Problem 1. Write the following computer programs to simulate a mini data encryption system (MDES). Since it is just a simulation, the bit and the binary strings in the following can be expressed as integers 0 and 1. 1. Let Z32 corresponding to 26 English characters, space, dot (.), comma (.), question mark (?) and two brackets (left bracket and right bracket). So the following corre- spondence are used. ? (D. 26 27 28 29 30 31 Each element in Z32 can be expressed as a 5-bit string. Write a program to translate English text to binary strings according to the above correspondence. Also write a program to do the inverse. 2. Write a program to implement a function f as follows. The inputs of the function are a bitstring B (plaintext) of length 8 and a round key K which is a bitstring of length 12. First, B is expanded into 12 bits according to the following: 1 2 3 4 3 4 5 6 5 6 7 8 For example, 10110101 is expanded to 101111010101.) Then the expanded string is XORed with the round key K. The resulting 12-bit is split into two parts B and B2 1 such that each part has 6 bits. Finally, Bi passes through S-box S, and B2 passes through S2 (using a method similar to that in DES). The output of f is a 8-bit string obtained from the output of two S-boxes. The S-boxes are as follows. Si 15 1 8 14 6 11 3 13 4 7 15 2 0 14 7 11 10 4 13 8 10 1 3 15 3 4 9 7 2 13 12 0 5 10 8 14 12 0 1 10 6 9 11 5 13 1 5 8 12 6 93 2 15 4 2 11 6 7 12 0 5 14 9 and S2 7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15 13 8 11 5 6 15 0 3 4 7 2 12 1 10 14 9 10 6 9 0 12 11 7 13 15 13 14 5 2 8 4 3 15 0 6 10 1 13 8 9 4 5 11 12 7 2 14 3. Write a program of a encryption system as follows. First use the program in 1 to translate the English text to binary strings. Then divide the plaintext (binary strings) into blocks of 16 bitstrings. Each block is divided into Lo and Ro where Lo comprises the first 8 bits and Ro the last 8 bits. Then use the following iterations for 1 Sis2, where f is defined in 2: Li R-1 Ri Li-1 e f (Ri-1, Ki). The key is a 24-bit binary string. The first round key uses the first 12 bits and the second round key uses the last 12 bits. The output (ciphertext block) is L2R2. 4. Suppose the plaintext is "how do you like computer science" and the key is {101101010010100101101011}. Use the above programs to compute the ciphertext. The ciphertext is written in English letters (from the correspondence described in 1.). Problem 1. Write the following computer programs to simulate a mini data encryption system (MDES). Since it is just a simulation, the bit and the binary strings in the following can be expressed as integers 0 and 1. 1. Let Z32 corresponding to 26 English characters, space, dot (.), comma (.), question mark (?) and two brackets (left bracket and right bracket). So the following corre- spondence are used. ? (D. 26 27 28 29 30 31 Each element in Z32 can be expressed as a 5-bit string. Write a program to translate English text to binary strings according to the above correspondence. Also write a program to do the inverse. 2. Write a program to implement a function f as follows. The inputs of the function are a bitstring B (plaintext) of length 8 and a round key K which is a bitstring of length 12. First, B is expanded into 12 bits according to the following: 1 2 3 4 3 4 5 6 5 6 7 8 For example, 10110101 is expanded to 101111010101.) Then the expanded string is XORed with the round key K. The resulting 12-bit is split into two parts B and B2 1 such that each part has 6 bits. Finally, Bi passes through S-box S, and B2 passes through S2 (using a method similar to that in DES). The output of f is a 8-bit string obtained from the output of two S-boxes. The S-boxes are as follows. Si 15 1 8 14 6 11 3 13 4 7 15 2 0 14 7 11 10 4 13 8 10 1 3 15 3 4 9 7 2 13 12 0 5 10 8 14 12 0 1 10 6 9 11 5 13 1 5 8 12 6 93 2 15 4 2 11 6 7 12 0 5 14 9 and S2 7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15 13 8 11 5 6 15 0 3 4 7 2 12 1 10 14 9 10 6 9 0 12 11 7 13 15 13 14 5 2 8 4 3 15 0 6 10 1 13 8 9 4 5 11 12 7 2 14 3. Write a program of a encryption system as follows. First use the program in 1 to translate the English text to binary strings. Then divide the plaintext (binary strings) into blocks of 16 bitstrings. Each block is divided into Lo and Ro where Lo comprises the first 8 bits and Ro the last 8 bits. Then use the following iterations for 1 Sis2, where f is defined in 2: Li R-1 Ri Li-1 e f (Ri-1, Ki). The key is a 24-bit binary string. The first round key uses the first 12 bits and the second round key uses the last 12 bits. The output (ciphertext block) is L2R2. 4. Suppose the plaintext is "how do you like computer science" and the key is {101101010010100101101011}. Use the above programs to compute the ciphertext. The ciphertext is written in English letters (from the correspondence described in 1.)