Binary sequences with low autocorrelation have important applications in communication systems and cryptography. In this paper, the autocorrelation values of binary Whiteman generalized cyclotomic sequences of order six and period pq are discussed. Our result shows that the autocorrelation of these sequences is four-valued and that the corresponding values are in {-1,3,-5,pq} if the parameters are chosen carefully.

In this letter, we present an improved method for the independence test procedure in the convolutional multicast algorithm proposed by Erez and Feder. We employ the linear independence test vectors to check the independence of the partial encoding vectors in the main program of Erez's convolutional multicast algorithm. It turns out that compared with the previous approach of computing the determinants of the correlative matrices, carrying out the independence test vectors can reduce the computational complexity.

In this paper, we consider the crosscorrelation of two interleaved sequences of period 4N constructed by Gong and Tang which has been proved to possess optimal autocorrelation. Results show that the interleaved sequences achieve the largest crosscorrelation value 4.

In this letter, we first introduce a new generalized cyclotomic sequence of order two of length pq, then we calculate its linear complexity and minimal polynomial. Our results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for use in stream cipher cryptosystems.

In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

Pseudorandom sequences with low autocorrelation magnitude play important roles in various environments. Let N be a prime with N=Mf+1, where M and f are positive integers. A new method to construct M-sequences of period 4N is given. We show that these new sequences have low autocorrelation magnitude.

Binary sequences with high linear complexity and high 2-adic complexity have important applications in communication and cryptography. In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences which have high linear complexity is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, the result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

Based on a unified representation of generalized cyclotomic classes, every generalized cyclotomic sequence of order d over $Z_{p_{1}^{e_{1}}p_{2}^{e_{2}}cdots p_{r}^{e_{r}}}$ is shown to be a sum of d-residue sequences over $Z_{p_{s}^{e_{s}}}$ for $sin {1,2,cdots,r }$. For d=2, by the multi-rate approach, several generalized cyclotomic sequences are explicitly expressed by Legendre sequences, and their linear complexity properties are analyzed.

This paper contributes to a new generalized cyclotomic sequences of order two with respect to p1e1p2e2… ptet. The emphasis is on the linear complexity and autocorrelation of new prime-square sequences and two-prime sequences, two special cases of these generalized cyclotomic sequences. Our method is based on their characteristic polynomials. Results show that these sequences possess good linear complexity. Under certain conditions, the autocorrelation functions of new prime-square sequences and two-prime sequences may be three-valued.

Radio Frequency Identification (RFID) plays a crucial role in IoT development. With the extensive use of RFID, the fact that a single RFID tag integrates multiple applications has become a mainstream. To facilitate users to use the multi-application RFID tag and revoke some applications in the tag securely and efficiently, a secure RFID application revocation scheme is proposed in this paper. In the scheme, each response for the challenge between tag and reader is different, and a group has the feature of many tags. Even if the group index number and corresponding group are revealed, a specific tag does not be precisely found and tracked. Users are anonymous completely. The scheme also allows users to set the validity period for an application or some applications. If the application contains the validity period and expires, the server will remove the validity period and revoke the application automatically in the tag when the RFID tag accesses server again. The proposed scheme cannot only be used in multi-application RFID tag but also be used in one-application RFID tag. Furthermore, compared with other existing schemes, the scheme provides a higher level of security and has an advantage of performance. Our scheme has the ability of mutual authentication and Anti-replay by adding a random number r2, and it is easy to against synchronization attack. Security proof is given in our paper and performance advantage are mainly reflected in the following points such as forward security, synchronization, storage complexity, computational complexity, etc. Finally, the proposed scheme can be used in multi-application RFID tag to promote the development of the IoT.

This paper contributes to k-error linear complexity of some generalized cyclotomic binary sequences of length 2pm and pm constructed in recent years. By defining related reference sequences, we find that these sequences possess very low k-error linear complexity for some certain values of the parameter k even though they have high linear complexity. Moreover, we point out that (p-1)-tuple distributions of all these sequences are not span. Thus they should be selected carefully for use in stream cipher systems.

The linear complexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linear complexity properly. Recently, Zhou designed an algorithm for computing the k-error linear complexity of 2pn periodic sequences over GF(q). In this paper, we develop a genetic algorithm to confirm that one can't get the real k-error linear complexity for some sequenes by the Zhou's algorithm. Analysis indicates that the Zhou's algorithm is unreasonable in some steps. The corrected algorithm is presented. Such algorithm will increase the amount of computation, but is necessary to get the real k-error linear complexity. Here p and q are odd prime, and q is a primitive root (mod p2).

In this paper, we modify the Legendre-Sidelnikov sequence which was defined by M. Su and A. Winterhof and consider its exact autocorrelation values. This new sequence is balanced for any p,q and proved to possess low autocorrelation values in most cases.

In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for cryptographic applications.

This correspondence contributes to some d-form functions and d-form sequences. A property of d-form functions is obtained firstly. Then we present a way to construct d-form sequences and extended d-form sequences with ideal autocorrelation. Based on our result, many sequences with ideal autocorrelation can be constructed by the corresponding difference-balanced d-form functions.

Binary sequences with good autocorrelation and large linear complexity have found many applications in communication systems. A construction of almost difference sets was given by Cai and Ding in 2009. Many classes of binary sequences with three-level autocorrelation could be obtained by this construction and the linear complexity of two classes of binary sequences from the construction have been determined by Wang in 2010. Inspired by the analysis of Wang, we deternime the linear complexity and the minimal polynomials of another class of binary sequences, i.e., the class based on the WG difference set, from the construction by Cai and Ding. Furthermore, a generalized version of the construction by Cai and Ding is also presented.

The concept of witness hiding was proposed by Feige and Shamir as a natural relaxation of zero-knowledge. Prior constructions of witness hiding protocol for general hard distribution on NP language consist of at least three rounds. In this paper we construct a two-round witness hiding protocol for all hard distributions on NP language. Our construction is based on two primitives: point obfuscation and adaptive witness encryption scheme.