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The authors extend the work of Bellare, Boldyreva and Staddon on the systematic analysis of randomness reuse to construct multi-recipient encryption schemes to the case where randomness is reused across different cryptographic primitives. They find that through the additional binding introduced through randomness reuse, one can actually obtain a security amplification with respect to the standard black-box compositions, and achieve a stronger level of security. They introduce stronger notions of security for encryption and signatures, where challenge messages can depend in a restricted way on the random coins used in encryption, and show that two variants of the KEM/DEM paradigm give rise to encryption schemes that meet this enhanced notion of security.
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