blocks of 64 bits were used, which have 264 possibilities, whose of this block and the succeeding block, for use during the encryption of the 64 succeeding block. table storing costs at least 2 known plaintexts and memory space. Usually, stream ciphers use blocks of either one bit or eight bits (one Nowadays, the standard block size is 128 bits. character). c Eli Biham - May 3, 2005 85 Block Ciphers (4) c Eli Biham - May 3, 2005 86 Block Ciphers (4) Block Ciphers The Data Encryption Standard - DES Block ciphers are substitution ciphers in which the plaintext and the cipher- 1. The most widely used cipher in civilian applications. text blocks are binary vectors of length N. When N = 64 there are 264 different plaintexts/ciphertexts, and when N = 128 there are 2128 different 2. Developed by IBM; Evolved from Lucifer. plaintexts/ciphertexts. 3. Accepted as an US NBS standard in 1977, and later as an international N For each key the encryption function EK( ) is a permutation from 0; 1 to standard. itself. · f g 4. A block cipher with N = 64 bit blocks. D ( ) is the decryption function (the inverse permutation), K · such that DK(EK( )) = EK(DK( )) = Identity. 5. 56-bit keys (eight bytes, in each byte seven bits are used; the eighth bit · · can be used as a parity bit). 6. Exhaustive search requires 256 encryption steps (255 on average). c Eli Biham - May 3, 2005 87 Block Ciphers (4) c Eli Biham - May 3, 2005 88 Block Ciphers (4) The Data Encryption Standard - DES (cont.) DES Outline £ ¡ ¢ ¤ 7. Iterates a round-function 16 times in 16 rounds ( ). The round- Plaintext (P) Key (K) function mixes the data with the key. IP PC-1 K1 C D 8. Each round, the key information entered to the round function is called a F ROL1 ROL1 PC-2 subkey. The subkeys K1, . , K16 are computed by a key scheduling K2 algorithm. F ROL1 ROL1 K3 PC-2 F ROL2 ROL2 Ki PC-2 F ROL ROL K13 PC-2 F ROL2 ROL2 K14 PC-2 F ROL2 ROL2 K15 PC-2 F ROL2 ROL2 K16 PC-2 F ROL1 ROL1 PC-2 FP Ciphertext (T) c Eli Biham - May 3, 2005 89 Block Ciphers (4) y c Eli Biham - May 3, 2005 90 Block Ciphers (4) y The F -Function The Initial Permutation (IP) input (32 bits) The following tables describe for each output bit the number of the input bit whose value enters to the output bit. For example, in IP , the 58'th bit in the E input becomes the first bit of the output. 48 bits subkey (48 bits) 1 IP: FP=IP− : S1 S2 S3 S4 S5 S6 S7 S8 S1 S2 S3 S4 S5 S6 S7 S8 E E E E E E E E K K K K K K K K 58 50 42 34 26 18 10 2 40 8 48 16 56 24 64 32 60 52 44 36 28 20 12 4 39 7 47 15 55 23 63 31 S1 S2 S3 S4 S5 S6 S7 S8 I I I I I I I I 62 54 46 38 30 22 14 6 38 6 46 14 54 22 62 30 64 56 48 40 32 24 16 8 37 5 45 13 53 21 61 29 S1 S2 S3 S4 S5 S6 S7 S8 57 49 41 33 25 17 9 1 36 4 44 12 52 20 60 28 59 51 43 35 27 19 11 3 35 3 43 11 51 19 59 27 S1 S2 S3 S4 S5 S6 S7 S8 O O O O O O O O 61 53 45 37 29 21 13 5 34 2 42 10 50 18 58 26 P 63 55 47 39 31 23 15 7 33 1 41 9 49 17 57 25 output (32 bits) c Eli Biham - May 3, 2005 91 Block Ciphers (4) c Eli Biham - May 3, 2005 92 Block Ciphers (4) The P Permutation and the E Expansion The S Boxes P Permutes the order of 32 bits. E Expands 32 bits to 48 bits by duplicating S box S1: 16 bits twice. 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 P : E: 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 16 7 20 21 32 1 2 3 4 5 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 29 12 28 17 4 5 6 7 8 9 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13 1 15 23 26 8 9 10 11 12 13 5 18 31 10 12 13 14 15 16 17 2 8 24 14 16 17 18 19 20 21 S box S2: 32 27 3 9 20 21 22 23 24 25 19 13 30 6 24 25 26 27 28 29 15 1 8 14 6 11 3 4 9 7 2 13 12 0 5 10 22 11 4 25 28 29 30 31 32 1 3 13 4 7 15 2 8 14 12 0 1 10 6 9 11 5 0 14 7 11 10 4 13 1 5 8 12 6 9 3 2 15 13 8 10 1 3 15 4 2 11 6 7 12 0 5 14 9 c Eli Biham - May 3, 2005 93 Block Ciphers (4) c Eli Biham - May 3, 2005 94 Block Ciphers (4) The S Boxes (cont.) The S Boxes (cont.) S box S3: S box S5: 10 0 9 14 6 3 15 5 1 13 12 7 11 4 2 8 2 12 4 1 7 10 11 6 8 5 3 15 13 0 14 9 13 7 0 9 3 4 6 10 2 8 5 14 12 11 15 1 14 11 2 12 4 7 13 1 5 0 15 10 3 9 8 6 13 6 4 9 8 15 3 0 11 1 2 12 5 10 14 7 4 2 1 11 10 13 7 8 15 9 12 5 6 3 0 14 1 10 13 0 6 9 8 7 4 15 14 3 11 5 2 12 11 8 12 7 1 14 2 13 6 15 0 9 10 4 5 3 S box S4: S box S6: 7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15 12 1 10 15 9 2 6 8 0 13 3 4 14 7 5 11 13 8 11 5 6 15 0 3 4 7 2 12 1 10 14 9 10 15 4 2 7 12 9 5 6 1 13 14 0 11 3 8 10 6 9 0 12 11 7 13 15 1 3 14 5 2 8 4 9 14 15 5 2 8 12 3 7 0 4 10 1 13 11 6 3 15 0 6 10 1 13 8 9 4 5 11 12 7 2 14 4 3 2 12 9 5 15 10 11 14 1 7 6 0 8 13 c Eli Biham - May 3, 2005 95 Block Ciphers (4) c Eli Biham - May 3, 2005 96 Block Ciphers (4) The S Boxes (cont.) The S Boxes (cont.) S box S7: How to interpret the S boxes: The representation of the S boxes use the first and sixth bits of the input as a 4 11 2 14 15 0 8 13 3 12 9 7 5 10 6 1 line index (between 0 and 3), and the four middle bits as the row index (between 13 0 11 7 4 9 1 10 14 3 5 12 2 15 8 6 0 and 15). 1 4 11 13 12 3 7 14 10 15 6 8 0 5 9 2 6 11 13 8 1 4 10 7 9 5 0 15 14 2 3 12 Thus, the input values which correspond to the standard description of the S boxes are S box S8: 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 13 2 8 4 6 15 11 1 10 9 3 14 5 0 12 7 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 1 15 13 8 10 3 7 4 12 5 6 11 0 14 9 2 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 7 11 4 1 9 12 14 2 0 6 10 13 15 3 5 8 2 1 14 7 4 10 8 13 15 12 9 0 3 5 6 11 c Eli Biham - May 3, 2005 97 Block Ciphers (4) c Eli Biham - May 3, 2005 98 Block Ciphers (4) The S Boxes (cont.) The Key Scheduling Algorithm Note that all the operations are linear, except for the S boxes.
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