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Is size of key space divisible by size of message space for a encryption scheme following perfect secrecy?

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In a perfectly secret encryption scheme, any ciphertext c can be decrypted in |K| ways and it should decrypt to any message with equal probability (assume messages are uniformly distributed over message space). Does this imply that |K|(size of key space) is always divisible by |M| (size of message space) for perfect secrecy?

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