A remark on the Independence Heuristic in the Dual Attack

Ducas and Pulles in Does the Dual-Sieve Attack on Learning with Errors even Work? especially report on experiments they made comparing the distributions of scores for random targets and BDD targets. They discovered that the distribution of scores for BDD targets deviate from the predictions made under the independence heuristic. Here, we want to derive approximations for the distributions which take into account the dependency that occur in the scores. These approximations allow to find heuristic estimates for the success probability of distinguishing between the two distributions