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Joint State Theorems for Public-Key Encryption and Digital Signature Functionalities with Local Computation

Ralf Küsters and Max Tuengerthal

Composition theorems in simulation-based approaches allow to build complex protocols from sub-protocols in a modular way. However, as first pointed out and studied by Canetti and Rabin, this modular approach often leads to impractical implementations. For example, when using a functionality for digital signatures within a more complex protocol, parties have to generate new verification and signing keys for every session of the protocol. This motivates to generalize composition theorems to so-called joint state theorems, where different copies of a functionality may share some state, e.g., the same verification and signing keys. In this paper, we present a joint state theorem which is more general than the original theorem of Canetti and Rabin, for which several problems and limitations are pointed out. We apply our theorem to obtain joint state realizations for three functionalities: public-key encryption, replayable public-key encryption, and digital signatures. Unlike most other formulations, our functionalities model that ciphertexts and signatures are computed locally, rather than being provided by the adversary. To obtain the joint state realizations, the functionalities have to be designed carefully. Other formulations are shown to be unsuitable. Our work is based on a recently proposed, rigorous model for simulation-based security by K{\"u}sters, called the IITM model. Our definitions and results demonstrate the expressivity and simplicity of this model. For example, unlike Canetti's UC model, in the IITM model no explicit joint state operator needs to be defined and the joint state theorem follows immediately from the composition theorem in the IITM model.