Abstract

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.

Instructions:

1. The calculations and proofs in this document are based on the assumption of normal distributions for different Hamming weights.
2. To replicate the probability calculation, ensure that you have the correct values for the noise variance (\(\sigma_{\text{noise}}^2\)) and other constants like \(c\), \(d\), and \(\text{avg.HW}\).
3. Follow the steps outlined in the probability calculation to derive the conditional probability \(P(HW = 0 | x)\).
4. Use the final expression to evaluate the likelihood of an observed value corresponding to \(HW = 0\).
5. The result is particularly useful when applying statistical analysis to cryptographic protocols where Hamming weight distributions play a role.

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Probability Calculation for Hamming Weight Distributions

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