(Known plaintext attack for affine cipher.) Suppose the plaintext starts with if and the corresponding ciphertext is PQ. This means (8, 5) → (15, 16). This gives the simultancous equations 8a + B = 15 (mod 26) 6a +ß = 16 (mod 26) Solve this in modular arithmetic to get the keys a = 17, B = 9.

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