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This paper provides security analysis for the public-key encryption scheme DHIES (formerly named DHES and DHAES), which was proposed in [7] and is now in several draft standards. DHIES is a Diffie-Hellman based scheme that combines a symmetric encryption method, a message authentication code, and a hash function, in addition to number-theoretic operations, in a way which is intended to provide security against chosen-ciphertext attacks. In this paper we find natural assumptions under which DHIES achieves security under chosen-ciphertext attack. The assumptions we make about the Diffie-Hellman problem are interesting variants of the customary ones, and we investigate relationships among them, and provide security lower bounds. Our proofs are in the standard model; no random-oracle assumption is required.