We present a new approach to the design of IND-CCA2 secure hybrid encryption schemes in the standard model. Our approach provides an efficient generic transformation from 1-universal to 2-universal hash proof systems. The transformation involves a randomness extractor based on a 4-wise independent hash function as the key derivation function. Our methodology can be instantiated with efficient schemes based on standard intractability assumptions such as Decisional Diffie-Hellman, Quadratic Residuosity, and Pailliera??s Decisional Composite Residuosity. Interestingly, our framework also allows to prove IND-CCA2 security of a hybrid version of 1991a??s Damg?Yrda??s ElGamal public-key encryption scheme under the DDH assumption.