Since you are not trying to verify if two "messages" are identical in a word-to-word sense, it would not be practical to go down the hash-function way.
This sounds more like a "pattern recognition" problem.
The typical approach in this kind of problems is to obtain a set of features from the signal and then, given the features of some query signal, see if they match. The matching there is more in the sense of Euclidean Distance between vectors of features. Of course, other metrics of distance can be used too. This is captured in a straightforward way in the case of the Nearest Neighbour algorithm.
Usually, in the case of speech signals and voice recognition, the Mel Frequency Cepstral Coefficients are used as this vector of features you are after.
You might also find this response useful, as well as this repository.
Hope this helps.