No single party has access to the SGX enclave address. Only the enclave itself can construct/sign a transaction using that key when it receives approvals from 6 of 8 Bridge Nodes. In this sense, the enclave here is functioning as a cross-chain smart contract.
For any additional questions, please visit our knowledge base or contact a support team member via the chat button at support.avax.network.
Chat with Ava Labs | Use Apps on Avalanche | Validate on Avalanche