Vision-Language Retrieval-Augmented Generation (VLRAG) systems have been widely applied to Large Vision-Language Models (LVLMs) to enhance their generation ability. However, the reliance on external multimodal knowledge databases renders VLRAG systems vulnerable to malicious poisoning attacks. In this paper, we introduce PoisonedEye, the first knowledge poisoning attack designed for VLRAG systems. Our attack successfully manipulates the response of the VLRAG system for the target query by injecting only one poison sample into the knowledge database. To construct the poison sample, we follow two key properties for the retrieval and generation process, and identify the solution by satisfying these properties. Besides, we also introduce a class query targeted poisoning attack, a more generalized strategy that extends the poisoning effect to an entire class of target queries. Extensive experiments on multiple query datasets, retrievers, and LVLMs demonstrate that our attack is highly effective in compromising VLRAG systems.

The N4 interface, which connects the Session Management Function (SMF) and the User Plane Function (UPF) via the PFCP protocol in the 5G core network, is vulnerable to attacks such as unauthorized access and signaling injection. These threats can lead to session interruptions and denial-of-service (DoS) attacks. Due to the stealthy nature of such anomalies, existing detection methods struggle with issues such as sample imbalance and ambiguous category boundaries. To address these challenges, this paper proposes a dual-stage anomaly detection framework based on the distribution characteristics of signaling. First, we statistically analyze the distributional differences between normal and abnormal PFCP signaling to uncover behavioral patterns and define precise categories of anomalies, each associated with a specific probabilistic model. Then, a Dual-Stage Abnormal Detection Framework (DSAF) is developed, integrating a KNN-based distance detector with a deep learning classifier to achieve hierarchical detection of abnormal signaling on the N4 interface. Experimental results on a real-world PFCP dataset demonstrate that the proposed method outperforms mainstream detection approaches in terms of accuracy, recall, and F1 score, providing solid theoretical and technical support for signaling security in 5G core networks.

As the brain of B5G networks, the core networks enable more ubiquitous intelligent connectivity over previous generations of mobile networks, thanks to the decentralized user plane close to edges. As mitigation against abnormal signaling attacks on edge core networks, signal protection mechanisms for the user planes at the N4 interface are widely investigated. However, the prior art fails to adequately address the distribution characteristics of abnormal signaling at this interface, where single-point defences are insufficient for the complexities of beyond 5G (B5G) distributed architecture. This article proposes a decentralized federated anomaly signaling protection framework, called B5GCASP, based on a functionally layered anomalous signaling detection model (FLAD). Mainly, B5GCASP analyses abnormal signaling distribution under the packet forwarding control protocol (PFCP) at the N4 interface, distinguishing significant and nonsignificant anomalies. Coupled with a decentralized, federated detection mechanism, B5GCASP creates a comprehensive point-and-area detection architecture. Extensive experiments on the 5GC PFCP dataset show that B5GCASP achieves higher accuracy and faster detection of abnormal signaling compared to single-point defending baselines, which offer robust anomaly signaling protection for the B5G core network.

Deep learning models have become ubiquitous in myriad application areas due to their remarkable performance. This success would not be possible without the high-quality datasets for model training that are contributed by numerous data owners. Datasets have not only become valuable assets for data owners, but also contain sensitive information that raises concerns about privacy leakage. This gives rise to urgent needs for data owners to verify that model developers have stopped using their datasets immediately upon receiving data deletion requests, as mandated by the right to be forgotten regulation. In this paper, we provide an affirmative answer by proposingDuplexGuard: a novel framework for deletion right verification via a duplex watermarking approach. During watermark injection, for each owner's dataset,DuplexGuardgenerates duplex subsets of watermarked samples, i.e., the ambush subset and the surfacing subset. This duplex design is capable of offering a combination of watermark behaviors before and after data deletion, therefore allowing it to signify all potential dataset usage statuses.DuplexGuardalso proposes a new two-way handshake protocol for issuing data deletion requests to provide more robust and decisive verification for the deletion right. Extensive experiments on multiple benchmark datasets demonstrate thatDuplexGuardis effective and reliable in verification.

