I'm searching for a way to backup a secret that only the end user knows the information with 2 trusted hosts.
But trusted hosts shouldn't have access to secret at any time.
First basic version : Alice encrypt secret using Server A public key Alice encrypt encrypted secret using Server B public key. Alice store this double encrypted secret somewhere safe
To restore : Alice ask server B to decrypt double encrypted secret Alice ask server A to decrypt result Alice get secret ... but server A also !
It could work if : to restore : Alice ask server B to decrypt double encrypted secret Alice encrypt result using a magical encryption mechanism (?) Alice ask server A to decrypt this information (homomorphic ??) Alice receive result and decrypt using a magical decryption mechanism (?) Alice get secret ... and server A got just an encrypted information !
Is an encryption mechanism like this exists ?
Is there an alternative approach to my goal ?