On the Existence of Boolean Functions with Optimal Resistance against Fast Algebraic Attacks
نویسندگان
چکیده
It has been pointed out that an n-variable Boolean function f has optimal resistance against fast algebraic attacks if and only if there does not exist a nonzero n-variable Boolean function g of degree lower than n 2 such that fg = h and deg(g) + deg(h) < n. In this corresponding, we show that there does not exist an n-variable Boolean function with optimal resistance against fast algebraic attacks for most values of n.
منابع مشابه
Efficient Computation of Algebraic Immunity for Algebraic and Fast Algebraic Attacks
In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSR-based stream ciphers. An algorithm is described which permits to compute the algebraic immunity d of a Boolean function with n variables in O(D) operations, for D ≈ ` n d ́ , rather than in O(D) operations necessary in all p...
متن کاملOn the immunity of Boolean functions against fast algebraic attacks using bivariate polynomial representation
In the last decade, algebraic and fast algebraic attacks are regarded as the most successful attacks on LFSR-based stream ciphers. Since the notion of algebraic immunity was introduced, the properties and constructions of Boolean functions with maximum algebraic immunity have been researched in a large number of papers. However, it is unclear whether these functions behave well against fast alg...
متن کاملEvolving balanced Boolean functions with optimal resistance to algebraic and fast algebraic attacks, maximal algebraic degree, and very high nonlinearity
Using simulated annealing, we derive several equivalence classes of balanced Boolean functions with optimum algebraic immunity, fast algebraic resistance, and maximum possible algebraic degree. For numbers n of input bits less than 16, these functions also possess superior nonlinearity to all Boolean functions so far obtained with said properties.
متن کاملEfficient probabilistic algorithm for estimating the algebraic properties of Boolean functions for large n
Although several methods for estimating the resistance of a random Boolean function against (fast) algebraic attacks were proposed, these methods are usually infeasible in practice for relative large input variables n (for instance n ≥ 30) due to increased computational complexity. An efficient estimation the resistance of Boolean function (with relative large input variables n) against (fast) ...
متن کاملOn the Resistance of Prime-variable Rotation Symmetric Boolean Functions against Fast Algebraic Attacks
Boolean functions used in stream ciphers should have many cryptographic properties in order to help resist different kinds of cryptanalytic attacks. The resistance of Boolean functions against fast algebraic attacks is an important cryptographic property. Deciding the resistance of an n-variable Boolean function against fast algebraic attacks needs to determine the rank of a square matrix of or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012