%!TEX root = paper.tex

\section{Conclusion}
\label{sec:conclusion}

We propose a new algorithm for key reconstruction that is faster than Guo's 
et al. algorithm, and uses significantly less interaction with the secret key holder
than needed by the latter.
Our algorithm has lower asymptotic complexity, which suggest it scales
much better for higher security levels. Our experimental analysis of the algorithm
shows that it performs much better than Guo's et al. algorithm for all security parameters.

The proposed algorithm is different in nature than the one by Guo et al.: it is based on linear algebra instead of
a pruned depth-first search in a tree. It can also be straightforwardly
parallelized, which is not the case for the Guo's et al. approach.
Our algorithm has a small probability of failing in recovering the key,
but we show how to select the parameters in
such a way that the probability of
failure becomes negligible. 

For future works, it would be interesting to study how the use of other decoding algorithms impacts on the number of decoding trials needed for the attack.
Another possible research question is to consider variants of the proposed algorithm
that are successful
with even fewer knowledge
about both spectrums.
This is important because it is related to the determination of the lifetime
of a QC-MDPC secret key.




