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In terms of Cryptocurrency, the transaction of two different cryptocurrencies between two parties is made possible by atomic swap feature. These two parties may have their wallets (accounts) on different blockchains altogether and yet are able to go through with the transaction. This is also called Atomic cross-chain trading.
For a transaction to go through, a protocol known as smart contract is established. This smart contract has a set of rules that confirms the authenticity of the transaction on both the sides and has two outcomes, either all the terms mentioned in the smart contract are verified and the transaction is executed successfully or it is found invalid and the transaction is terminated.
Usually there are three parties involved in a transaction, the sender, the mediator and the recipient. Due to the decentralized nature of atomic swaps, there is no mediator / middleman. The transactions now involve only two parties and the authentication & transactions are executed by the smart contracts through the distributed blockchain network. These transactions are safe and secure .
To make the transactions happen instantly between blockchains, lightning network is used. A lightning network offers privacy, security and low trading fees. This is the future.
Smart Contracts are self-executing contracts that take care of the entire verification, transfer and updation process in the blockchain network.
You can read up more about How atomic swap works HERE.