{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T09:44:28Z","timestamp":1766223868057,"version":"3.48.0"},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,4,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present BTLE (Broadcast Time-Lock Exchange Protocol), a two-step protocol that aims to decentralize exchange of funds between two blockchains in scenarios similar to online exchanges. BTLE leverages time-lock puzzles to achieve that. In the first phase, the BTLE-MA protocol allows for a matching between a market maker and one of the competing market takers. In the second phase, the BTLE-AS algorithm allows the exchange between the market maker and the winning market taker. It is not necessary to use both the BTLE-MA and BTLE-AS algorithms in a decentralized-exchange scenario: existing atomic swaps based on hashed time-lock contract (HTLC) can benefit from BTLE-MA and can be adapted to an exchange where there are multiple possible participants. Moreover, BTLE computations are off-chain, so BTLE can be used in those blockchain pairs where at least one of the two does not have a scripting language or where the pair do not have the same hash function in common. This solves a limitation of HTLC-based atomic swaps. We also propose a new time-lock puzzle based on Pell conic calculations as an alternative to the classical time-lock puzzle of Rivest et al. BTLE has been implemented and tested. Experiments demonstrate that this new time-lock puzzle based on the Pell conic is superior for the intended goal. With an\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_jmc-2024-0044_eq_001.png\"\/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <m:mi>N<\/m:mi>\n                        <\/m:math>\n                        <jats:tex-math>N<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -bit modulus of 2,000 bits, the RSW-TL approach resolves the puzzle in approximately 100\u00a0s, whereas our BM-TL method requires over 4,000\u00a0s, significantly reducing the number of squaring operations needed.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2024-0044","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T16:24:15Z","timestamp":1744734255000},"source":"Crossref","is-referenced-by-count":0,"title":["BTLE: Atomic swaps with time-lock puzzles"],"prefix":"10.1515","volume":"19","author":[{"given":"Fadi","family":"Barbara","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica, Universit\u00e0 di Torino , Via Pessinetto, 12, 10149 , Torino (TO) , Italy"}]},{"given":"Enrico","family":"Guglielmino","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche, Politecnico di Torino , Corso Duca degli Abruzzi, 24, 10129 , Torino (TO) , Italy"}]},{"given":"Nadir","family":"Murru","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Trento , Via Sommarive 14, 38123 , Povo (TN) , Italy"}]},{"given":"Claudio","family":"Schifanella","sequence":"additional","affiliation":[{"name":"Dipartimento di Informatica, Universit\u00e0 di Torino , Via Pessinetto, 12, 10149 , Torino (TO) , Italy"}]}],"member":"374","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"key":"2025122009205504238_j_jmc-2024-0044_ref_001","doi-asserted-by":"crossref","unstructured":"Garay JA, Kiayias A, Leonardos N. 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