Question

14. The encryption for 128 different symbols is given by the following equation: C=(K1×M+K2) modulo 128 ; where C and M represent the cipher and the message, respectively. For K1=11 and K2=17, encrypt M=70. Find the corresponding decryption function. Give the message that follows from C=20 for the same K1 and K2 values.

Answer 1

Using given encryption function and values for K1 and K2, the encrypted value of M=70 was found to be 35. A decryption function was constructed using the multiplicative inverse of K1 modulo 128, which is 35. Using this decryption function, the original message corresponding to C=20 was decrypted as M=105.

Step-by-step explanation:

The encryption function provided is C=(K1×M+K2) modulo 128, and we are given K1=11 and K2=17. To encrypt M=70, we substitute these values into the encryption function to get C=(11× 70 + 17) modulo 128.

Now let's perform the encryption: C=(11× 70 + 17) modulo 128 = (770 + 17) modulo 128 = 787 modulo 128 = 35. Thus, the encrypted value of M=70 with K1=11 and K2=17 is C=35.

To decrypt a message, we need to find the inverse of K1 modulo 128, which gives us a value K1-1 such that (K1×K1-1) modulo 128=1. Finding the multiplicative inverse can be done using the Extended Euclidean algorithm. In this case, the multiplicative inverse of 11 modulo 128 is 35. So the decryption function D(M) can be written as M = (K1-1 × (C - K2)) modulo 128, where M is the decrypted message.

To decrypt C=20, we substitute the values into the decryption function: M= (35 × (20 - 17)) modulo 128 = (35× 3) modulo 128 = 105 modulo 128 = 105. So, the original message corresponding to C=20 is M=105.