Alice wants to securely send Bob an arbitrary number M from the set {0, 1, . . . , N − 1} for some positive integer N. She wants to have a scheme with perfect secrecy. She heard of the One Time Pad (OTP), but OTP is for bitstrings, not numbers. She decides to use the following scheme. The key space is {0, 1, . . . , N − 1}. A ciphertext C for M is computed as (M + K) mod N and decryption performs (C − K) mod N. Prove that this scheme is perfectly secure

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