So... I am considering working with Gröbner bases and cryptanalysis for my thesis... and I have a mentor professor... but at the current moment I am unable to get in touch with him for help.
As a summer seminar project I am giving a talk about the attached article. I have asked the only other professor that I consider knowledgeable in the subject matter and he was unable to help me with Question 1
I seem to have run into a kink with the definition and last example on the bottom of page 5.
1. I do not know what the plus is above the F in the definition
2. I can not quite get how they reduced the polynomial to get what they got.
Did they have to apply the algorithm twice?
3. on page 7, why is LM(f2)=xyz^2?
(which i think is sort of the same issue I am having in question 2)
and if you're feeling generous....
4. Do you think you could explain the Buchberger Algorithm in layman's terms.
Thanks for your help.