Perfect secrecy refers to how well a message is hidden in a given ciphertext (encoded/encrypted message). Perfect secrecy and cryptographic secrecy are two related and contrasting notions.

In perfect secrecy, the attacker, despite unlimited resources to inspect the ciphertext, has no better knowledge of the message before and after the inspection. Cryptographic secrecy (used widely in practice in all online communication systems) on the contrary derives secrecy by assuming that the adversary is limited in computational power.

A simple analogy to grasp these two notions of secrecy is the following: Alice decides to write down a number between 1 and 10 on a piece of paper. To hide it from her friend Eve who wants to know exactly what the number is, Alice puts the number inside a box with a combination lock. This is the notion of computational secrecy. If the lock has too many, a trillion for sake of argument, combinations, we can safely say Alice’s secret is safe. However, if Alice never writes down the number of a piece of paper, Eve has no way of knowing the specific number. Eve already knows that the number is between 1 and 10, but has no more information and no way to obtain more.

This is perfect secrecy. It is important to note that the first hiding approach does not have the property of perfect secrecy because Eve can simply open the combination (since she theoretically has unlimited resources at her disposal) and know Alice’s number.

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