Final answer:
To decrypt a message encrypted with the affine cipher, apply the inverse function of the encryption function. Solve the equation (17p+3) mod 26 = X to find the inverse function. Decrypt the given message XJEOSXTQXT to AJWAXAJAQA.
Step-by-step explanation:
To decrypt a message encrypted using the affine cipher, we need to apply the inverse function of the encryption function. In this case, the encryption function is given as f(p) = (17p+3) mod 26, where p represents the plaintext letter and f(p) represents the corresponding encrypted letter. To find the inverse function, we need to find the value of p that satisfies the equation (17p+3) mod 26 = X, where X is the encrypted letter.
Let's solve this equation for p:
(17p+3) mod 26 = X
Subtracting 3 from both sides:
17p mod 26 = X - 3
Multiplying both sides by the multiplicative inverse of 17 mod 26:
p = (X - 3) * 23 mod 26
Now, we can substitute the value of X and calculate p using the given message XJEOSXTQXT:
- (X - 3) = (23 - 3) mod 26 = 20
- p = 20 * 23 mod 26 = 0
Since p = 0, the decrypted letter is A. Therefore, the decrypted message for XJEOSXTQXT is AJWAXAJAQA.
To decrypt the message encrypted using an affine cipher, one must apply the inverse function of the given encryption formula after finding the modular inverse of the multiplicative component.
The student's question involves decrypting a message that was encrypted using an affine cipher. The given function for the affine cipher is f(p) = (17p + 3) mod 26. To decrypt the message 'XJEOSXTQXT', one must find the modular inverse of the multiplicative component (17 in this case) and use this inverse to reverse the encryption formula. However, this function is used for encryption, and decryption would require the use of its inverse function. Typically, the inverse function would be of the form f-1(c) = a-1(c - b) mod 26, where a-1 is the modular inverse of 17 mod 26, c is the ciphertext letter, and b is the additive component 3. Once the modular inverse is found, we can apply the inverse function to each letter of the ciphertext to retrieve the original plaintext.