Graded Cryptographic Primitives

TL;DR: This thesis studies a particular functionality for privacy-preserving systems, that allows a user to demonstrate a proof showing that the user has been approved by a number of authorities, without revealing their identities, and introduces a new notion “grade” for these systems.

Abstract: This thesis studies a particular functionality for privacy-preserving systems, that allows a user to demonstrate a proof showing that the user has been approved by a number of authorities, without revealing their identities. We first consider this functionality for two fundamental cryptosystems: digital signature schemes, and public key encryption schemes, and introduce a new notion “grade” for these systems. Within this scope, we formalize two new primitives, graded signatures and graded encryption. Graded signature schemes enable a user to consolidate a set of signatures on a message m originating from l different signers. The resulting consolidated signature object on m reveals nothing more than the grade of the signature and the validity of the original signatures without leaking the identity of the signers. On the other hand, graded encryption schemes allow a sender to specify a numerical grade i for the ciphertext during the encryption depending on the importance of the message. Users can only decrypt messages directed to their identity at grade i as long as they have contacted i authorities in sequential order. We present efficient constructions and useful applications such as multi-stage games (e.g., “who wants to be a millionaire”) played in a distributed fashion for graded encryption and anonymous petition system