cryptographic applications 2 The plaintext THEBEACH was encr

cryptographic applications

2) The plaintext THEBEACH was encrypted using the ane function 7x + 23. What is the ciphertext? What is the decryption function? Verify that it works.

Solution

Given function: 7x+23

Cipher text:

T - 19: 7*19 + 23 = 156 = 0 mod 26

H - 7: 7*7 + 23 = 72 = 20 mod 26

E - 4: 7*4 + 23 = 51 = 25 mod 26

B - 1: 7*1 + 23 = 30 = 4 mod 26

E - 4: 7*4 + 23 = 51 = 25 mod 26

A - 0: 7*0 + 23 = 23 = 23 mod 26

C - 2: 7*2 + 23 = 37 = 11 mod 26

H - 7: 7*7 + 23 = 72 = 20 mod 26

Thus, converting this to letters, we get auzezxlu.

Therefore, The Cipher text is AUZEZXLU

Decryption Function: Let us FInd the decryptionfunction y= 7x + 23 (mod 26)

                                                      y-23 = 7x mod 26

the inverse of 7 modulo 26, as 7x = 1 mod 26, 7^-1 = 15 (mod 26)

                                                     x=15(y-23) = 15y+7