Dingyi Pei

Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

In this correspondence, first we give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.

A Key Predistribution Scheme Based on 3-Designs

In wireless distributed sensor networks, it is important for sensor nodes to communicate securely each other. In order to ensure this security, many approaches have been proposed recently. One of them is to use key predistribution scheme (KPS). In this paper, we shall use the Mobius plane to present a key predistribution scheme for distributed sensor networks. The secure connectivity and resilience of the resulting sensor network will be analyzed in this paper. This KPS constructed in our paper has some better properties than the ones of KPSs constructed in [5],[7] and [9].

A Class of Key Predistribution Schemes Based on Orthogonal Arrays

Pairwise key establishment is a fundamental security service in sensor networks; it enables sensor nodes to communicate securely with each other using cryptographic techniques. In order to ensure this security, many approaches have been proposed recently. One of them is to use key predistribution schemes (KPSs) by means of combinatorial designs. In this paper, we use the Bush’s construction of orthogonal arrays to present a class of key predistribution schemes for distributed sensor networks. The secure connectivity and resilience of the resulting sensor network are analyzed. This KPS constructed in our paper has some better properties than those of the existing schemes.

Identification and construction of Boolean functions with maximum algebraic immunity

AbstractBoolean 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 only if two correlative matrices have column full rank. Recently, a smaller matrix was used in the odd case. We find that one or two smaller matrices can be used in the even case and consequently present several sufficient and necessary conditions for Boolean functions with maximum algebraic immunity. This result advances the ability to identify whether Boolean functions on even variables achieve maximum algebraic immunity. We also present a construction algorithm for n-variable Boolean functions with maximum algebraic immunity, specially with the Hamming weights of

A novel key pre-distribution scheme for wireless distributed sensor networks

\sum {_{i = 0}^{\left\lceil {\frac{n} {2}} \right\rceil - 1} } \left( {\begin{array}{*{20}c} n \\ i \\ \end{array} } \right)

Practical construction of ring LFSRs and ring FCSRs with low diffusion delay for hardware cryptographic applications

. It is easily realized for not too large n and helps construct balanced Boolean functions with maximum algebraic immunity on even variables. Furthermore, we present a sufficient and necessary condition for balanced Boolean functions to achieve maximum algebraic immunity and optimum algebraic degree, and modify the construction algorithm to construct Boolean functions on odd variables with maximum algebraic immunity, optimum algebraic degree and high nonlinearity.

Eisenstein series of 3/2 weight and one conjecture of Kaplansky

Boolean functions used in stream ciphers against algebraic attacks are required to have a necessary cryptographic property-high algebraic immunity (AI). In this paper, Boolean functions of even variables with the maximum AI are investigated. The number of independent annihilators at the lowest degree of Boolean functions of even variables with the maximum AI is determined. It is shown that when n is even, one can get an (n + 1)-variable Boolean function with the maximum AI from two n-variable Boolean functions with the maximum AI only if the Hamming weights of the two functions satisfy the given conditions. The nonlinearity of the Boolean functions obtained in this way is computed. Similarly, one can get an (n + 2)-variable Boolean function with the maximum AI from four n-variable Boolean functions with the maximum AI. The nonlinearity of a class of Boolean functions with the maximum AI is determined such that their Hamming weights are either the maximum or the minimum.

Results on the immunity of Boolean functions against probabilistic algebraic attacks

AbstractA novel key pre-distribution scheme for sensor networks is proposed, which enables sensor nodes to communicate securely with each other using cryptographic techniques. The approach uses the rational normal curves in the projective space with the dimension n over the finite field