Notes

• Merkle proofs are the core of hash-based proofs, affecting proof size and verifier work
• Index distribution is uniform random sampling with replacement, allowing precise performance analysis
• Derived the exact distribution of proof size and verifier work, including expected values, variances, and probability mass functions
• Supports compressed multi-proofs and pure verifier-end implementation, improving efficiency
• Analysis extends to imperfect trees and mixed branch trees, adapting to different vector lengths
• Provides efficient calculation methods and approximate formulas, suitable for practical applications

• Merkle证明是哈希证明系统的核心，影响证明大小和验证者工作量
• 索引分布为均匀随机有放回抽样，允许精确性能分析
• 推导了证明大小和验证者工作量的期望值、方差和概率质量函数
• 支持压缩多证明和纯验证者端实现，提升效率
• 分析可扩展至非完美树和混合分支树，适应不同向量长度
• 提供了高效计算方法和近似公式，适用于实际应用场景