Welcome to the resource topic for 2005/449
Title:
On the Boolean functions With Maximum Possible Algebraic Immunity : Construction and A Lower Bound of the Count
Authors: Longjiang Qu, Guozhu Feng, Chao Li
Abstract:This paper gives a construction method which can get a large class
of Boolean functions with maximum algebraic immunity(AI) from one
such giving function. Our constructions get more functions than any
previous construction. The cryptographic properties, such as
balance, algebraic degree etc, of those functions are studied. It
shows that we can construct Boolean functions with better
cryptographic properties, which gives the guidance for the design of
Boolean functions to resist algebraic attack, and helps to design
good cryptographic primitives of cryptosystems. From these
constructions, we show that the count of the Boolean functions with
maximum AI is bigger than {2^{2^{n-1}}} for n odd, bigger than
{2^{2^{n-1}+\frac{1}{2}\binom{n}{\frac{n}{2}} }} for n even,
which confirms the computer simulation result that such boolean
functions are numerous. As far as we know, this is the first bound
about this count.
ePrint: https://eprint.iacr.org/2005/449
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .