Accumulators provide compact representations of large sets and enjoy compact membership witnesses. Besides constant-size witnesses, public-key accumulators provide efficient updates of both the accumulator itself and the witness; however, they come with two drawbacks: they require a trusted setup and – without knowledge of the secret trapdoors – their performance is not practical for real-world applications with large sets. Recent improvements in the area of secure multi-party computation allow us to replace the trusted setup with a distributed generation of the public parameters. In this paper, we introduce multi-party public-key accumulators dubbed dynamic linear secret-shared accumulators. We present versions of dynamic public-key accumulators in bilinear groups giving access to more efficient witness generation and update algorithms that utilize the shares of the secret trapdoors sampled by the parties generating the public parameters. Specifically, for the t-SDH-based accumulators, we provide a maliciously-secure variant sped up by a secure multi-party computation (MPC) protocol (IMACC'19) built on top of SPDZ. For this scheme, a performant proof-of-concept implementation is provided, which substantiates the practicability of public-key accumulators in this setting. With our implementation in two MPC frameworks, MP-SPDZ and FRESCO, we obtain more efficient accumulators for both medium-sized (2^10) and large (2^14 and above) accumulated sets. Finally, we explore applications of dynamic linear secret-shared accumulators to revocations schemes of group signatures and credentials system. In particular, we consider it as part of Sovrin’s system for anonymous credentials where credentials are issued by the a foundation of trusted nodes. Hence, our accumulators naturally fit this setting.