Math Problem Statement

Extract all the text in a format

Use the affine cipher function f(x) = (3x + 14) (mod 26) to: a) Encipher REPUBLICAN. b) Decipher ZCAGWPQV.

Solution

Here's the extracted text from the image in a clear format:


Waleed Khalid Roll No F24610019

Q: 6

Use the affine cipher function f(x)=(3x+14)mod26f(x) = (3x + 14) \mod 26
to: a) Encipher REPUBLICAN.
b) Decipher ZCAGWPQV.

Plaintext: REPUBLICAN

R & : 18 & \\ E & : 5 & \\ P & : 15 & \\ U & : 20 & \\ B & : 1 & \\ L & : 11 & \\ I & : 8 & \\ C & : 2 & \\ A & : 0 & \\ N & : 13 & \\ \end{align*}$$ **Calculation for Enciphering:** - $$3x + 14$$: 68, 29, 62, 77, 20, 50, 41, 23, 17, 56 - $$(3x + 14) \mod 26$$: 26, 16, 3, 10, 25, 20, 24, 15, 23, 4 **Ciphertext**: PCJYTXOWQD --- ### Calculation Steps: **Modulo Operations:** - $$68 \mod 26 = 16$$ → Reminder: P - $$29 \mod 26 = 3$$ → Reminder: C - $$62 \mod 26 = 10$$ → Reminder: J - $$77 \mod 26 = 25$$ → Reminder: Y - $$20 \mod 26 = 20$$ → Reminder: T - $$50 \mod 26 = 24$$ → Reminder: X - $$41 \mod 26 = 15$$ → Reminder: O - $$23 \mod 26 = 23$$ → Reminder: W - $$17 \mod 26 = 17$$ → Reminder: Q - $$56 \mod 26 = 4$$

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Math Problem Analysis

Mathematical Concepts

Affine Cipher
Modular Arithmetic
Encryption
Decryption

Formulas

f(x) = (3x + 14) mod 26

Theorems

Modular Arithmetic Theorem
Affine Cipher Encryption and Decryption Rules

Suitable Grade Level

Grades 10-12