## 2 Related Works
### Leakage Resilience of IBE  
According to the ability of side-channel attacks, the leakage-resilient model is divided into the bounded-leakage case and continuous-leakage case. As for the bounded leakage case [30], the leakage amount of the secret information of the system cannot exceed a given limit. As for the continuous-leakage case [31], its private key is usually updated, and the life cycle of the cryptographic mechanism is divided into multiple time cycles by performing corresponding operations (such as key update). In each time cycle, the adversary can obtain some related context for one private key and the exposed amount for this same secret value cannot exceed the leakage parameters set by the system, but the entire execution process can have an unlimited amount of leakage. The continuous-leakage model is closer to the application requirements of the real environment. Cryptographic researchers have done some research on the leakage resilience of some cryptosystems such as the PKE cryptosystem [32], identity-based cryptographic mechanism [33; 34; 35], attribute-based cryptographic mechanism [36; 37], key exchange protocol [38], and signature [39]. Research on leakage resilience of cryptographic mechanisms is a hot topic in cryptography research. At present, leakage-resilient achievements mainly occur in identity-based cryptosystems. The work [40] proposed the first identity-based encryption (IBE) construction with leakage resilience and provided the security proof without a random oracle. [PERSON]. [41] proposed an IB-HPS and provided an encryption scheme against bounded-leakage attacks under IB-HPS. [PERSON] et al. [42] designed an IBE against bounded-leak attacks. [PERSON] et al. applied hash proof technology to a variant scheme of [PERSON]'s IBE with CCA security and constructed a new and effective leakage-resilient IBE. The reference [43] put forward a leakage-resilient IBE by using the global hash structure. Their construction was implemented through the deterministic linear Diffie-Hellman assumption under the relative-leakage model using a random oracle. The reference [44] provided an IBE with leakage resilience with leakage parameters that were not limited by the length of the message to be encrypted. [PERSON] et al. [45] provided several specific examples of IB-HPS. The paper [46] pointed out that the IBE against continuous side-channel attacks had stronger practicability. In the continual-leakage-resilient circumstances, the system refreshed the private key and erased the old key periodically. In this process, the public key was unchanged. The leakage of this model only existed between key refreshes. Specifically, the leakage between two consecutive refreshes was limited, but the overall amount of leakage was unlimited. In the case that the hardware did not leak information and in the continuous-leakage model, [PERSON] et al. [47] proposed an IBE against continual-leakage attacks without a random oracle. [PERSON] et al. [48] provided a secure big data storage system that was able to resist continuous key leakage. The paper [49] pointed out that blockchain technology could be used to solve the problem of data-tampering prevention in a decentralized environment. The paper [50] provided a comprehensive review of the latest research progress on resilient and dependable management approaches. They provided seven classifications, systematically analyzed the advantages and disadvantages of the schemes, and pointed out the schemes that could be further studied. Because the leakage circumstances for different application environments are different, the actual application requirements of different environments in reality cannot be met with a constant leakage boundary. To dynamically set the leakage boundary of an IBE mechanism according to the requirements of the application environment, the authors of [51] designed a leakage-resilient IBE mechanism with flexible changes in the leakage boundary.