A method comprises associating a first logical storage device with a first host device, wherein data encrypted using a private key of the first host device is written to the first logical storage device, generating a copy of the first logical storage device, associating the copy of the first logical storage device with a second logical storage device, wherein data encrypted using a private key of a second host device is written to the second logical storage device, and providing the second host device with access to an encrypted version of a public key of the first host device, encrypted using a public key of the second host device, to allow the second host device to obtain the public key of the first host device. The second host device can thereby access particular data of the second logical storage device written using the private key of the first host device.