1. Is the affine cipher e(x) = 15x + 11 (mod 75) invertible? Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus), if no, explain why. = 2. Is the affine cipher e(x) = 16x +11 (modI75) invertible? Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus) if no, explain why.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Learning Target N5:** *I can encode English sentences into numbers and reverse the process. I can perform basic affine ciphers and find decryption functions. I can correctly state why an affine cipher is or is not invertible.*

1. **Is the affine cipher \( e(x) = 15x + 11 \ (\text{mod}\ 75) \) invertible?** Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus); if no, explain why.

2. **Is the affine cipher \( e(x) = 16x + 11 \ (\text{mod}\ 75) \) invertible?** Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus); if no, explain why.
Transcribed Image Text:**Learning Target N5:** *I can encode English sentences into numbers and reverse the process. I can perform basic affine ciphers and find decryption functions. I can correctly state why an affine cipher is or is not invertible.* 1. **Is the affine cipher \( e(x) = 15x + 11 \ (\text{mod}\ 75) \) invertible?** Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus); if no, explain why. 2. **Is the affine cipher \( e(x) = 16x + 11 \ (\text{mod}\ 75) \) invertible?** Yes or no. If yes, find the inverse (fully reduced with positive terms modulo the modulus); if no, explain why.
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