Methods and systems for group authentication using the naccache-stern cryptosystem in accordance with a prescribed rule

Abstract

A method for group authentication using a public key cryptosystem that includes a public key and a private key, comprising the steps of providing a Private Key Share to a Tool of each Entity of each Group encompassed by a Boolean Expression of a prescribed Rule based upon the private key, encrypting a random number using the public key of the public key cryptosystem to generate a ciphertext challenge at a Verification Device, conveying the ciphertext challenge to the Tool of each Entity in communication with the Verification Device, generating a response to the ciphertext challenge using the Private Key Share of the Tool of each Entity in communication with the Verification Device, transmitting the response generated by each Entity in communication with the Verification Device to the Verification Device, combining the responses received from the Entities in communication with the Verification Device, determining whether any combination of the responses equals the random number wherein any combination that equals the random number identifies an Authenticated Group and any combination that does not equal the random number identifies a non-authenticated Group, and effecting an apposite course of action with respect to an Operation governed by the prescribed Rule based upon the outcome of the determining step.