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Is a cryptosystem perfectly secure if there are at least as many keys as there are plaintexts?

My guess is yes but I am not sure, new to cyptosystems

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  • $\begingroup$ See One-time-Pad. Also, note that the keys must be generated uniformly random. $\endgroup$ – kelalaka Mar 14 at 14:53
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    $\begingroup$ Hint: What about cryptosystems that don't make good (or any) use of their key? $\endgroup$ – SEJPM Mar 14 at 14:55
  • $\begingroup$ Take the definition of a perfectly secure crypto-system and try to use counting arguments on the sizes of the sets of the possible keys and possible plaintexts $\endgroup$ – yacovm Mar 14 at 21:46

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