This method contrasts with traditional atomic swaps, which leave a transparent trail on the blockchain, potentially compromising the confidentiality of the transaction participants. TAS utilizes advancements in cryptographic technologies, namely Schnorr signatures, Taproot, and zero-knowledge proofs, to execute exchanges discreetly. These technologies enable the disguise of swap transactions as regular Bitcoin payments, making them indistinguishable to external observers.

The process of a TAS initiates when both parties, Alice and Bob, agree on the public keys for the transaction. Alice starts by generating a random value, which she uses to create an escrow public key and an alternative spending path. She constructs a funding transaction with specific spend conditions and sends it to the Bitcoin network. To maintain privacy, Alice also generates zero-knowledge proofs to prove her knowledge of the random value without disclosing it. After receiving these proofs along with other necessary data, Bob validates everything before locking his funds with similar conditions. Once Alice reveals the random value, Bob can access the secret key needed to spend the funds from Alice's lock.

For implementing TAS effectively, the use of MuSig aggregation for creating the escrow public key is recommended, as well as adopting the P2TR method for forming addresses that blend seamlessly with regular Bitcoin addresses. The Poseidon hash function is identified as being zk-friendly, facilitating zero-knowledge procedures involving elliptic curve points, with the 0xPARC library suggested for these operations. These recommendations ensure the secure and efficient execution of TAS, upholding the privacy of blockchain transactions.

A recent demonstration of this protocol was conducted between Bitcoin and Ethereum, showcasing its potential for real-world application. The exchange included distinct transactions where Alice and Bob locked and then withdrew assets from each other's chains using specific parameters and transactions. For those interested in exploring this technology further, the source code for the demonstration is available at this GitHub repository, and detailed insights can be found in a comprehensive document provided here.