DHIES is built in a generic way from lower-level primitives: a symmetric encryption scheme, a message authentication code, group operations in an arbitrary group, and a cryptographic hash function. In particular, the underlying group may be an elliptic-curve group or the multiplicative group of integers modulo a prime number.
We show that DHIES has not only the ``basic'' property of secure encryption (namely privacy under a chosen-plaintext attack) but also achieves privacy under an adaptive chosen-ciphertext attack. (And hence it also achieves non-malleability.)
The proofs of security are based on appropriate assumptions about the hardness of the Diffie-Hellman problem and the assumption that the underlying symmetric primitives are secure. The assumptions are all standard in the sense that no random oracles are involved.
We suggest that DHIES provides an attractive starting point for developing public-key encryption standards based on the Diffie-Hellman assumption. DHIES is already part of several draft standards.