Abstract The universal composability paradigm allows for the modular design and analysis of cryptographic protocols. It has been widely and successfully used in cryptography. However, devising a coherent yet simple and expressive model for universal composability is, as the history of such models shows, highly non-trivial. For example, several partly severe problems have been pointed out in the literature for the UC model. In this work, we propose a coherent model for universal composability, called the IITM model (“Inexhaustible Interactive Turing Machine”). A main feature of the model is that it is stated without a priori fixing irrelevant details, such as a specific way of addressing of machines by session and party identifiers, a specific modeling of corruption, or a specific protocol hierarchy. In addition, we employ a very general notion of runtime. All reasonable protocols and ideal functionalities should be expressible based on this notion in a direct and natural way, and without tweaks, such as (artificial) padding of messages or (artificially) adding extra messages. Not least because of these features, the model is simple and expressive. Also the general results that we prove, such as composition theorems, hold independently of how such details are fixed for concrete applications. Being inspired by other models for universal composability, in particular the UC model and because of the flexibility and expressivity of the IITM model, conceptually, results formulated in these models directly carry over to the IITM model.

Abstract In frameworks for universal composability, complex protocols can be built from sub-protocols in a modular way using composition theorems. 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 (composition) 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 proposed in the literature are shown to be unsuitable. Our work is based on 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.

Canetti's universal composition theorem and the joint state composition theorems by Canetti and Rabin are useful and widely employed tools for the modular design and analysis of cryptographic protocols. However, these theorems assume that parties participating in a protocol session have pre-established a unique session ID (SID). While the use of such SIDs is a good design principle, existing protocols, in particular real-world security protocols, typically do not use pre-established SIDs, at least not explicitly and not in the particular way stipulated by the theorems. As a result, the composition theorems cannot be applied for analyzing such protocols in a modular and faithful way. In this paper, we therefore present universal and joint state composition theorems which do not assume pre-established SIDs. In our joint state composition theorem, the joint state is an ideal functionality which supports several cryptographic operations, including public-key encryption, (authenticated and unauthenticated) symmetric encryption, MACs, digital signatures, and key derivation. This functionality has recently been proposed by Küsters and Tuengerthal and has been shown to be realizable under standard cryptographic assumptions and for a reasonable class of environments. We demonstrate the usefulness of our composition theorems by several case studies on real-world security protocols, including IEEE 802.11i, SSL/TLS, SSH, IPsec, and EAP-PSK. While our applications focus on real-world security protocols, our theorems, models, and techniques should be useful beyond this domain.

Formal analysis of security protocols based on symbolic models has been very successful in finding flaws in published protocols and proving protocols secure, using automated tools. An important question is whether this kind of formal analysis implies security guarantees in the strong sense of modern cryptography. Initiated by the seminal work of Abadi and Rogaway, this question has been investigated and numerous positive results showing this so-called computational soundness of formal analysis have been obtained. However, for the case of active adversaries and protocols that use symmetric encryption computational soundness has remained a challenge.

For most basic cryptographic tasks, such as public-key encryption, digital signatures, authentication, key exchange, and many other more sophisticated tasks, ideal functionalities have been formulated in the simulation-based security approach, along with their realizations. Surprisingly, however, no such functionality exists for symmetric encryption, except for a more abstract Dolev-Yao style functionality. In this paper, we fill this gap. We propose two functionalities for symmetric encryption, an unauthenticated and an authenticated version, and show that they can be implemented based on standard cryptographic assumptions for symmetric encryption schemes, namely IND-CCA security and authenticated encryption, respectively, provided that the environment does not create key cycles or cause these-called commitment problem. We also illustrate the usefulness of our functionalities in applications, both in simulation-based and game-based security settings.

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-keyencryption, replayable public-key encryption, and digital signatures. Unlike most other formulations, our functionalities model that cipher texts 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.