## 1 Introduction  
The IIoT, which has ubiquitous interconnection, integrated perception, intelligent optimization, and security protection, is regarded as a key technology in the era of Industry 4.0 [1]. However, it is a significant issue for industrial systems to meet the rising energy demand of IIoT applications due to the expanding number of IIoT nodes and performance requirements [2]. A vast amount of energy trading data are exposed to security threats, which could result in significant economic issues, due to the dynamic and expansive character of the IIoT system. In the traditional energy Internet, transactions are often verified, stored, and managed by a trusted center, which also records all transaction data. According to [3], this centralized operation mode has some drawbacks and can easily become the target of network attackers. In the context of the IIoT, energy trading is currently moving from a centralized to a distributed model [4]. Neither the producer nor the consumer of energy can be regarded as a trustworthy entity in the dispersed P2P trade environment [5]. Building confidence in the trading platform is therefore essential for its acceptance in the consumer sector. Decentralization, distrust, distributed sharing, and tamper-proof transaction records are all benefits of the P2P system powered by blockchain, which has been investigated and used in energy trading recently [1, 4, 5, 6, 7, 8, 9, 10]. The IIoT energy trading combined with blockchain technology mainly faces the following problems: first, some existing research schemes send all private transactions to the blockchain for execution, which greatly limits the scalability of energy trading. Second, the block will grow bigger and take longer to construct if the transaction data is entirely recorded on the blockchain. It is recommended to write the least amount of information feasible when taking into account the throughput and transaction delay of the blockchain [11]. Finally, the existing transaction models generally ignore some important practical constraints, such as privacy disclosure caused by frequent transactions [12]. The analysis of this data over time may reveal the user's trading habits and other private data. In the energy trading process, it is best to conceal or limit the transaction information. Given the above problems, this paper proposes cloud-assisted privacy protection energy trading based on IBS and homomorphic encryption in IIoT. The proposed scheme uses PCN [13] to realize off-chain transactions and cloud-assisted off-chain storage--that is, not all data are saved on the blockchain, only indexes or abstracts, and the actual data are saved by the cloud service provider (CSP). In addition, the proposed scheme combines an identity-based signature with Paillier homomorphic encryption. On the one hand, it provides pseudonyms for nodes participating in blockchain network transactions. It creates a pseudonym for each node and uses that pseudonym for transactions to maintain anonymity. On the other hand, the confidentiality of the transaction amount is realized by Paillier [14] homomorphic encryption. The contributions of this paper are as follows:  
* We propose a uniform energy trading framework built on the blockchain in light of the IIoT energy trade scenarios now in use. This design reduces duplicate data transmitted to the blockchain and increases transaction efficiency by combining PCN-based off-chain transactions and cloud-assisted off-chain storage. * Using IBS and Paillier homomorphic encryption, we propose a privacy protection mechanism and apply it to off-chain transactions on the blockchain, allowing transactions using pseudonyms to protect node identity privacy and transaction data information security. * We have carried out simulation experiments, and the experimental results prove the effectiveness and feasibility of the scheme. The rest of this paper is organized as follows.