In this paper, the linear complexity and minimal polynomials of Legendre sequences over Fq have been calculated, where q = pm and p is a prime number. Our results show that Legendre sequences have high linear complexity over Fq for a large part of prime power number q so that they can resist the linear attack method.

We regard a De Bruijn sequence of order n as a bijection on $mathbb{F}_2^n$ and consider the transition mappings between them. It is shown that there are only two conjugate transformations that always transfer De Bruijn sequences to De Bruijn sequences.

In recent years, Graph Neural Networks has received enormous attention from academia for its huge potential of modeling the network traits such as macrostructure and single node attributes. However, prior mainstream works mainly focus on homogeneous network and lack the capacity to characterize the network heterogeneous property. Besides, most previous literature cannot the model latent influence link under microscope vision, making it infeasible to model the joint relation between the heterogeneity and mutual interaction within multiple relation type. In this letter, we propose a latent influence based self-attention framework to address the difficulties mentioned above. To model the heterogeneity and mutual interactions, we redesign the attention mechanism with latent influence factor on single-type relation level, which learns the importance coefficient from its adjacent neighbors under the same meta-path based patterns. To incorporate the heterogeneous meta-path in a unified dimension, we developed a novel self-attention based framework for meta-path relation fusion according to the learned meta-path coefficient. Our experimental results demonstrate that our framework not only achieves higher results than current state-of-the-art baselines, but also shows promising vision on depicting heterogeneous interactive relations under complicated network structure.

In this paper, we first propose a notion of multiple authorities attribute-based designated confirmer signature scheme with unified verification. In a multiple authorities attribute-based designated confirmer signature scheme with unified verification, both the signer and the designated confirmer can run the same protocols to confirm a valid signature or disavow an invalid signature. Then, we construct a multiple authorities attribute-based designated confirmer signature scheme with unified verification. Finally, we prove the correctness and security of the proposed scheme.

In this paper, new classes of binary generalized cyclotomic sequences of period 2pm+1qn+1 are constructed. These sequences are balanced. We calculate the linear complexity of the constructed sequences with a simple method. The results show that the linear complexity of such sequences attains the maximum.

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.

Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.

Periodic sequences, used as keys in cryptosystems, plays an important role in cryptography. Such periodic sequences should possess high linear complexity to resist B-M algorithm. Sequences constructed by cyclotomic cosets have been widely studied in the past few years. In this paper, the linear complexity of n-periodic cyclotomic sequences of order 2 and 4 over 𝔽p has been calculated, where n and p are two distinct odd primes. The conclusions reveal that the presented sequences have high linear complexity in many cases, which indicates that the sequences can resist the linear attack.

Jacobi sequences have good cryptography properties. Li et al. [X. Li et al., Linear Complexity of a New Generalized Cyclotomic Sequence of Order Two of Length pq*, IEICE Trans. Fundamentals, vol.E96-A, no.5, pp.1001-1005, 2013] defined a new modified Jacobi sequence of order two and got its linear complexity. In this corresponding, we determine the linear complexity and minimal polynomials of the new modified Jacobi sequence of order d. Our results show that the sequence is good from the viewpoint of linear complexity.

Permutation polynomials over Zpn are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Zpn to be permutations, and this equivalent condition can help us to analysis the randomness of such functions. Our results provide a method to distinguish permutation polynomials from random functions. We also introduce how to improve the randomness of permutation polynomials over Zpn.