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Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. - Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions. - Weakly adaptive adversary. Our second bound considers n/2 + k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties. Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality. 

Abstract Thermally activated annealing in semiconductors faces inherent limitations, such as dopant diffusion. Here, a nonthermal pathway is demonstrated for a complete structural restoration in predamaged germanium via ionization‐induced recovery. By combining experiments and modeling, this study reveals that the energy transfer of only 2.4 keV nm⁻¹from incident ions to target electrons can effectively annihilate pre‐existing defects and restore the original crystalline structure at room temperature. Moreover, it is revealed that the irradiation‐induced crystalline‐to‐amorphous (c/a) transformation in Ge is reversible, a phenomenon previously considered unattainable without additional thermal energy imposed during irradiation. For partially damaged Ge, the overall damage fraction decreases exponentially with increasing fluence. Surprisingly, the recovery process in preamorphized Ge starts with defect recovery outside the amorphous layer and a shrinkage of the amorphous thickness. After this initial stage, the remaining damage decreases slowly with increasing fluence, but full restoration of the pristine state is not achieved. These differences in recovery are interpreted in the framework of structural differences in the initial defective layers that affect recovery kinetics. This study provides new insights on reversing the c/a transformation in Ge using highly‐ionizing irradiation and has broad implications across materials science, radiation damage mitigation, and fabrication of Ge‐based devices.