Question

The affine cipher $y=m x+b \bmod 26$ has an inverse cipher for only 12 different choices of $m$. What is the effect of increasing the alphabet size from 26 to 27 ? How about 29? 30?

   The affine cipher $y=m x+b \bmod 26$ has an inverse cipher for only 12 different choices of $m$. What is the effect of increasing the alphabet size from 26 to 27 ? How about 29? 30?
Applied Algebra: Codes, Ciphers and Discrete Algorithms
Applied Algebra: Codes, Ciphers and Discrete Algorithms
Darel W. Hardy, Fred… 2nd Edition
Chapter 4, Problem 14 ↓

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The encryption function for the affine cipher is given by: \[ y = (m x + b) \mod n \] where \( x \) is the plaintext letter's numeric value, \( y \) is the ciphertext letter's numeric value, \( m \) and \( b \) are keys of the cipher, and \( n \) is the size of  Show more…

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The affine cipher $y=m x+b \bmod 26$ has an inverse cipher for only 12 different choices of $m$. What is the effect of increasing the alphabet size from 26 to 27 ? How about 29? 30?
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