Laplace noise generation for two-party computational differential privacy

Computing a differentially private function using secure function evaluation prevents private information leakage both in the process, and from information present in the function output. However, the very secrecy provided by secure function evaluation poses new challenges if any of the parties are malicious. We first show how to build a two party differentially private secure protocol in the presence of malicious adversaries. We then relax the utility requirement of computational differential privacy to reduce computational cost, still giving security with rational adversaries. Finally, we provide a modified two-party computational differential privacy definition and show correctness and security guarantees in the rational setting.