Non-interactive zero-knowledge proofs (NIZKs) are a powerful cryptographic tool, with numerous potential applications. However, succinct NIZKs (e.g., zk-SNARK schemes) necessitate a trusted party to generate and publish some public parameters, to be used by all provers and verifiers. This party is trusted to *correctly* run a probabilistic algorithm (specified by the the proof system) that outputs the public parameters, and publish them, without *leaking* any other information (such as the internal randomness used by the algorithm); violating either requirement may allow producing convincing "proofs" of false statements. This trust requirement poses a serious impediment to deploying NIZKs in many applications, because a party that is trusted by all users of the envisioned system may simply not exist. In this work, we show how public parameters for a class of NIZKs can be generated by a multi-party protocol, such that if at least one of the parties is honest, then the result is secure (in both aforementioned senses) and can be subsequently used for generating and verifying numerous proofs without any further trust. We design and implement such a protocol, tailored to efficiently support the state-of-the-art NIZK constructions with short and easy-to-verify proofs (Parno et al. IEEE S&P '13; Ben-Sasson et al. USENIX Sec '14; Danezis et al. ASIACRYPT '14). Applications of our system include generating public parameters for systems such as Zerocash (Ben-Sasson et al. IEEE S&P '13) and the scalable zero-knowledge proof system of (Ben-Sasson et al. CRYPTO '14).