To tackle the problems of questioning the authenticity of products faced in e-commerce live streaming and the low data integrity in the process of product transactions, the concept of traceability and a product authentication scheme that integrates blockchain technology and traceability are proposed. The proposed scheme deploys the product authentication strategy on the Ethereum blockchain in the form of a smart contract and calls the product authentication method on the traceability body by executing the smart contract to realize the authentication of product quality. A combination of on-chain and off-chain is used to store private information to guarantee information integrity. Security analysis results show that the proposed scheme can make the risk of information leakage lower and data security higher under the premise of achieving product certification. A system simulation experiment shows that the solution can meet product certification requirements and have a favorable impact on the live commerce industry.

This paper studies the leaderless consensus of the stochastic multi-agent systems based on partial differential equations–ordinary differential equations (PDE-ODEs). Compared with the traditional state coupling, the most significant difference between this paper is that the space state coupling is designed. Two boundary couplings are investigated in this article, respectively, collocated boundary measurement and distributed boundary measurement. Using the Lyapunov directed method, sufficient conditions for the stochastic multi-agent system to achieve consensus can be obtained. Finally, two simulation examples show the feasibility of the proposed spatial boundary couplings.

On the Existence of Multiple RSA Private Keys: It is known that, given an RSA modulus, , the public key and the corresponding private key satisfy the modulo congruence , where . Usually, the private key can be computed efficiently using the extended Euclidean algorithm, and it is common knowledge that the private key is unique in the sense of modular . This paper shows that there exist multiple private keys ; they all satisfy that . This paper also presents the exact relationship between an RSA public key and a corresponding private key.

To address the problem that the traditional access-control model is no longer suitable for access control and authorization in the super business system—which has the characteristics of many businesses and complex permissions—a business entity-based access-control model (BE-BAC) is proposed in this paper. The BE-BAC model realizes the relationship between users, business entities, and business permissions. Firstly, according to the characteristics of the super business system, the concept of business entity is put forward, introducing the composition and relationship of the business entity. Secondly, the business entity is introduced into the access-control model, formally describing the basic relationship, constraint, mapping, and authorization strategy of the BE-BAC model. Finally, the access-control workflow, based on the business entity, is designed, and the security analysis and comprehensive comparison of the model are carried out. Compared with the existing access-control model, the BE-BAC model has higher security and flexibility, and better protects resources, through more secure access-request decisions.