  Byzantine agreement allows n processes to decide on a common value, in spite
of arbitrary failures. The seminal Dolev-Reischuk bound states that any
deterministic solution to Byzantine agreement exchanges Omega(n^2) bits. In
synchronous networks, solutions with optimal O(n^2) bit complexity, optimal
fault tolerance, and no cryptography have been established for over three
decades. However, these solutions lack robustness under adverse network
conditions. Therefore, research has increasingly focused on Byzantine agreement
for partially synchronous networks. Numerous solutions have been proposed for
the partially synchronous setting. However, these solutions are notoriously
hard to prove correct, and the most efficient cryptography-free algorithms
still require O(n^3) exchanged bits in the worst case. In this paper, we
introduce Oper, the first generic transformation of deterministic Byzantine
agreement algorithms from synchrony to partial synchrony. Oper requires no
cryptography, is optimally resilient (n >= 3t+1, where t is the maximum number
of failures), and preserves the worst-case per-process bit complexity of the
transformed synchronous algorithm. Leveraging Oper, we present the first
partially synchronous Byzantine agreement algorithm that (1) achieves optimal
O(n^2) bit complexity, (2) requires no cryptography, and (3) is optimally
resilient (n >= 3t+1), thus showing that the Dolev-Reischuk bound is tight even
in partial synchrony. Moreover, we adapt Oper for long values and obtain
several new partially synchronous algorithms with improved complexity and
weaker (or completely absent) cryptographic assumptions.
