Motivated by the need for robust and scalable computation in peer-to-peer networks, we design the first scalable protocols for these problems for a network whose degree is polylogarithmic in its size. By scalable, we mean that each uncorrupted processor sends and processes a number of bits that is only polylogarithmic in n. (We assume no limit on the number of messages sent by corrupted processors.) With high probability, our Byzantine Agreement protocol results in agreement among a 1..O(1= ln n) fraction of the uncorrupted processors. With constant probability, our Leader Election protocol elects an uncorrupted leader and ensures that a 1..O(1= ln n) fraction of the uncorrupt processors know this leader.

We assume a full information model. Thus, the adversary is assumed to have unlimited computational power and has access to all communications, but does not have access to processors' private random bits.