Transfers on Spark

Leaf ownership is transferred by adjusting the SE’s key such that the combined key (SE+User) remains the same before and after the transfer, but control shifts from the sender to the receiver.

Original Combined Key:
$(\text{PubKey}_{\text{Combined}} = \text{PubKey}_{\text{Sender}} + \text{PubKey}_{\text{SE}})$

After Transfer:
$(\text{PubKey}_\text{Combined} = \text{PubKey}_\text{Receiver} + \text{PubKey}'_\text{SE})$

We do this by tweaking the SE key with the difference between the sender and receiver private keys. Note that no private keys are ever revealed through this process.

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Transfer Process

To transfer ownership of a leaf, the SE adjusts its key so that the combined public key (SE + User) remains the same, but control shifts from the sender to the receiver. This is achieved by the SE tweaking its key by the difference between the senders and receivers private keys. By doing so, the SEs new key, when combined with the receivers key, equals the original combined key, ensuring the UTXO can still be spent under the original spending conditions.

This key adjustment allows the transfer of control without revealing any private keys or requiring an on-chain transaction. The SE securely deletes the old private key associated with the sender and collaborates with the receiver to sign a new exit transaction with a lower timelock than the previous one. This process effectively transfers control of the leaf to the receiver, who now has full control over the UTXO.