BTLE: Atomic swaps with time-lock puzzles

• Published in: Journal of mathematical cryptology Vol. 19; no. 1; pp. 281 - 310
• Main Authors: Barbara, Fadi, Guglielmino, Enrico, Murru, Nadir, Schifanella, Claudio
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 15.04.2025; Walter de Gruyter GmbH
• Subjects: 11T71; Algorithms; atomic swaps; Blockchain; decentralized exchange; Exchanging; Hash based algorithms; Markets; time lock puzzle
• ISSN: 1862-2984; 1862-2976; 1862-2984
• DOI: 10.1515/jmc-2024-0044

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 -bit modulus of 2,000 bits, the RSW-TL approach resolves the puzzle in approximately 100 s, whereas our BM-TL method requires over 4,000 s, significantly reducing the number of squaring operations needed.