We initiate the study of indifferentiability for public key encryption and other public key primitives. Our main results are definitions and constructions of public key cryptosystems that are indifferentiable from ideal cryptosystems, in the random oracle model. Cryptosystems include Public key encryption, Digital signatures, Non-interactive key agreement. Our schemes are based on standard public key assumptions. By being indifferentiable from an ideal object, our schemes satisfy any security property that can be represented as a single-stage game and can be composed to operate in higher-level protocols.