Cryptoasset custodial system with different cryptographic keys controlling access to separate groups of private keys

Methods, systems, and apparatus, including medium-encoded computer program products, for secure storage and retrieval of information, such as private keys, useable to control access to a blockchain, include, in at least one aspect, a method including: identifying for an action an associated private-keys group out of different private-keys groups, each having an associated cryptographic group key; decrypting, at a first computer, a first level of encryption of a private key associated with the action using the associated cryptographic group key; decrypting, at a second computer distinct from the first computer, a second level of encryption of the private key associated with the action using a hardware-based cryptographic key used by the second computer; using, at the second computer, the private key associated with the action in a process of digitally signing data to authorize the action; and sending the digitally signed data to a third computer to effect the action.