## 2 Related Works
### Our Motivations and Contributions  
[PERSON] et al. [52] designed a novel leakage-resilient hierarchical IBE mechanism to provide anonymity protection for recipients. [PERSON] et al. [53] constructed a hierarchical IBE with anonymity against leakage attacks and provided the application scenario of the scheme. The work [54] proposed an anonymous IBE using a dual-system technique. Their construction was implemented with the aid of the composite order bilinear group and was secure in the fully adaptive identity model. [PERSON] et al. [55] designed a completely secure leakage-resilient IBE mechanism with a wildcard key derivation function. Because no anonymous IBBE against leakage attacks had been put forward, this paper constructed an anonymous IBBE scheme against side-channel attacks. A secret sharing scheme proposed by [PERSON] et al. [56] could resist persistent side-channel attacks and mainly benefited from the state partitioning technology. Since then, state partitioning technology has been widely used to construct some cryptographic systems with special performance. [PERSON] et al. [57] ensured the security of their scheme for simultaneous continuous state partition exposure and tampering attacks with the help of general reference strings, nonextensible code, and other technologies. [PERSON] et al. [58] divided their code into two parts. By using the refresh process based on state partitioning, the nonextensible code could resist persistent leakage attacks. For some schemes based on state partitioning, the state is usually divided into two parts, but there are also four and eight parts [59; 60]. Since the dual-system technology [61] was introduced as the security proof, a lot of work has been carried out along this main line. In the dual-system technology, the key and ciphertext appear in two states: normal and semifunctional. Normal ciphertext is correctly decrypted by any key, but semifunctional ciphertext is not correctly decrypted by the semifunctional key. The orthogonality of subgroup elements can be fully utilized to carry effective information and hide invalid information. The references [37; 39; 46] proved the leakage-resilient security of some schemes through dual-system encryption technology. Among the anonymous broadcast encryption schemes, there is no leakage-resilient encryption scheme at present. On the basis of [62], this paper provides an anonymous broadcast encryption scheme against continual side-channel attacks. We used the following two figures to illustrate the differences between this scheme and the original scheme in [62]. Figure 1 shows the encryption and decryption system of the scheme in [62]. Figure 2 shows the encryption and decryption system of our scheme. There were two main technical differences. The first was the use of extractors. The second was the use of state partitioning technology, which divided the decryption step into two stages. CSP denotes the cloud server provider. The encryption algorithm and decryption algorithm will be specified in Section 4. First, we divided a private key into two states through the state partitioning technology. The private key had a fixed size, which was an important index to be considered in the broadcast encryption scheme. This was different from some current leakage-resilient encryption schemes. Some current encryption schemes obtain certain entropy through lengthening of the private key. This private key has sufficient redundancy to ensure that the security of the private key can be maintained in case of leakage in side-channel attacks. Secondly, because the key for encrypting the plaintext was the encapsulated symmetric key, the symmetric key was subject to leakage-resilient processing through the extractor technology. Thus, the symmetric key could resist side-channel attacks, and the relative leakage ratio for the private key could almost reach 1. Thirdly, the scheme given in this paper was anonymous. The presented scheme could effectively provide privacy protection for the receiver.