Number Theory question ciphers The cipher given by the trans

Number Theory question, ciphers

The cipher given by the transformation C = aP + b (mod TV), where a and N are relatively prime, is called affine transformation. Explain why do we require a and N to be relatively prime numbers. What would be wrong with this cipher if (a, N) notequalto 1? Find the order of integer operations required to find the inverse of a modulo N. (Assume that N is an n-bit integer and a

Solution

(a) The multiplicative inverse of \'a\' only exists if \'a\' and N are coprime. Hence without the restriction on \'a\' decryption might not be possible.