Mathematics – Algebraic Geometry
Scientific paper
2006-05-09
Mathematics
Algebraic Geometry
19 pages
Scientific paper
The vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect non-linearity (APN) to study resistance to the differential attacks. Up to now, the study of functions APN was especially devoted to power functions. Recently, Budaghyan and al. showed that certain quadratic polynomials were APN. Here, we will give a criterion so that a function is not almost perfectly non-linear. H. Janwa showed, by using Weil's bound, that certain cyclic codes could not correct two errors. A. Canteaut showed by using the same method that the functions powers were not APN for a too large value of the exponent. We use Lang and Weil's bound and a result of P. Deligne on the Weil's conjectures (or more exactly improvements given by Ghorpade and Lachaud) about surfaces on finite fields to generalize this result to all the polynomials. We show therefore that a polynomial cannot be APN if its degree is too large.
No associations
LandOfFree
Borne sur le degré des polynômes presque parfaitement non-linéaires does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Borne sur le degré des polynômes presque parfaitement non-linéaires, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Borne sur le degré des polynômes presque parfaitement non-linéaires will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-675806