arXiv subjects
Publications and source records attributed to Tongjiang Yan.
This paper contributes to compute 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences. Results show that 2-adic complexity of these sequences is good enough to resist the attack by the rational approximation algorithm.
Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on interleaving technique and Ding-Helleseth-Lam sequences (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-017-0398-5). And its linear complexity has been proved to be large enough to resist the B-M Algorighm (BMA) by Fan (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-018-0456-7). In this paper, we study the 2-adic complexity of this class of binary sequences. Our result shows that the 2-adic complexity of this class of sequence is no less than one half of its period, i.e., its 2-adic complexity is large enough to resist the Rational Aproximation Algorithm (RAA).
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of period $4N$ with optimal autocorrelation values have been constructed by Tang and Gong based on interleaving certain kinds of sequences of period $N$. In this paper, we use the interleaving technique to construct a binary sequence with the optimal autocorrelation of period $2N$, then we calculate its autocorrelation values and its distribution, and give a lower bound of linear complexity. Results show that these sequences have low autocorrelation and the linear complexity satisfies the requirements of cryptography.
Let $p,q$ be distinct primes satisfying $\mathrm{gcd}(p-1,q-1)=d$ and let $D_i$, $i=0,1,\cdots,d-1$, be Whiteman's generalized cyclotomic classes with $Z_{pq}^{\ast}=\cup_{i=0}^{d-1}D_i$. In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets $D_0^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i}$ and $D_1^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i+1}$. As an application, we determine a lower bound on the 2-adic complexity of modified Jacobi sequence. Our result shows that the 2-adic complexity of modified Jacobi sequence is at least $pq-p-q-1$ with period $N=pq$. This indicates that the 2-adic complexity of modified Jacobi sequence is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).
Compared with the perfect complementary sequence sets, quasi-complementary sequence sets (QCSSs) can support more users to work in multicarrier CDMA communications. A near-optimal periodic QCSS is constructed in this paper by using an optimal quaternary sequence set and an almost difference set. With the change of the values of parameters in the almost difference set, the near-optimal QCSS can become asymptotically optimal and the number of users supported by the subcarrier channels in CDMA system has an exponential growth.
Let $p$ be an odd prime, $n$ a positive integer and $g$ a primitive root of $p^n$. Suppose $D_i^{(p^n)}=\{g^{2s+i}|s=0,1,2,\cdots,\frac{(p-1)p^{n-1}}{2}\}$, $i=0,1$, is the generalized cyclotomic classes with $Z_{p^n}^{\ast}=D_0\cup D_1$. In this paper, we prove that Gauss periods based on $D_0$ and $D_1$ are both equal to 0 for $n\geq2$. As an application, we determine a lower bound on the 2-adic complexity of a class of Ding-Helleseth generalized cyclotomic sequences of period $p^n$. The result shows that the 2-adic complexity is at least $p^n-p^{n-1}-1$, which is larger than $\frac{N+1}{2}$, where $N=p^n$ is the period of the sequence.
Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been applied in stream cipher. In general, it is difficult to give both the linear complexity and 2-adic complexity of a periodic binary sequence. Cai and Ding \cite{Cai Ying} gave a class of sequences with almost optimal autocorrelation by constructing almost difference sets. Wang \cite{Wang Qi} proved that one type of those sequences by Cai and Ding has large linear complexity. Sun et al. \cite{Sun Yuhua} showed that another type of sequences by Cai and Ding has also large linear complexity. Additionally, Sun et al. also generalized the construction by Cai and Ding using $d$-form function with difference-balanced property. In this paper, we first give the detailed autocorrelation distribution of the sequences was generalized from Cai and Ding \cite{Cai Ying} by Sun et al. \cite{Sun Yuhua}. Then, inspired by the method of Hu \cite{Hu Honggang}, we analyse their 2-adic complexity and give a lower bound on the 2-adic complexity of these sequences. Our result show that the 2-adic complexity of these sequences is at least $N-\mathrm{log}_2\sqrt{N+1}$ and that it reach $N-1$ in many cases, which are large enough to resist the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).
Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular,Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences of order 2. In this paper, we consider the generalized sequences of order 4. Under certain conditions, the linear complexity of these sequences of order 4 is developed over a finite field F_l. Results show that in many cases they have high linear complexity.
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight distribution is determined. Results show that they are at most 4-weight linear codes. Additionally, these codes can be used in secret sharing schemes.
Cyclic codes have wide applications in data storage systems and communication systems. Employing two-prime Whiteman generalized cyclotomic sequences of order 6, we construct several classes of cyclic codes over the finite field GF}(q) and give their generator polynomials. And we also calculate the minimum distance of some cyclic codes and give lower bounds of the minimum distance for some other cyclic codes.
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low autocorrelations are presented.
A general construction of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic and this construction, several classes of binary sequences with optimal autocorrelation and other low autocorrelation are presented.
This paper gives the linear complexity of binary Ding-Helleseth generalized cyclotomic sequences of any order.
For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{(p^{m}-1)^{2}}{2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of period $p^{n}-1$ and its decimated sequence by the above $d$ is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by $4\sqrt{p^{n}}-1$.