Federated recommender system (RS), a prevailing distributed paradigm, has been spawning significant interest in exploiting locally stored but tremendous data to predict items best aligned with clients. However, federated RS suffers severely from a single point of failure due to the dependency on the central server, leading to potential denial of service (DoS) attacks. To address this security weakness, in this paper, we propose a decentralized privacy-preserving federated graph convolutional network for RS, dubbed DeFedGCN. Specifically, DeFedGCN aggregates local updates by a decentralized consensus-reaching process and customizes local models for personalized recommendation, where the aggregation is enhanced by local differential privacy to resist model inversion attacks. More importantly, to promote the recommendation performance, DeFedGCN conducts asub-graph expansionbased on the private set interaction to explore high-order interactions among clients and items. Theoretical analysis confirms the effectiveness and privacy guarantee of DeFedGCN. Additionally, we conduct extensive experiments on four widespread real-world databases. The recommendation performance of DeFedGCN outperforms the state-of-the-art federated RS algorithms without security protection against DoS attacks by up to 7.4%.

Federated learning (FL) is becoming a major driving force behind machine learning as a service, where customers (clients) collaboratively benefit from shared local updates under the orchestration of the service provider (server). Representing clients' current demands and the server's future demand, local model personalization and global model generalization are separately investigated, as the ill-effects of data heterogeneity enforce the community to focus on one over the other. However, these two seemingly competing goals are of equal importance rather than black and white issues, and should be achieved simultaneously. In this paper, we propose the first algorithm to balance personalization and generalization on top of game theory, dubbed PAGE, which reshapes FL as a co-opetition game between clients and the server. To explore the equilibrium, PAGE further formulates the game as Markov decision processes, and leverages the reinforcement learning algorithm, which simplifies the solving complexity. Extensive experiments on four widespread datasets show that PAGE outperforms state-of-the-art FL baselines in terms of global and local prediction accuracy simultaneously, and the accuracy can be improved by up to 35.20% and 39.91%, respectively. In addition, biased variants of PAGE imply promising adaptiveness to demand shifts in practice.

Federated learning (FL) enhanced by local differential privacy (LDP) has gained promising privacy-preserving capabilities against privacy attacks on local contributions. In this context, noise-discounting LDP methods have been widely investigated to provide better model performance and stronger privacy guarantees. However, prior art calibrate privacy guarantees by distinct LDP definitions, resulting in nonuniform privacy-preserving capabilities. In this article, aligned with the standard LDP definition, we proposed QP-LDP, a noise-discounting algorithm for FL, which can yield better model performance without any privacy loss. Specifically, QP-LDP precisely disturbs noncommon components of quantized local contributions, which are selected by an extended multiparty private set intersection process. In particular, QP-LDP can comprehensively protect two types of local contributions, i.e., local models and gradients for prevailing FedAvg and FedSGD, respectively. Through theoretical analysis, QP-LDP provides component-level indistinguishability for clients’ private local contributions and rigorous convergence guarantees for the global model. Extensive experiments on four widespread databases show that, compared to the standard LDP method, the global model prediction accuracy and convergence rate achieved by QP-LDP can be improved by up to 14.99% and 23.08%, respectively. More importantly, QP-LDP achieves the same level of privacy-preserving capabilities against privacy attacks as the standard LDP method.

Adversarial training (AT) is the most commonly used mechanism to improve the robustness of deep neural networks. Recently, a novel adversarial attack against intermediate layers exploits the extra fragility of adversarially trained networks to output incorrect predictions. The result implies the insufficiency in the searching space of the adversarial perturbation in adversarial training. To straighten out the reason for the effectiveness of the intermediate-layer attack, we interpret the forward propagation as the Clustering Effect, characterizing that the intermediate-layer representations of neural networks for samples i.i.d. to the training set with the same label are similar, and we theoretically prove the existence of Clustering Effect by corresponding Information Bottleneck Theory. We afterward observe that the intermediate-layer attack disobeys the clustering effect of the AT-trained model. Inspired by these significant observations, we propose a regularization method to extend the perturbation searching space during training, named sufficient adversarial training (SAT). We give a proven robustness bound of neural networks through rigorous mathematical proof. The experimental evaluations manifest the superiority of SAT over other state-of-the-art AT mechanisms in defending against adversarial attacks against both output and intermediate layers. Our code and Appendix can be found at https://github.com/clustering-effect/SAT.

Bent functions have flat absolute Walsh-Hadamard spectra and negabent functions have flat absolute nega-Hadamard spectra. Those properties are wide applications in cryptography for constructing cryptographically strong functions and error correcting codes for better performance. In this paper, we present a new construction of quadratic and cubic negabent functions over finite fields. Those functions can be represented as the sum of the three components: one is the trace function of the monomial term λx3or it multiplying by the trace function of x; the second, the sum of all the quadratic monomial functions except for one; and the third, the product of two linear functions where the parameter λ and variable x belong to an arbitrary binary finite field of 2nelements for n odd.

