{"ID":2859405,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.06023","arxiv_id":"2510.06023","title":"Optimal Good-Case Latency for Sleepy Consensus","abstract":"In the context of Byzantine consensus problems such as Byzantine broadcast (BB) and Byzantine agreement (BA), the good-case setting aims to study the minimal possible latency of a BB or BA protocol under certain favorable conditions, namely the designated leader being correct (for BB), or all parties having the same input value (for BA). We provide a full characterization of the feasibility and impossibility of good-case latency, for both BA and BB, in the synchronous sleepy model. Surprisingly to us, we find irrational resilience thresholds emerging: 2-round good-case BB is possible if and only if at all times, at least $\\frac{1}{\\varphi} \\approx 0.618$ fraction of the active parties are correct, where $\\varphi = \\frac{1+\\sqrt{5}}{2} \\approx 1.618$ is the golden ratio; 1-round good-case BA is possible if and only if at least $\\frac{1}{\\sqrt{2}} \\approx 0.707$ fraction of the active parties are correct.","short_abstract":"In the context of Byzantine consensus problems such as Byzantine broadcast (BB) and Byzantine agreement (BA), the good-case setting aims to study the minimal possible latency of a BB or BA protocol under certain favorable conditions, namely the designated leader being correct (for BB), or all parties having the same in...","url_abs":"https://arxiv.org/abs/2510.06023","url_pdf":"https://arxiv.org/pdf/2510.06023v1","authors":"[\"Yuval Efron\",\"Joachim Neu\",\"Ling Ren\",\"Ertem Nusret Tas\"]","published":"2025-10-07T15:22:29Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"cs.DC\"]","methods":"[]","has_code":false}