arXiv subjects

Jinjin Chai

Publications and source records attributed to Jinjin Chai.

3 recordsLinked to original sources

arXiv2022

Boolean Functions of Binary Type-II and Type-II/III Complementary Array Pair

The sequence pairs of length $2^{m}$ projected from complementary array pairs of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III and of size $\mathbf{2}^{(m-1)}\times2$ are complementary sequence pairs Type-II and Type-III respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths $2^{m}$ ($m=1,2,3,4$) shows that they are all projected from the aforementioned complementary array pairs, whose algebraic normal forms satisfy specified expressions. It's natural to ask whether the conclusion holds for all $m$. In this paper, we proved that these expressions of algebraic normal forms determine all the binary complementary array pairs of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III of size $\mathbf{2}^{(m-1)}\times2$ respectively.

cs.IT↗

arXiv2019

New Characterizations for the Multi-output Correlation-Immune Boolean Functions

Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distribution when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting side-channel attacks (SCA). In this paper, three new methods are proposed to characterize the $t$ th-order CI multi-output Boolean functions ($n$-input and $m$-output). The first characterization is to regard the multi-output Boolean functions as the corresponding generalized Boolean functions. It is shown that a generalized Boolean functions $f_g$ is a $t$ th-order CI function if and only if the Walsh transform of $f_g$ defined here vanishes at all points with Hamming weights between $1$ and $t$. Compared to the previous Walsh transforms of component functions, our first method can reduce the computational complexity from $(2^m-1)\sum^t_{j=1}\binom{n}{j}$ to $m\sum^t_{j=1}\binom{n}{j}$. The last two methods are generalized from Fourier spectral characterizations. Especially, Fourier spectral characterizations are more efficient to characterize the symmetric multi-output CI Boolean functions.

cs.IT↗

arXiv2019

The Fourier Spectral Characterization for the Correlation-Immune Functions over Fp

The correlation-immune functions serve as an important metric for measuring resistance of a cryptosystem against correlation attacks. Existing literature emphasize on matrices, orthogonal arrays and Walsh-Hadamard spectra to characterize the correlation-immune functions over $\mathbb{F}_p$ ($p \geq 2$ is a prime). %with prime $p$. Recently, Wang and Gong investigated the Fourier spectral characterization over the complex field for correlation-immune Boolean functions. In this paper, the discrete Fourier transform (DFT) of non-binary functions was studied. It was shown that a function $f$ over $\mathbb{F}_p$ is $m$th-order correlation-immune if and only if its Fourier spectrum vanishes at a specific location under any permutation of variables. Moreover, if $f$ is a symmetric function, $f$ is correlation-immune if and only if its Fourier spectrum vanishes at only one location.

cs.IT↗