In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desired Walsh spec...
Published in Journal of Systems Science and Complexity
Boolean functions with optimal algebraic immunity (OAI functions) are important cryptographic primitives in the design of stream ciphers. During the past decade, a lot of work has been done on constructing such functions, among which mathematics, especially finite fields, play an important role. Notably, the approach based on decompositions of addi...
Published in Tatra Mountains Mathematical Publications
The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National Uni...
Published in Journal of Systems Science and Complexity
This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have opt...
Published in Journal of Applied and Industrial Mathematics
The algebraic immunity of a Boolean function of n variables is known to be at most ⌈n/2⌉. We prove the upper bound ⌈n/4⌉ + 1 for the algebraic immunity of the Dillon bent functions constructed with the use of linear functions which is almost two times less than the available maximum bound.
Published in Mathematical Notes
The calculation of the exact value of the rth order nonlinearity of a Boolean function (the power of the distance between the function and the set of functions is at most r) or the derivation of a lower bound for it is a complicated problem (especially for r > 1). Lower bounds for nonlinearities of different orders in terms of the value of algebrai...
Published in Science China Information Sciences
In this paper, we show a construction of multi-output Boolean functions with optimal algebraic immunity. And, the relationship between the algebraic immunity of a multi-output Boolean function and those of its component functions is studied. We show that all the component functions, together with their nonzero linear combination, of the multi-outpu...
Published in Science China Information Sciences
Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. In this paper, we investigate n-variable (n even and n ⩾ 12) RSBFs to achieve maximum algebraic immunity (AI), and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known ...
Published in Journal of Computer Science and Technology
This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almo...
Published in Science China Information Sciences
Boolean functions with maximum algebraic immunity have been considered as one class of cryptographically significant functions. It is known that Boolean functions on odd variables have maximum algebraic immunity if and only if a correlative matrix has column full rank, and Boolean functions on even variables have maximum algebraic immunity if and o...
