This paper presents recent advances in the identification problem taking into account the accuracy, complexity and privacy leak of different decoding algorithms. Using a model of different actors from literature, we show that it is possible to use more accurate decoding algorithms using reliability information without increasing the privacy leak relative to algorithms that only use binary information. Existing algorithms from literature have been modified to take advantage of reliability information, and we show that a proposed branch-and-bound algorithm can outperform existing work, including the enhanced variants.