Hello,
I'm currently a student in Master of Theoretical Computer Science, and currently doing my internship in a Crypto group, so I have already a good background in mathematics and cryptology (by the way, I should go to the EuroCrypt conference at the end of the month). So I shouldn't have any problem to implement one of these programs, and providing a GUI is also perfect, I really like to explain things with drawing (I spent hours to draw Tikz figure...).
I can for example begin to do the first project, I think it's quite easy to make people visualize it, but if you prefer me to do another one it's not a problem at all... I'm just curious to know if you would like me to insist more on the computation part (how to compute for example the inverse), or just on the graphical result (this polynomial + this polynomial = this polynomial). I would also be interesting to do some job on the lattice, (famous to be quantum-proof) that I'd like to understand better.
And I would like also to know if you want me to use a given language, or if I'm free to use whichever program I want to use (I though to use Python because it's present nearly anywhere, but If you have another option, I can also program in C++/Qt, or anything else).
All the best,
Léo.