There is a significant recent interest in collaboratively training a machine learning (ML) model without collecting data to a central server. Federated learning (FL) emerges as an efficient solution mitigating systemic privacy risks and communication costs. However, conventional FL inherited from parameter server designs relies too much on a central server, which may lead to privacy risks, communication bottlenecks, or a single point of failure. In this paper, we propose an asynchronous and hierarchical local gradient aggregation and global model update algorithm, FedDual, under three different security considerations for FL in large decentralized networks. Particularly, FedDual preserves privacy by introducing local differential privacy (LDP) and aggregates local gradients asynchronously and hierarchically via a pair-wise gossip algorithm, which is more competitive than previous gossip-based decentralized FL methods in terms of privacy preservation and communication efficiency, and offers more computational efficiency compared to existing blockchain-assisted decentralized FL methods. Further, we devise a noise cutting trick based on Private Set Intersection (PSI) to mitigate the prediction performance loss of the global model caused by the leveraged LDP. Rigorous analyses show that FedDual helps decentralized FL achieve the same convergence rate of$\mathcal {O}\left({\frac {1}{T}}\right) $as centralized ML theoretically. Ingenious experiments on MNIST, CIFAR-10, and FEMNIST confirm that the model prediction performance gained from FedDual is close to centralized ML. More importantly, the proposed noise cutting trick helps FedDual to train better global models than LDP-based FL methods in terms of prediction performance and convergence rate.

In this paper, we further investigate the constructions of complementary sequence sets (CSSs) and complete complementary codes (CCCs) by Butson-type Hadamard matrices. By taking the algebraic structure of Butson-type Hadamard (BH) matrices into consideration, we obtain the explicit representation of the$\delta $-linear terms and$\delta $-quadratic terms, which are ingredients to construct CSSs and CCCs. In particular, we derive the$\delta $-quadratic terms determined by DFT matrices and BH matrices constructed from 2-level autocorrelation sequences, which yields two type of new contructions. We show that inequivalent BH matrices produce different CSSs and CCCs, which proves that our constructed CSSs and CCCs are new. As a consequence of the first type of the constructions, not only a large number of$p$-ary CSSs and CCCs of size$p$($p$prime) have been proposed, which were never reported in the literature, but also a theory linking these CSSs of$p$-ary sequences and the generalized Reed-Muller codes proposed by Kasami et al. is shown. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using$p^{n}$subcarriers. As a consequence of the second type of the constructions, we reveal an extremely fascinating hidden connection between the sequences in aperiodic CSSs and CCCs and the sequences with ideal period 2-level autocorrelation, through their trace representations and permutation polynomials over finite fields.

Federated learning (FL), an attractive and promising distributed machine learning paradigm, has sparked extensive interest in exploiting tremendous data stored on ubiquitous mobile devices. However, conventional FL suffers severely from resource heterogeneity, as clients with weak computational and communication capabilities may be unable to complete local training using the same local training hyper-parameters. In this article, we propose Dap-FL, a deep deterministic policy gradient (DDPG)-assisted adaptive FL system, in which local learning rates and local training epochs are adaptively adjusted by all resource-heterogeneous clients through locally deployed DDPG-assisted adaptive hyper-parameter selection schemes. Particularly, the rationality of the proposed hyper-parameter selection scheme is confirmed through rigorous mathematical proof. Besides, due to the thoughtlessness of security consideration of adaptive FL systems in previous studies, we introduce the Paillier cryptosystem to aggregate local models in a secure and privacy-preserving manner. Rigorous analyses show that the proposed Dap-FL system could protect clients’ private local models against chosen-plaintext attacks and chosen-message attacks in a widely used honest-but-curious participants and active adversaries security model. More importantly, through ingenious and extensive experiments, the proposed Dap-FL achieves higher model prediction accuracy than two state-of-the-art RL-assisted FL methods, i.e., 6.03% higher than DDPG-based FL and 7.85% higher than DQN-based FL. In addition, experimental results also show that the proposed Dap-FL achieves higher global model prediction accuracy and faster convergence rates than conventional FL, and the comprehensiveness of the adjusted local training hyper-parameters is validated.

