Abstract: A method of encrypting a passcode is disclosed. In one embodiment, the method includes: receiving an indication of a portion of the passcode; calculating a plaintext value based at least in part on the indication, wherein the plaintext value represents an encoded portion of the passcode; encrypting the plaintext value into ciphertext using a homomorphic encryption system; and updating a cumulative encryption string by executing a cumulative operation to aggregate the ciphertext corresponding to the encoded portion into the cumulative encryption string computed for a previous portion of the passcode, wherein the cumulative operation is dictated by a homomorphic property of the homomorphic encryption system.

Abstract: A method for encrypting a passcode is disclosed. In one embodiment, the method includes: receiving an indication of a portion of the passcode from a user; encoding the portion of the passcode; encrypting the encoded portion into ciphertext using a homomorphic encryption system; updating a cumulative encryption string by executing a cumulative operation to aggregate the ciphertext corresponding to the encoded portion into the cumulative encryption string computed for a previous portion of the passcode, wherein the cumulative operation is dictated by a homomorphic property of the homomorphic encryption system; and generating a passcode message based at least in part on the cumulative encryption string, wherein the passcode message includes a message authentication code.

Abstract: A number of unique identifiers is determined by, at a device, receiving a request to determine the number of unique identifiers, outputting a response to the request, and receiving data representing the number of the unique identifiers based on the response to the request. The data representing the number of the unique identifiers is free of information indicative of an identity of a source of the unique identifiers.