This is the mathematical basis for the post-quantum signature algorithm "ring-TESLA".
My thesis revolved around patching first-order fault attacks against this scheme. A handful of such attacks had already been described, but I was able to show that one of them is not feasible and find a previously unknown attack.
Finding and patching these vulnerabilities involved compiling the source code, disassembling the binary file and then looking for ways an adversary could introduce errors in the computation. Then I devised mechanisms to prevent those errors from revealing information about the private key. These then had to be implemented in the source code in a way that would not be optimized away during compilation or introduce new vulnerabilities.
Finally I evaluated the effect of these countermeasures on the performance of the algorithm. Except for one countermeasure, all were very efficient, both speed and size wise.
You can download the thesis, source code and a paper I co-authored below.