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However, most known ACCS schemes assume specific scripting functionalities of the underlying blockchains, such as Hash Time Locked Contracts (HTLC). In addition, these schemes are typically only applicable to certain digital signature schemes, like Schnorr or Elliptic Curve Digital Signature Algorithm\u00a0(ECDSA) signatures. In this paper, we propose a generic ACCS scheme, independent from the underlying blockchains. To the best of our knowledge, this is the first solution of this kind. Our results are as follows. First, we define a formal system model of ACCS. Next, we present a generic ACCS scheme meets our model. This scheme admits atomicity in cross-chain swaps without the need for a Trusted Third Party (TTP)\u00a0and protects users\u2019 privacy. Finally, by using the Non-Interactive Zero-Knowledge\u00a0(NIZK) proof protocol as a tool, we instantiate our generic scheme for Elliptic Curve Discrete Logarithm Problem-based (ECDLP-based)\u00a0signatures. In addition, we implement our scheme, and the experimental results show that our protocol outperforms the existing ACCS schemes, such as the HTLC-based schemes.<\/jats:p>","DOI":"10.1186\/s42400-023-00202-8","type":"journal-article","created":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T03:18:34Z","timestamp":1717298314000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Atomic cross-chain swap based on private key exchange"],"prefix":"10.1186","volume":"7","author":[{"given":"Zeshuo","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Tao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,2]]},"reference":[{"key":"202_CR1","doi-asserted-by":"publisher","first-page":"56","DOI":"10.3390\/healthcare7020056","volume":"7","author":"CC Agbo","year":"2019","unstructured":"Agbo CC, Mahmoud QH, Eklund JM (2019) Blockchain technology in healthcare: a systematic review. 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