Probability Calculation for Hamming Weight Distributions

This document presents the probability calculation for distinguishing Hamming weight distributions. Given two distinct Hamming weight scenarios (HW = 0 and HW = 1), we derive the probability that an observed value \(x\) originates from the HW = 0 distribution. Utilizing Bayes' theorem, we calculate the conditional probability and provide the final expression for \(P(HW = 0 \mid x)\). This result is fundamental for evaluating the likelihood of an observed value associated with a specific Hamming weight, particularly useful in statistical analysis of distributions in cryptographic contexts.本文阐述了区分汉明权重分布概率的计算方法。针对两种不同的汉明权重情形（汉明权重为0和汉明权重为1），我们推导出观察值(x)起源于汉明权重为0分布的概率。运用贝叶斯定理，我们计算条件概率，并给出(P(HW = 0 mid x))的最终表达式。此结果对于评估与特定汉明权重相关的观察值的可能性至关重要，尤其在密码学环境中的分布统计分析中尤为有用。