The set of perfect sequences with optimal cross-correlation has applications in communication and radar systems. Many different constructions, which are called optimal sets of perfect sequences according to Sarwate bound, have been studied in the literature. However, Song et al. and Zhang et al. recently showed that the set size of these constructions can be improved, since the term related to size vanishes for perfect sequences in Sarwate bound. Until now, we don’t know whether the set size of these constructions is optimal, though they are all called optimal sets. We studied the problem of the set size of perfect sequences with optimal cross-correlation, and showed that the set size must be upper bounded by the length of the perfect sequences in this paper.

With the deployment of local differential privacy (LDP), federated learning (FL) has gained stronger privacy-preserving capability against inference-type attacks. However, existing LDP methods reduce global model performance. In this paper, we propose a QP-LDP algorithm for FL to obtain a better-performed global model without losing privacy guarantees defined by the original LDP. Different from previous LDP methods for FL, QP-LDP improves the global model performance by precisely disturbing the non-common components of quantized local contributions. In addition, QP-LDP comprehensively protects two types of local contributions. Through security analysis, QP-LDP provides the probability indistinguishability of clients' private local contributions at a component-level. More importantly, ingenious experiments show that with the deployment of QP-LDP, the global model outperforms that in the original LDP-based FL in terms of prediction accuracy and convergence rate.

Federated learning (FL) combined with local differential privacy (LDP) has attracted considerable attention due to its privacy-preserving capability against inference-type attacks, e.g., model inversion attacks and membership inference attacks. However, the noise introduced by LDP reduces the global model performance, while decreasing the noise by setting a larger privacy budget sacrifices the privacy guarantees. In this paper, we propose a layer-wise LDP for the FL system, dubbed LLDP, which disturbs various layers of a local model according to clients’ self-assigned privacy budgets. With the deployment of LLDP, clients could train a highly accurate and rapid-converged global model without loosing privacy guarantees. Through extensive security analyses, the proposed LLDP scheme helps the entire local model achieve (ε,δ)-LDP, and the probability indistinguishability of the local model is achieved under the widespread semi-honest threat model. Ingenious experiments show that LLDP improves the global model prediction and convergence rate by 3.38% and 4.76% on the CIFAR-10 dataset compared to the state-of-the-art LDP method with the same privacy budget. In addition, given the same training target (loss value), LLDP requires a 26.67% lower privacy budget, providing stronger privacy guarantees against model inversion attacks.

As a smart transportation application of the Internet of Things, the Internet of Vehicles (IoV) depresses the chances of traffic accidents, while improving transportation efficiency and user driving experience. However, as the number of vehicles continues to grow, the original ground-based IoV system is difficult to meet the ever-increasing demand. To this end, space–air–ground-integrated network (SAGIN) incorporates satellite systems, aerial network and terrestrial communications. However, because SAGIN integrates multiple network services and communication modes, which makes SAGIN more vulnerable to various types of attacks and security threats. This article first presents the dominating security threats in data storage, transmission and sharing of space–air–ground integrated vehicular network (SAGIVN). Moreover, for guaranteeing the safety and effectiveness of the model, we advance a safe and effective encrypted data retrieval and sharing scheme in SAGIVN (ERDSS) for possible threats, the ERDSS can execute fuzzy retrieval over misspelling keywords and sort results by relevance scores to realize precise retrieval. We perform a comprehensive security discussion and execute experiments based on real-world data sets. The consequences demonstrate that the ERDSS is safe and efficient.

Research on mobile cyber–physical systems (MCPSs) that have the superiorities of cyber–physical systems (CPSs) and expand their application range has become a trend in recent years. The applications of MCPS in fields, such as intelligent transportation systems, smart home appliances, and mobile education, have also become increasingly mature. However, MCPS also has some shortcomings that need to be solved urgently. Sensors carried on mobile devices collect data and upload huge amounts of data to the cloud for statistics and analysis. Mobile devices need to directly interact with the cloud, causing both parties to bear huge computing and communication costs. Since the interaction process includes data sharing and storage, it is particularly important to protect the data itself and the security of sharing. Searchable encryption ensures the safety of communication among the MPEs and the cloud, while protecting the privacy of data on the cloud. However, the existing searchable encryption technology cannot provide efficient and reliable data storage and sharing services for MPEs in MCPS under the premise of ensuring security. In this article, we present a secure and efficient data sharing and privacy protection scheme in MCPS on the basis of the edge computing model (NESPS). Meanwhile, the introduction of edge computing (EC) significantly reduces the communication consumption between the device and the cloud. Furthermore, attribute-based encryption (ABE) enables the NESPS to achieve fine-grained management of device authorities. Moreover, we have carried out security analysis and simulation on the NESPS, the results demonstrate that the NESPS meets the proposed requirements.

