A new aspect for security notions: Secure randomness in public-key encryption schemes

In this paper, we introduce a framework in which we can uniformly and comprehensively discuss security notions of public-key encryption schemes even for the case where some weak generator producing seemingly random sequences is used to encrypt plaintext messages. First, we prove that indistinguishability and semantic security are not equivalent in general. On the other hand, we derive some sufficient condition for the equivalence and show that polynomial-time pseudo-randomness is not always necessary for the equivalence.