Ring Confidential Transactions (RingCT) is a typical privacy-preserving protocol for blockchain, which is used for the most popular anonymous cryptocurrency Monero in recent years. RingCT provides the user's identity anonymity based on the linkable ring signature. At the cost of that, the transaction size is increased linearly to the involved users. In this article, we aim to overcome this inefficient aspect of RingCT by introducing the linkable threshold ring signature (LTRS). We first propose a construction of threshold ring signatures for homomorphic cryptosystems, and present an efficient instantiation based on the intractability assumption of the discrete logarithm problem. Based on this framework, an efficient LTRS scheme and a novel construction of the RingCT protocol are presented. Our proposed RingCT protocol enables multiple payers to co-construct an anonymous transaction without revealing their secret account keys, and it is more concise under multiple input accounts. For a transaction with a ring size of 100 and the input accounts number of 64, the communication overhead is about 4% of the original RingCT protocol.

Anonymous cryptocurrencies are distributed applications based on blockchain technology that enhance the anonymity of user transactions. However, they also provide cover for many criminal activities. Existing traceable modifications of anonymous transaction protocols do not support public verification of the traceability of transactions, meaning dishonest users can still evade tracing by forging partial proofs. In this paper, we first propose EPoK, which is a partially extractable zero-knowledge proof scheme designed to address this issue. We provide the instantiation of EPoK, as well as its formal security proofs. Combined with EPoK and the classic anonymous transaction protocol RingCT, we propose a traceable anonymous transaction protocol TRCT for tracing participants’ addresses and transaction amounts in anonymous transactions. Compared to previous works, TRCT is the first to implement public verification of the transaction’s traceability while still maintaining anonymity. This ensures that users cannot forge relevant proofs to evade tracing. We present and prove the security properties of TRCT, and experimentally compare its efficiency with the original RingCT protocol. The result shows that the extra overhead generated by TRCT is small.

Immutability is widely recognized as one of the blockchain’s key security attributes. However, in recent years, incidents involving the use of blockchain for disseminating illegal or malicious information have raised concerns over its strict immutability. To address these issues, redactable blockchains are proposed as a novel solution, permitting authorized content redactions without compromising the structural integrity of the blockchain. Unfortunately, current solutions are unable to restrict the abuse of redaction privilege, except for relying on a trusted authority or committee, which contradicts the trustlessness principle of blockchain. In this paper, we propose a controlled redactable blockchain protocol that allows for a limited number of redactions and supports a transparent setup. The cryptographic tools enabling this functionality are our proposed t -times chameleon hash ( t -CH) and signature ( t -CS) schemes, where generating more than t collisions will expose the trapdoor. We present security models, discrete logarithmbased instantiations, and formal security proofs for both t -CH and t -CS. Subsequently, we present the construction of our redaction protocol in both permissioned and permissionless settings. Finally, we experimentally demonstrate the effectiveness of the proposed protocol in practice.

As one of the crucial features of the blockchain technique, immutability plays the most important role in winning the so-called praise of the "trust machine" for blockchain. However, there are two sides to everything. The property of immutability of blockchain is applied maliciously sometimes, say publishing harmful or even dangerous data and hindering authorities’ law enforcement. To address this issue, authorized redactability of blockchain was introduced to support block modification without lowering the fundamental basis of security and trust that is cherished on the blockchain. During the past years, several techniques of redactable blockchain were proposed, mainly based on the well-known chameleon hashing. Different from existing methodologies, we propose a new redactable blockchain scheme for permissioned settings in this paper. We first employ the trapdoor verifiable delay function to attach a time-lapse proof to each block. Moreover, the trapdoor is used to quickly construct a chain fork to redact blocks that are authorized to alter. Our proposal does not need to rollback irrelevant blocks. As a remarkable and unique feature, our proposal realizes the property of strong synchronization of redaction, which means that all nodes in the blockchain will have identical views on the chain even after some blocks are altered. Security analysis shows that the consistency of the chain is guaranteed, and the long-range attack can be resisted effectively. The performance comparison shows that our method is feasible and practical.

Immutability has always been a core attribute of blockchain to ensure a trusted public ledger. However, in recent years, many malicious actions on blockchain have raised controversy over strict immutability. As a practical matter, it is necessary to design redactable blockchain protocols in some cases. Previous studies have proposed methods to implement redaction features in permissionless blockchains. However, in these protocols, parties can refuse to accept redacted blocks without affecting their mining. It makes these protocols lack feasibility in practice. In this paper, we present Chainknot, a redactable blockchain protocol with forced synchronization. We use the incentives of permissionless blockchain to effectively facilitate the review of a redaction proposal, and design a novel blockchain structure that ensures the acceptance of modified blocks by parties. In addition, we present instantiations of Chainknot on the PoW-based and PoS-based blockchain systems, with further improvements for efficiency and security, respectively. The experimental results show that the additional latency our protocol imposes on the original immutable blockchain system is negligible (less than 4%).

The immutability of blockchain has exposed its limitations in adapting to rapidly evolving legal requirements and preventing malicious misuse. To address these issues, transaction-level redactable blockchain solutions based on the policy-based chameleon hash (PCH) have been introduced. These solutions allow users to create transactions and encrypt trapdoors under specific attribute policies. However, current transaction-level rewriting schemes face two security challenges: Firstly, transactions encrypted with the invalid trapdoor are difficult to rewrite; Secondly, due to lacking version detection on transactions, malicious modifiers may rollback the version of the transaction to launch a reversion attack. In this paper, we present a resilient and redactable blockchain (RRB) with 2-level rewriting and transaction version detection. Specifically, we propose a new redactable blockchain structure that supports both transaction-level and block-level rewriting. To tackle the invalid trapdoor problem, we propose two protocols: a fine-grained, controllable transaction-level rewriting protocol and a centrally controlled block-level rewriting protocol. Moreover, for the transaction reversion attack, we design a version detection mechanism for RRB by using an accumulator. Through security analysis and performance evaluation, we demonstrate the security and practicality of our RRB scheme.