Cytography related

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It neccessary, because we need multiplicative inverse of a: a^-1 ...................................................

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If we suppose that a and N, are not relatively prime, that cipher won't be unique. Lets consider different P1 and P2. For them we should have C1 = aP1 + b (mod N) and C2 = aP2 + b (mod N) and C1, C2 also should be diffrent. They are different if and only if (a * P1 mod N) and (a * P2 mod N) are not equal. And statements A: (a * P1 mod N) != (a * P2 mod N) B: P1 != P2 are equivalent if and only if (a, N) = 1. If (a, N) != 1, than statements A and B are not equivalent, which means there is possible situation when P1 and P2 are different, but (a * P1 mod N) and (a * P2 mod N) are equal. So different P1 and P2 have the same ciphers.

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