The researches of Golay complementary sequences (GCSs) over 16 and 64 quadrature amplitude modulation (QAM) from 2001 to 2008 were generalized to$4^{q} $-QAM GCSs of length$2^{m}$by Li (the generalized cases I-III for$q\ge 2$) in 2010 and Liu et al. (the generalized cases IV-V for$q\ge 3$) in 2013. Those sequences are presented by the combination of the quaternary standard GCSs and compatible offsets. By providing new compatible offsets based on the factorization of the integer$q$, we propose two new constructions of$4^{q} $-QAM GCSs, which have the generalized cases I-V as special cases. The numbers of the proposed GCSs are equal to the product of the number of the quaternary standard GCSs and the number of the compatible offsets. Denote the number of prime factors of$q$counted with multiplicity by$\Omega (q)$. The number of new offsets in our first construction is lower bounded by a polynomial of$m$with degree$\Omega (q)$, while the numbers of offsets in the generalized cases I-III and IV-V are a linear polynomial and a quadratic polynomial of$m$, respectively. If$q$has a prime factor larger than 2, the number of new offsets in our second construction is lower bounded by a polynomial of$m$with degree$\Omega (q)+1$. As an example, the new offsets in our two constructions for$q=6$, whose number is bounded by a cubic polynomial, is also given. The proof in this paper implies that all the mentioned GCSs over QAM can be regarded as projections of Golay complementary arrays of size$2\times 2\times \cdots \times 2$.

Many artificial intelligence technologies have been applied for extracting useful information from massive industrial big data. However, the privacy issues are usually overlooked in many existing methods. In this article, we propose an anonymous and privacy-preserving federated learning scheme for the mining of industrial big data. We explored the effect of the proportion of shared parameters on the accuracy through experiments, and found that sharing partial parameters can almost achieve the accuracy of sharing all the parameters. On this basis, our proposed federated learning scheme reduces the privacy leakage by sharing fewer parameters between the server and each participant. Specifically, we leverage differential privacy on shared parameters with Gaussian mechanism to provide strict privacy preservation; the effect of different ε and δ on accuracy is tested; and we keep track of δ-when it reaches a certain threshold, training shall be stopped. What's more, we employ a proxy server as the middle layer between the server and all the participants to achieve anonymity of participants; it is worth noting that this can also reduce the communication burden on the federated learning server. Finally, we provide the security analysis and performance evaluations by comparing with other schemes.

A new method to construct q-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size N is proposed by using desired para-unitary (PU) matrices.The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given.A general form of these functions only depends on a basis of the functions from ZN to Zq and representatives in the equivalent class of Butson-type Hadamard (BH) matrices.Especially, the realization of Golay pairs from the our general form exactly coincides with the standard Golay pairs.The realization of ternary complementary sequences of size 3 is first reported here.For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before.Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly.From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the Walsh matrices of order 2.This suggests that the proposed method with the BH matrices of higher orders will yield a large number of new CSSs and CCCs with the exponentially increasing number of the sequences of low peak-to-mean envelope power ratio.

Anomaly detection is a typical method to find abnormal behaviors in smart grid, where the data may contain both categorical and numerical attributes with distinct significance. The k-prototypes algorithm is one of the most common algorithms for clustering mixed categorical and numerical data, however, it does not consider the significance of different attributes towards the clustering process. In this paper, we propose a weight based k-prototypes algorithm for anomaly detection in smart grid. Specifically, we first introduce an improved cost function to measure the categorical and numerical attributes uniformly and assign the weight to each attribute. We also propose two entropy metrics to calculate weight values and embed them into the k-prototypes algorithm for mixed data clustering in smart grid. Finally, we compare our proposed algorithm with existing clustering algorithms and the experimental results show that our algorithm is effective for anomaly detection in smart grid.

The previous constructions of quadrature amplitude modulation (QAM) Golay complementary sequences (GCSs) were generalized as 4q-QAM GCSs of length 2mby Li (the generalized cases I-III for q ≥ 2) in 2010 and Liu (the generalized cases IV-V for q ≥ 3) in 2013 respectively. Those sequences are given by the weighted sum of q quaternary standard GCSs, which is represented as q-dimensional vectorial generalized Boolean functions (V-GBFs). In this paper, we present a new construction for 4q-QAM GCSs of length 2m. The new construction includes the generalized cases I-III as special cases. If q is a composite number, a great number of new GCSs other than the sequences in the generalized cases I-V will arise. For the cases q = 4 and q = 6, we show that the ratios of the number of new GCSs and the generalized cases I-V are greater than seven and six respectively if m is large enough.

