The classical distributed key generation protocols (DKG) are resurging due to their widespread applications in blockchain. While efforts have been made to improve DKG communication, practical large-scale deployments are still yet to come due to various challenges, including the heavy computation and communication (particularly broadcast) overhead in their adversarial cases. In this paper, we propose a practical DKG for DLog-based cryptosystems, which achieves (quasi-)linear computation and communication per-node cost with the help of a common coin, even in the face of the maximal amount of Byzantine nodes. Moreover, our protocol is secure against adaptive adversaries, which can corrupt less than half of all nodes. The key to our improvements lies in delegating the most costly operations to an Any-Trust group together with a set of techniques for adaptive security. This group is randomly sampled and consists of a small number of individuals. The population only trusts that at least one member in the group is honest, without knowing which one. Moreover, we present a generic transformer that enables us to efficiently deploy a conventional distributed protocol like our DKG, even when the participants have different weights. Additionally, we introduce an extended broadcast channel based on a blockchain and data dispersal network (such as IPFS), enabling reliable broadcasting of arbitrary-size messages at the cost of constant-size blockchain storage.