Attribute-based encryption (ABE) mechanism on lattices can against quantum attack and guarantees fine-grained access control of encrypted data, and it has been widely used in cloud computing and privacy protection. However, the high complexity of the trapdoor generation and delegation and preimage sampling are the main barriers for the development of ABE schemes in a post-quantum world. Thus, we proposed a security and efficient multi-authority ABE scheme from lattices in this paper. The scheme is based on the theory of MP12 and is proved to be secure under the standard model. In this scheme, we construct an optimized sampling algorithm to generate a $\mathbb {Z}_{q}$ -invertible matrix with a lower runtime. Based on it, combining the trapdoor generation and delegation algorithm in MP12, we designed multiple attribute authorities which can manage different attribute sets and generate private keys for the user independently. In addition, the Shamir’s secret sharing technique is introduced to support policies expressed in any monotone access structures. Compared with the existing related schemes, the proposed scheme can improve the functional agility and the flexibility of the access policy prominently, and it also can achieve a better performance with less lattice dimension, trapdoor storage occupation, and ciphertext expansion rate. The analysis shows that our scheme is feasible and superior in the large-scale distributed environment.

The public key encryption with equality test (PKEET) allows the cloud server to judge whether two different ciphertexts are generated by the same message without decryption. Through this technique, PKEET provides an effective solution for building secure outsourced databases, and has made some rich achievements. This paper combines multivariate public key encryption and equality test, and proposes the first multivariate public key encryption scheme with equality test (MPKEET), which inherits the advantages of both primitives. Moreover, the equality test algorithm proposed in this paper is based on a straight line. Compared with the schemes based on bilinear pairing, it is simpler and easier to implement. And our MPKEET scheme achieves desirable security, which can resist linearization equation attacks, differential attacks, XL attacks, Gröbner basis attacks and the attack of quantum computer, when appropriate parameters are selected.

Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users’ public keys by using users’ identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user’s identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into $l^{\prime }$ segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when $l^{\prime }$ is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.

Software-Defined Networking (SDN), as a new network architecture, has brought convenience, but also suffered from the threat of Distributed Denial of Service (DDoS) attack. However, most existing DDoS attack detection schemes for SDN employ only a single detection method, leading to imbalances in detection speed, system overhead, and detection accuracy. Even though a few schemes improve detection efficiency and accuracy through two-stage detection, they still suffer from low system flexibility and do not support dynamic threshold adjustment. In order to resolve these issues, we propose an adaptive two-stage DDoS attack detection scheme with Dynamic Threshold Adjustment (ATS-DTA for short), which contains three sub-modules. More specifically, by dividing DDoS attack detection into two modules: a conditional entropy-based network traffic anomaly detection phase and a DDoS attack detection phase based on machine learning methods. Additionally, an adaptive threshold adjustment module is introduced to improve the system’s flexibility. Finally, the experimental results show that our scheme, compared to related schemes, not only significantly improves detection accuracy and speed but also supports flexible and dynamic threshold adjustment. Specifically, our method achieves an average accuracy improvement of 1.91% and a precision increase of 1.23% over baseline methods, underscoring its effectiveness in adapting to complex and evolving network environments. These advantages illustrate that our ATS-DTA scheme provides a more balanced, efficient, and reliable solution for DDoS detection in dynamic network scenarios.

Attribute-based encryption (ABE) is a good choice for one-to-many communication and fine-grained access control of the encryption data in a cloud environment. Fully homomorphic encryption (FHE) allows cloud servers to make valid operations on encrypted data without decrypting. Attribute-based fully homomorphic encryption (ABFHE) from lattices not only combines the bilateral advantages/facilities of ABE and FHE but also can resist quantum attacks. However, in the most previous ABFHE schemes, the growth of ciphertext size usually depends on the total number of system’s attributes which leads to high communication overhead and long running time of encryption and decryption. In this paper, based on the LWE problem on lattices, we propose an attribute-based fully homomorphic scheme with short ciphertext. More specifically, by classifying the system’s attributes and using the special structure matrix in MP12, we remove the dependency of ciphertext size on system’s attributes and the ciphertext size is no longer increased with the total number of system’s attributes. In addition, by introducing the function in the homomorphic operations, we completely rerandomize the error term in the new ciphertext and have a very tight and simple error analysis using sub-Gaussianity. Besides, performance analysis shows that when and according to the parameter suggestion given by Micciancio and Dai et al., the size of ciphertext in our scheme is reduced by at least 73.3%, not to mention . The larger the , the more observable of our scheme. The short ciphertext in our construction can not only reduce the communication overhead but also reduce the running time of encryption and decryption. Finally, our scheme is proved to be secure in the standard model.