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Semi-Regular Bits and Pieces
John Perry’s slides from his talk at Sage Days 12 in San Diego are available on the Sage wiki.
In my Diplomarbeit I had an algorithm for computing Gröbner bases of block ciphers called “Gröbner surfing”: “Instead of computing a reduced Gröbner basis for all rounds $rgb_F$ it computes the reduced Gröbner basis $rgb_{i+1}$ up to round $i + 1$ recursively as $$rgb_{i+1} = rgb(gb_i + round_{i+1})$$ with $rgb_0 = rgb(round_0)$ where $$rgb(round_i)$$ denotes any algorithm returning a reduced Gröbner basis for a given finite set of polynomials $round_i$.” This obviously is a tiny subset of what $F_5$ does: computing the Gröbner basis for $\langle f_i,\dots,f_m \rangle$ from the Gröbner basis of $\langle f_{i+1},\dots,f_m \rangle$. So nothing new here, move along.
I’m going to the Fast Software Encryption (FSE) 2009 workshop in Leuven to present our paper “Algebraic Techniques in Differential Cryptanalysis”. The full list of accepted papers is available online.
