Explore a comprehensive lecture on Proof-of-Work (PoW) based distributed cryptography without trusted setup, delving into Bitcoin's design principles and their differences from traditional multi-party computation. Learn about the concept of majority in terms of computing power, the verification process through Proofs of Work, and Bitcoin's implementation of the bulletin board. Examine the challenges in Bitcoin's solution and Satoshi's approach, as well as the motivation behind starting from scratch. Gain insights into the "Bitcoin network model," the modeling of computing power, and the main results of the research. Discover the key tool of a "PoW-based secure broadcast protocol" and understand its implications for adversarial behavior in the network. Analyze the importance of challenges not being known in advance for Proofs of Work and explore potential solutions and their associated problems in this cutting-edge cryptographic discussion.