Blockchain-enabled digital currency systems, referred to as blockchains for brevity, have become an important method for asset management. Additionally, numerous efforts have been made to facilitate asset swap between two different blockchains, further enhancing asset circulation. However, few works address the general scenario in which one trader swaps assets from$n_{1}$different blockchains with another trader using assets from$n_{2}$different blockchains, referred to as$n_{1} \sim n_{2}$swap. This paper proposes OSwap, the first$n_{1} \sim n_{2}$swap scheme that ensures atomicity without relying on synchronous blockchain communication. By leveraging third-party steps fromverifiable witness encryption based on threshold signatures(VweTS), OSwap allows privacy-conscious traders to swap assets independently, without interactive third-party involvement. It also integratesverifiable timed discrete logarithmschemes to support asset redemption under abnormal cases, maintaining atomicity and indistinguishability. We formally prove the security of OSwap under the universal composable framework with static corruption. We compare OSwap with the closest existing scheme for successful$n_{1} \sim n_{2}$swap, where the trader holding assets on$n_{1}$blockchains pays the counterparty holding assets on$n_{2}$blockchains first. The comparison demonstrates that OSwap reduces the number of required transactions from$2n_{1} + 2n_{2}$to$n_{1} + 2n_{2}$, while also supporting a broader range of signature types. Moreover, when fewer than 4 third parties are involved and both$n_{2}$and the threshold value in VweTS are set to 1, OSwap achieves lower running time cost.

Cross-chain transfer significantly enhances asset management among multiple blockchains. While existing cross-chain transfer schemes facilitate transferring asset ownership of users between a source blockchain and a target blockchain, they do not consider a complex scenario involvingmsource blockchains and one target blockchain (termedm∼1 cross-chain transfer). Furthermore, the variants of existing schemes for this scenario fail to concurrently achieve atomicity, unlinkability, and practical properties such as transaction aggregability, and non-collateralization, posing substantial limitations. To bridge this gap, we propose ShiftHub, the firstm∼1 cross-chain transfer scheme that simultaneously fulfills the above desired properties. ShiftHub guarantees atomicity and transaction aggregability by integratingexchange protocolswith a novelt-message-clustered redeem protocol. Unlinkability is achieved by additionally incorporating commonly used assumptions such as fixed-amount transfers, while the need for sender collateralization is eliminated by enabling the reuse of locked assets. Compatible with any blockchains that employadaptor signaturesorBLS signaturesfor transaction authentication, ShiftHub requires only signature verification and timelock functionalities on chain, ensuring near-universal blockchain compatibility. We formally prove the security of ShiftHub under static corruption using the universal composability framework. Extensive evaluation shows that ShiftHub offers superior performance over the existing scheme variant with the closest underlying protocols to ShiftHub, in terms of both off-chain and on-chain overhead, when completingm∼1 cross-chain transfer. Particularly, ShiftHub reduces the number of required transactions by (2m− 1)/3m.

Blockchain-enabled digital currency systems have typically operated in isolation, lacking necessary mechanisms for seamless interconnection. Consequently, transferring assets across distinct currency systems remains a complex challenge, with existing schemes often falling short in ensuring security, privacy, and practicality. This paper proposes P2C2T - a privacy-preserving cross-chain transfer scheme. It is the first scheme to address atomicity, unlinkability, indistinguishability, non-collateralization, and required functionalities across diverse currency systems. P2C2T is based on threshold anonymous atomic locks (TA2L), also proposed by us, serving as the cornerstone for guaranteeing atomic cross-chain transfer while obscuring the payment relationships between users. By combining TA2L with verifiable timed discrete logarithm schemes, P2C2T renders cross-chain transactions indistinguishable from regular intra-chain ones. Notably, P2C2T eliminates the collateralization of senders and imposes minimal requirements on underlying blockchains, specifically on the ability to verify signatures. We substantiate the security of TA2L based on a proposed cryptographic notion called threshold blind conditional signatures and demonstrate the security of P2C2T through necessary proofs. Additionally, we compare the performance of P2C2T with an existing scheme that has properties closest to P2C2T. The comparison reveals that P2C2T reduces overhead by at least 85.488% in terms of running time, communication cost, and storage cost when completing a cross-chain transfer. We further conduct cross-chain transfers and intra-chain payments using the Bitcoin testnet and Litecoin testnet to illustrate the privacy and practicality of P2C2T.

Blockchain has attracted more and more attention of academia, industry, and government in recent decades. Different usage demands have inspired various blockchain designs, forming different blockchain systems, which leads to information islands. Many cross-chain technologies have been proposed to link different blockchains together and expand the utility of blockchain. Nevertheless, the cross-chain technology is still in its infancy, which faces many problems that retard its wide application, for example, the issues related to security, privacy, and effectiveness. In order to further investigate cross-chain technologies, it is essential to understand its current state of arts. Although there are some surveys about cross-chain technologies driven by specific demands, the literature still lacks a comprehensive survey focusing on security, privacy, and effectiveness of cross-chain technologies. In this paper, we provide a review on existing cross-chain technologies based on a comprehensive set of criteria on security, privacy, and other performance. We first propose a blockchain interoperability architecture for the purpose of analyzing potential threats and problems regarding security, privacy, and effectiveness. We then summarize a set of criteria regarding these quality attributes. Next, we comprehensively review the representative works on cross-chain technologies according to a taxonomy based on applied types of techniques and cross-chain purposes. In each work review, we provide a serious discussion on its pros and cons by employing our proposed criteria. Finally, based on our review and analysis, we figure out a number of open issues and step ahead to direct future research directions on cross-chain technologies.