Proving Cryptographic C Programs Secure with General-Purpose Verification Tools

Security protocols, such as TLS or Kerberos, and security devices such as the Trusted Platform Module (TPM), Hardware Security Modules (HSMs) or PKCS#11 tokens, are central to many computer interactions. Yet, such security critical components are still often found vulnerable to attack after their deployment, either because the specification is insecure, or because of implementation errors. Techniques exist to construct machine-checked proofs of security properties for abstract specifications. However, this may leave the final executable code, often written in lower level languages such as C, vulnerable both to logical errors, and low-level flaws. Recent work on verifying security properties of C code is often based on soundly extracting, from C programs, protocol models on which security properties can be proved. However, in such methods, any change in the C code, however trivial, may require one to perform a new and complex security proof. Our goal is therefore to develop or identify a framework in which security properties of cryptographic systems can be formally proved, and that can also be used to soundly verify, using existing general-purpose tools, that a C program shares the same security properties. We argue that the current state of general-purpose verification tools for the C language, as well as for functional languages, is sufficient to achieve this goal, and illustrate our argument by developing two verification frameworks around the VCC verifier. In the symbolic model, we illustrate our method by proving authentication and weak secrecy for implementations of several network security protocols. In the computational model, we illustrate our method by proving authentication and strong secrecy properties for an exemplary key management API, inspired by the TPM

INFORMATION THEORETIC SECRET KEY GENERATION: STRUCTURED CODES AND TREE PACKING

This dissertation deals with a multiterminal source model for secret key generation by multiple network terminals with prior and privileged access to a set of correlated signals complemented by public discussion among themselves. Emphasis is placed on a characterization of secret key capacity, i.e., the largest rate of an achievable secret key, and on algorithms for key construction. Various information theoretic security requirements of increasing stringency: weak, strong and perfect secrecy, as well as different types of sources: finite-valued and continuous, are studied. Specifically, three different models are investigated. First, we consider strong secrecy generation for a discrete multiterminal source model. We discover a connection between secret key capacity and a new source coding concept of ``minimum information rate for signal dissemination,'' that is of independent interest in multiterminal data compression. Our main contribution is to show for this discrete model that structured linear codes suffice to generate a strong secret key of the best rate. Second, strong secrecy generation is considered for models with continuous observations, in particular jointly Gaussian signals. In the absence of suitable analogs of source coding notions for the previous discrete model, new techniques are required for a characterization of secret key capacity as well as for the design of algorithms for secret key generation. Our proof of the secret key capacity result, in particular the converse proof, as well as our capacity-achieving algorithms for secret key construction based on structured codes and quantization for a model with two terminals, constitute the two main contributions for this second model. Last, we turn our attention to perfect secrecy generation for fixed signal observation lengths as well as for their asymptotic limits. In contrast with the analysis of the previous two models that relies on probabilistic techniques, perfect secret key generation bears the essence of ``zero-error information theory,'' and accordingly, we rely on mathematical techniques of a combinatorial nature. The model under consideration is the ``Pairwise Independent Network'' (PIN) model in which every pair of terminals share a random binary string, with the strings shared by distinct pairs of terminals being mutually independent. This model, which is motivated by practical aspects of a wireless communication network in which terminals communicate on the same frequency, results in three main contributions. First, the concept of perfect omniscience in data compression leads to a single-letter formula for the perfect secret key capacity of the PIN model; moreover, this capacity is shown to be achieved by linear noninteractive public communication, and coincides with strong secret key capacity. Second, taking advantage of a multigraph representation of the PIN model, we put forth an efficient algorithm for perfect secret key generation based on a combinatorial concept of maximal packing of Steiner trees of the multigraph. When all the terminals seek to share perfect secrecy, the algorithm is shown to achieve capacity. When only a subset of terminals wish to share perfect secrecy, the algorithm is shown to achieve at least half of it. Additionally, we obtain nonasymptotic and asymptotic bounds on the size and rate of the best perfect secret key generated by the algorithm. These bounds are of independent interest from a purely graph theoretic viewpoint as they constitute new estimates for the maximum size and rate of Steiner tree packing of a given multigraph. Third, a particular configuration of the PIN model arises when a lone ``helper'' terminal aids all the other ``user'' terminals generate perfect secrecy. This model has special features that enable us to obtain necessary and sufficient conditions for Steiner tree packing to achieve perfect secret key capacity

Efficient Wireless Security Through Jamming, Coding and Routing

There is a rich recent literature on how to assist secure communication between a single transmitter and receiver at the physical layer of wireless networks through techniques such as cooperative jamming. In this paper, we consider how these single-hop physical layer security techniques can be extended to multi-hop wireless networks and show how to augment physical layer security techniques with higher layer network mechanisms such as coding and routing. Specifically, we consider the secure minimum energy routing problem, in which the objective is to compute a minimum energy path between two network nodes subject to constraints on the end-to-end communication secrecy and goodput over the path. This problem is formulated as a constrained optimization of transmission power and link selection, which is proved to be NP-hard. Nevertheless, we show that efficient algorithms exist to compute both exact and approximate solutions for the problem. In particular, we develop an exact solution of pseudo-polynomial complexity, as well as an epsilon-optimal approximation of polynomial complexity. Simulation results are also provided to show the utility of our algorithms and quantify their energy savings compared to a combination of (standard) security-agnostic minimum energy routing and physical layer security. In the simulated scenarios, we observe that, by jointly optimizing link selection at the network layer and cooperative jamming at the physical layer, our algorithms reduce the network energy consumption by half