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Non-Interactive Key Exchange (NIKE) is a fundamental but much-overlooked cryptographic primitive. It appears as a major contribution in the ground-breaking paper of Diffie and Hellman, but NIKE has remained largely unstudied since then. In this paper, the authors provide different security models for this primitive and explore the relationships between them. They then give constructions for secure NIKE in the Random Oracle Model based on the hardness of factoring and in the standard model based on the hardness of a variant of the decisional Bilinear Diffie Hellman Problem for asymmetric pairings. They also study the relationship between NIKE and Public Key Encryption (PKE), showing that a secure NIKE scheme can be generically converted into an IND-CCA secure PKE scheme.
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