# A Redactable Blockchain Scheme Supporting Quantum-Resistance and Trapdoor Updates
## 1 Introduction
### Related Work  
This section outlines recent research in the field, focusing on two distinct editing techniques: those utilizing chameleon hashing and those abstaining from its use. **Chameleon Hashing**. [PERSON] et al. are the trailblazers in the exploration of redactable blockchains. Their approach involved substituting the hash algorithm G used in bitcoinwith an enhanced chameleon hash, which leveraged the MPC protocol to distribute trapdoors to a trusted subset capable of managing these trapdoors effectively [16]. Collaborating with Accenture, the authors further demonstrated the practical application of their concept on the Hyperledger Fabric platform. This pioneering research has aroused the research interest of many scholars, and based on the problems it exposed, there have been various kinds of research in recent years on the design of chameleon hash functions for security construction, trapdoor restriction, editing permissions restriction, data management, and consistency, respectively. In the realm of chameleon hash algorithms, several issues have garnered attention. To address efficiency and instantiation challenges, [PERSON] et al. introduced a chameleon hash for chosen-ciphertext attack (CCA) secure encryption of a random field R [19]. Responding to similar concerns, [PERSON] et al. introduced the concept of stronger full collision-resistance (F-CollRes) and developed a black box structure employing simulation-sound extractable non-interactive zero-knowledge proof (SSE-NIZK) through the utilization of a chameleon hash [20]. Building upon these developments, ref. [21] focused on constructing an identity-based chameleon hash (IBCH). Subsequently, a hierarchical identity-based chameleon hash (HIBCH) was proposed in [22], but these two schemes are more specifically applicable to hash signatures. Regarding trapdoor and edit permission management, [PERSON] et al. proposed policy-based chameleon hashing (PCH) by integrating attribute-based encryption (CP-ABE) and temporary trapdoors [23]. This redactable scheme combines keys and attributes and restricts edit permissions by formulating attribute policies. Nonetheless, its reliance on a fully trusted central authority creates a centrality problem. Therefore, [PERSON] et al. proposed a chameleon hash structure based on multi-authority decentralization (DPCH) [24], which effectively prevents conspiracy attacks, in contrast to [23]. [PERSON] et al. 's chameleon hash scheme with a changeable trapdoor (CHCT) enables the updating of trapdoors after computing hash collisions [25]. Recently, [PERSON] et al. introduced the concept of stateful chameleon hashing with revocable subkeys, constructed a redactable blockchain with a black box structure, supported full supervision, and allowed user data self-management [26]. Drawing inspiration from this work, our study also incorporates data self-management. Furthermore, addressing concerns about inconsistency, [PERSON] et al. took a step forward by designing an RSA-based accumulator structure aimed at consistency verification [27]. In addition, they devised edit chains, linking edit histories to counter traceability issues within the system. In recent years, post-quantum encryption technology has been gradually maturing and standardizing. [PERSON] et al. applied a lattice-based chameleon hash function in the context of editable blockchains, introducing the concept of quantum resistance [15]. Meanwhile, [PERSON] et al. devised a more comprehensive lattice-based blockchain editing scheme [28]. However, the former primarily focuses on the construction of the chameleon hash and introduces key sharing, while the latter requires further refinement in its scheme design. **Non-Chameleon Hashing**. [PERSON] et al. proposed an extended redactable model for single-chain transactions based on consensus control, in which editing operations are reached by sending mutating transactions or extending things and specifying the active transaction in this structure [29].