In some embodiments, the at least one first computing device is further configured to send the recovery private key to a recovery escrow service and to periodically send an arbitrary message to a recovery escrow service, wherein the arbitrary message is signed by the recovery private key, the recovery escrow service is further configured to publish the signed arbitrary message in a public repository, and the at least one first computing device is further configured to: retrieve the signed arbitrary message from the public repository, verify that the encryption of the signed arbitrary message is compatible with the recovery public key, and verify that the recovery escrow service has the recovery private key.

In some embodiments, the recovery escrow service in on an external computing device. In some embodiments, the at least one second computing device includes a mobile computing device. In some embodiments, the at least one second computing device is connected to the computer network, and a transaction is added to a ledger of the computer network, in accordance with the received signed at least a portion of the cryptographic key. In some embodiments, the encryption is carried out using a verifiable homomorphic ElGamal encryption.