V. This problem provides a numerical example of part of the encryption that goes one with...
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V. This problem provides a numerical example of part of the encryption that goes one with DES. (figures, tables,... for the DES encryption algorithm are provided below and in the slides). Show your work when answering these questions: a. Derive the key K, for the first round, if the main key K is the following: Key K in hexadecimal notation: OEDCBA987654321F Key K in binary notation: 0000 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 1111 b. If the 48-bit input to the 8 S-boxes is the following, what is the output from the S-boxes in binary? Input: 110011 011110 101010 101000 100101 111010 110011 001111 Figure C.1 General Depiction of DES Encryption Algorithm 64-bit plaintext ... Initial Permutation 64 Round 1 64 Round 2 Round 16 32-bit Swap 64 bits Inverse Initial Permutation 64-bit ciphertext K 48 K 48 K16 48 Permuted Choice 2 Permuted Choice 2 Permuted Choice 2 56 56 56 64-bit key ++..... Permuted Choice 1 HH 56 Left circular shift 56 Left circular shift Left circular shift Figure C.2 Single Round of DES Algorithm 32 bits- L-1 Lj 32 bits-> Ri-1 HE Expansion/ permutation (E table) 48 (XOR) 48 Substitution/choice (S-box) 32 Permutation (P) R X32 XOR 48 -K -28 bits- Ci-1 Left shift(s) C -28 bits- Di-1 Left shift(s) Permutation/contraction (Permuted Choice 2) D Figure C.3 Calculation of F(R, K) S1 R (32 bits) E 48 bits S2 S3 S4 + P 32 bits S5 S6 K (48 bits) S7 S8 Table C.2 Definition of DES S-Boxes S S S S 14 0 15 4 15 15 3 13 10 13 13 0 14 1 4 13 13 1 10 12 1 13 7 6 7 13 10 7 14 8 3 15 8 2 12 4 7 8 10 1 09 14 0 4 13 8 11 14 1 4 8 2 4 14 7 11 9 9 3 5 06 2 15 14 1 13 * 6 10 06 6 3 8 0 2 15 28 6 10 9 7 11 4 15 6 90 12 11 4 15 9 6 15 6 11 13 3 15 10 1 2 11 3 4 13 4 8 1 14 7 1 13 6 10 2 11 5 87 9 10 0 3 3 10 13 10 8 15 1 58 3 0 11 9 5 11 12 11 6 4 7 0 28 15 12 9 7 9 1 4 7 6 12 6 7 1 3 4 2 685 1 12 15 14 2 12 1 13 12 7 11 11 2 14 1 2 8 5 3 13 5 14 10 12 12 5 14 9 5 11 3 3 15 10 12 5 6 3 11 0 120 12 11 1 5 12 9 13 5 10 9 3 5 4 11 10 5 12 2 7 0 7 0 3 8 5 0 6 13 5 10 11 5 2 15 14 9 2 8 15 1 14 7 10 14 9 2 12 4 15 84 2 14 14 9 S So S S 14 4 11 12 10 9 4 13 1 11 13 2 8 1 2 15 4 3 2 11 0 6 11 14 15 2 2 1 7 11 12 10 1 4 4 11 11 1 15 13 13 8 4 12 14 11 7 15 2 50 12 2 14 15 7 8 4 8 4 1 10 7 1 9 13 12 2 9 7 12 4 1 6 10 9 7 4 13 14 2 0 6 3 8 12 13 5 15 15 7 2 12 6 10 9 8 4 10 1 7 3 7 11 14 8 1 8 13 8 13 5 5 6 10 15 3 7 6 10 11 1 4 0 13 14 10 14 7 9 0 9 12 15 3 12 13 15 0 14 1 13 3 15 10 9 5 206 15 12 12 0 3 4 1 10 6 5 9 4 14 10 9 7 3 6 10 14 9 7 5 10 13 5 5 12 2 1 0 8 0 015 14 3 14 5 9 8 6 3 0 11 3 8 4 7 3 13 6 08 13 5 6 110 14 10 2 0 14 0 5 3 15 8 15 3 5 5 11 11 5 9 2 6 1 50 3 12 12 7 9 2 5 8 6 11 Table C.3 DES Key Schedule Calculation (a) Input Key 1 9 17 25 33 41 49 57 57 1 10 19 63 7 14 21 2 10 18 26 34 42 50 58 49 58 2 = 55 62 6 13 3 11 19 27 35 43 51 59 41 50 59 3 47 54 61 12 5 20 28 36 44 52 60 33 42 51 60 39 46 53 5 (b) Permuted Choice One (PC-1) 