Face authentication is vulnerable to media-based virtual face forgery (MVFF) where adversaries display photos/videos or 3D virtual face models of victims to spoof face authentication systems. In this paper, we propose a liveness detection mechanism, called FaceCloseup, to protect the face authentication on mobile devices. FaceCloseup detects MVFF-based attacks by analyzing the distortion of face regions in a user's closeup facial videos captured by built-in camera on mobile device. It can detect MVFF-based attacks with an accuracy of 99.48%.

Complementary sequence sets (CSSs) and complete complementary codes (CCCs) have many applications in science and engineering, especially in wireless communications. A construction of CSS and CCC, having size M = 2mand length MK, where m and K are positive integers, is presented. The proposed construction is a generalized paraunitary (PU) algorithm that greatly increases the number of permutations from K! to (mK)! compared to those of previous PU constructions. Moreover, this new construction can be generalized to the case M = pm, where p is a positive integer. The increase in the number of permutations means that a wide range of CCCs and CSSs can be obtained.

In this paper, the discrete Fourier transform (DFT) of Boolean functions over the complex field is introduced and the locations of zero-valued Fourier spectrum are studied. Then a Fourier spectral characterization of correlation immune and resilient Boolean functions is investigated. It is shown that a Boolean function f is mth-order correlation immune if and only if the Fourier spectrum of f under any permutation of variables (or the equivalence class of f defined by Golomb in 1959) vanishes at a specified location. This is an analog of using Walsh-Hadamard spectra to characterize correlation immunity of the Boolean functions. In particular, if f is a symmetric function, f is correlation immune if and only if its Fourier spectrum vanishes at a specified location. Similarly, zero-valued Fourier spectrum can also be used to characterize resilient functions. The application of the Fourier spectral analysis on studying the peak-to-mean envelope power ratio of the sequences is also addressed.

In this paper, some questions on the distribution of the peak-to-mean envelope power ratio (PMEPR) of standard binary Golay sequences are solved. For n odd, we prove that the PMEPR of each standard binary Golay sequence of length 2nis exactly 2, and determine the location(s), where peaks occur for each sequence. For n even, we prove that the envelope power of such sequences can never reach 2n+1at time points t ∈ {(v/2u)|0 ≤ v ≤ 2u, v,u ∈ N}. We further identify eight sequences of length 24and eight sequences of length 26that have PMEPR exactly 2, and raise the question whether, asymptotically, it is possible for standard binary Golay sequences to have PMEPR less than 2 - ϵ, where, ϵ > 0.

In this paper, the sequence families of which maximum correlation is determined by the Weil bound of exponential sums are revisited. Using the same approach, two new constructions with large family sizes and low maximum correlation are given. The first construction is an analog of one recent result derived from the interleaved structure of Sidel'nikov sequences. For a primepand an integerM|(p-1), the newM-ary sequence families of periodpare obtained from irreducible quadratic polynomials and known power residue-based sequence families. The new sequence families increase family sizes of the known power residue-based sequence families, but keep the maximum correlation unchanged. In the second construction, the sequences derived from the Weil representation are generalized, where each new sequence is the elementwise product of a modulated Sidel'nikov sequence and a modulated trace sequence. For positive integersdpandM|(pn-1), the new family consists of (M-1)pndsequences with periodpn-1, alphabet sizeMp, and the maximum correlation bounded by (d+1)√{pn}+3.

A new elementary expression of the construction first proposed by Gurevich, Hadani, and Sochen is given, which avoids the explicit use of the Weil representation. The sequences in this signal set are given by both multiplicative character and additive character of finite field$\BBF_{p}$. Such a signal set consists of$p^{2}(p-2)$time-shift distinct sequences, the magnitude of the two-dimensional autocorrelation function (i.e., the ambiguity function) in both time and phase of each sequence is upper bounded by$2\sqrt {p}$at any shift not equal to (0, 0). Furthermore, the magnitude of their Fourier transform spectrum is less than or equal to 2. For a subset consisting of$p(p-2)$phase-shift distinct sequences in this signal set, the magnitude of the ambiguity function of any pair is upper bounded by$4\sqrt {p}$. A proof is given through finding a new expression of the sequences in the finite harmonic oscillator system. An open problem for directly establishing these assertions without involving the Weil representation is addressed.