A method is provided for communicating messages between sender and receiver computers, connectable via a network to a system of servers, based on authentication of receiver passwords, associated with respective receiver IDs, by the system. A method is also provided for receiving a message from a sender based on authentication of a receiver password, associated with a receiver ID, by a system of servers, in a network, wherein each server stores for the ID a ciphertext produced by encrypting the receiver password under a public key via a homomorphic threshold encryption scheme having a threshold, and a key-share of a secret key corresponding to that public key, and stores an encrypted message from the sender encrypted under the public key. Systems are provided including servers, for communicating messages between sender and receiver computers based on authentication of receiver passwords, associated with respective receiver IDs, by the system.