28 13 21 29 37 45 53 61 25 34 43 52 31 38 45 6 20 14 22 30 38 46 54 62 15 23 31 7 39 47 55 63 17 26 35 44 23 30 37 12 8 16 24 32 40 48 56 64 S 18 27 36 15 22 29 A S So S S 14 4 11 12 10 9 4 13 1 11 13 2 8 1 2 15 4 3 2 11 0 6 11 14 15 2 2 1 7 11 12 10 1 4 4 11 11 1 15 13 13 8 4 12 14 11 7 15 2 50 12 2 14 15 7 8 4 8 4 1 10 7 1 9 13 12 2 9 7 12 4 1 6 10 9 7 4 13 14 2 0 6 3 8 12 13 5 15 15 7 2 12 6 10 9 8 4 10 1 7 3 7 11 14 8 1 8 13 8 13 5 5 6 10 15 3 7 6 10 11 1 4 0 13 14 10 14 7 9 0 9 12 15 3 12 13 15 0 14 1 13 3 15 10 9 5 206 15 12 12 0 3 4 1 10 6 5 9 4 14 10 9 7 3 6 10 14 9 7 5 10 13 5 5 12 2 1 0 8 0 015 14 3 14 5 9 8 6 3 0 11 3 8 4 7 3 13 6 08 13 5 6 110 14 10 2 0 14 0 5 3 15 8 15 3 5 5 11 11 5 9 2 6 1 50 3 12 12 7 9 2 5 8 6 11 Table C.3 DES Key Schedule Calculation (a) Input Key 1 9 17 25 33 41 49 57 57 1 10 19 63 7 14 21 2 10 18 26 34 42 50 58 49 58 2 = 55 62 6 13 3 11 19 27 35 43 51 59 41 50 59 3 47 54 61 12 5 20 28 36 44 52 60 33 42 51 60 39 46 53 5 (b) Permuted Choice One (PC-1) 28 13 21 29 37 45 53 61 25 34 43 52 31 38 45 6 20 14 22 30 38 46 54 62 15 23 31 7 39 47 55 63 17 26 35 44 23 30 37 12 8 16 24 32 40 48 56 64 S 18 27 36 15 22 29 A 14 15 26 41 51 34 Round Number Bits Rotated 17 6 8 52 45 53 (c) Permuted Choice Two (PC-2) 11 21 16 31 33 46 24 10 7 37 48 42 1 23 27 47 44 50 (d) Schedule of Left Shifts 5 19 20 55 49 36 1 2 3 4 5 6 7 8 9 10 11 12 3 12 13 13 30 39 29 28 4 2 40 56 32 14 15 16 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 V. This problem provides a numerical example of part of the encryption that goes one with DES. (figures, tables,... for the DES encryption algorithm are provided below and in the slides). Show your work when answering these questions: a. Derive the key K, for the first round, if the main key K is the following: Key K in hexadecimal notation: OEDCBA987654321F Key K in binary notation: 0000 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 1111 b. If the 48-bit input to the 8 S-boxes is the following, what is the output from the S-boxes in binary? Input: 110011 011110 101010 101000 100101 111010 110011 001111 Figure C.1 General Depiction of DES Encryption Algorithm 64-bit plaintext ... Initial Permutation 64 Round 1 64 Round 2 Round 16 32-bit Swap 64 bits Inverse Initial Permutation 64-bit ciphertext K 48 K 48 K16 48 Permuted Choice 2 Permuted Choice 2 Permuted Choice 2 56 56 56 64-bit key ++..... Permuted Choice 1 HH 56 Left circular shift 56 Left circular shift Left circular shift Figure C.2 Single Round of DES Algorithm 32 bits- L-1 Lj 32 bits-> Ri-1 HE Expansion/ permutation (E table) 48 (XOR) 48 Substitution/choice (S-box) 32 Permutation (P) R X32 XOR 48 -K -28 bits- Ci-1 Left shift(s) C -28 bits- Di-1 Left shift(s) Permutation/contraction (Permuted Choice 2) D Figure C.3 Calculation of F(R, K) S1 R (32 bits) E 48 bits S2 S3 S4 + P 32 bits S5 S6 K (48 bits) S7 S8 Table C.2 Definition of DES S-Boxes S S S S 14 0 15 4 15 15 3 13 10 13 13 0 14 1 4 13 13 1 10 12 1 13 7 6 7 13 10 7 14 8 3 15 8 2 12 4 7 8 10 1 09 14 0 4 13 8 11 14 1 4 8 