In a public-key encryption scheme,
if a sender is not concerned about the security of a message and
is unwilling to generate costly randomness,
the security of the encrypted message can be compromised.
In this work, we characterize such \emph{lazy parties},
who are regraded as honest parties, but are unwilling to perform a costly task when they are not concerned about the security.
Specifically, we consider a rather simple setting in which
the costly task is to generate randomness used in algorithms,
and parties can choose either perfect randomness or a fixed string.
We model lazy parties as rational players who behave rationally to
maximize their utilities, and define a security game between the parties and an adversary.
Since a standard secure encryption scheme does not work in the setting,
we provide constructions of secure encryption schemes in various settings.
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