2 4 14 7 11 9 9 3 5 06 2 15 14 1 13 * 6 10 06 6 3 8 0 2 15 28 6 10 9 7 11 4 15 6 90 12 11 4 15 9 6 15 6 11 13 3 15 10 1 2 11 3 4 13 4 8 1 14 7 1 13 6 10 2 11 5 87 9 10 0 3 3 10 13 10 8 15 1 58 3 0 11 9 5 11 12 11 6 4 7 0 28 15 12 9 7 9 1 4 7 6 12 6 7 1 3 4 2 685 1 12 15 14 2 12 1 13 12 7 11 11 2 14 1 2 8 5 3 13 5 14 10 12 12 5 14 9 5 11 3 3 15 10 12 5 6 3 11 0 120 12 11 1 5 12 9 13 5 10 9 3 5 4 11 10 5 12 2 7 0 7 0 3 8 5 0 6 13 5 10 11 5 2 15 14 9 2 8 15 1 14 7 10 14 9 2 12 4 15 84 2 14 14 9 S So S S 14 4 11 12 10 9 4 13 1 11 13 2 8 1 2 15 4 3 2 11 0 6 11 14 15 2 2 1 7 11 12 10 1 4 4 11 11 1 15 13 13 8 4 12 14 11 7 15 2 50 12 2 14 15 7 8 4 8 4 1 10 7 1 9 13 12 2 9 7 12 4 1 6 10 9 7 4 13 14 2 0 6 3 8 12 13 5 15 15 7 2 12 6 10 9 8 4 10 1 7 3 7 11 14 8 1 8 13 8 13 5 5 6 10 15 3 7 6 10 11 1 4 0 13 14 10 14 7 9 0 9 12 15 3 12 13 15 0 14 1 13 3 15 10 9 5 206 15 12 12 0 3 4 1 10 6 5 9 4 14 10 9 7 3 6 10 14 9 7 5 10 13 5 5 12 2 1 0 8 0 015 14 3 14 5 9 8 6 3 0 11 3 8 4 7 3 13 6 08 13 5 6 110 14 10 2 0 14 0 5 3 15 8 15 3 5 5 11 11 5 9 2 6 1 50 3 12 12 7 9 2 5 8 6 11 Table C.3 DES Key Schedule Calculation (a) Input Key 1 9 17 25 33 41 49 57 57 1 10 19 63 7 14 21 2 10 18 26 34 42 50 58 49 58 2 = 55 62 6 13 3 11 19 27 35 43 51 59 41 50 59 3 47 54 61 12 5 20 28 36 44 52 60 33 42 51 60 39 46 53 5 (b) Permuted Choice One (PC-1) 28 13 21 29 37 45 53 61 25 34 43 52 31 38 45 6 20 14 22 30 38 46 54 62 15 23 31 7 39 47 55 63 17 26 35 44 23 30 37 12 8 16 24 32 40 48 56 64 S 18 27 36 15 22 29 A S So S S 14 4 11 12 10 9 4 13 1 11 13 2 8 1 2 15 4 3 2 11 0 6 11 14 15 2 2 1 7 11 12 10 1 4 4 11 11 1 15 13 13 8 4 12 14 11 7 15 2 50 12 2 14 15 7 8 4 8 4 1 10 7 1 9 13 12 2 9 7 12 4 1 6 10 9 7 4 13 14 2 0 6 3 8 12 13 5 15 15 7 2 12 6 10 9 8 4 10 1 7 3 7 11 14 8 1 8 13 8 13 5 5 6 10 15 3 7 6 10 11 1 4 0 13 14 10 14 7 9 0 9 12 15 3 12 13 15 0 14 1 13 3 15 10 9 5 206 15 12 12 0 3 4 1 10 6 5 9 4 14 10 9 7 3 6 10 14 9 7 5 10 13 5 5 12 2 1 0 8 0 015 14 3 14 5 9 8 6 3 0 11 3 8 4 7 3 13 6 08 13 5 6 110 14 10 2 0 14 0 5 3 15 8 15 3 5 5 11 11 5 9 2 6 1 50 3 12 12 7 9 2 5 8 6 11 Table C.3 DES Key Schedule Calculation (a) Input Key 1 9 17 25 33 41 49 57 57 1 10 19 63 7 14 21 2 10 18 26 34 42 50 58 49 58 2 = 55 62 6 13 3 11 19 27 35 43 51 59 41 50 59 3 47 54 61 12 5 20 28 36 44 52 60 33 42 51 60 39 46 53 5 (b) Permuted Choice One (PC-1) 28 13 21 29 37 45 53 61 25 34 43 52 31 38 45 6 20 14 22 30 38 46 54 62 15 23 31 7 39 47 55 63 17 26 35 44 23 30 37 12 8 16 24 32 40 48 56 64 S 18 27 36 15 22 29 A 14 15 26 41 51 34 Round Number Bits Rotated 17 6 8 52 45 53 (c) Permuted Choice Two (PC-2) 11 21 16 31 33 46 24 10 7 37 48 42 1 23 27 47 44 50 (d) Schedule of Left Shifts 5 19 20 55 49 36 1 2 3 4 5 6 7 8 9 10 11 12 3 12 13 13 30 39 29 28 4 2 40 56 32 14 15 16 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1
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lets do the calculations stepbystep a Deriving the key K1 for the first round 1 Convert the main key ... View the full answer
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