Proofs in simulation-based frameworks have the greatest rigor when they are machine checked. But the level of details in these proofs surpasses what the formal-methods community can handle with existing tools. Existing formal results consider streamlined versions of simulation-based frameworks to cope with this complexity. Hence, a central question is how to abstract details from composability results and enable their formal verification.In this paper, we focus on the modeling of system communication in composable security statements. Existing formal models consider fixed communication patterns to reduce the complexity of their proofs. However, as we will show, this can affect the reusability of security statements. We propose an abstract approach to modeling system communication in Constructive Cryptography that avoids this problem. Our approach is suitable for mechanized verification and we use CryptHOL, a framework for developing mechanized cryptography proofs, to implement it in the Isabelle/HOL theorem prover. As a case study, we formalize the construction of a secure channel using Diffie-Hellman key exchange and a one-time-pad.

Aharoni et al. [Ron Aharoni et al., 2010] proved the max-flow min-cut theorem for countable networks, namely that in every countable network with finite edge capacities, there exists a flow and a cut such that the flow saturates all outgoing edges of the cut and is zero on all incoming edges. In this paper, we formalize their proof in Isabelle/HOL and thereby identify and fix several problems with their proof. We also provide a simpler proof for networks where the total outgoing capacity of all vertices other than the source is finite. This proof is based on the max-flow min-cut theorem for finite networks.

Machine-checked proofs of security are important to increase the rigour of provable security. In this work we present a formalised theory of two fundamental two party cryptographic primitives: Σ-protocols and Commitment Schemes. Σ-protocols allow a prover to convince a verifier that they possess some knowledge without leaking information about the knowledge. Commitment schemes allow a committer to commit to a message and keep it secret until revealing it at a later time. We use CryptHOL (Lochbihler in Archive of formal proofs, 2017) to formalise both primitives and prove secure multiple examples namely; the Schnorr, Chaum-Pedersen and Okamoto Σ-protocols as well as a construction that allows for compound (AND and OR) Σ-protocols and the Pedersen and Rivest commitment schemes. A highlight of the work is a formalisation of the construction of commitment schemes from Σ-protocols (Damgard in Lecture notes, 2002). We formalise this proof at an abstract level using the modularity available in Isabelle/HOL and CryptHOL. This way, the proofs of the instantiations come for free.

Computer-aided cryptography increases the rigour of cryptographic proofs by mechanizing their verification. Existing tools focus mainly on game-based proofs, and efforts to formalize composable frameworks such as Universal Composability have met with limited success. In this paper, we formalize an instance of Constructive Cryptography, a generic theory allowing for clean, composable cryptographic security statements. Namely, we extend CryptHOL, a framework for game-based proofs, with an abstract model of Random Systems and provide proof rules for their equality and composition. We formalize security as a special kind of system construction in which a complex system is built from simpler ones. As a simple case study, we formalize the construction of an information-theoretically secure channel from a key, a random function, and an insecure channel.

Abstract Cardinality estimators like HyperLogLog are sketching algorithms that estimate the number of distinct elements in a large multiset. Their use in privacy-sensitive contexts raises the question of whether they leak private information. In particular, can they provide any privacy guarantees while preserving their strong aggregation properties? We formulate an abstract notion of cardinality estimators, that captures this aggregation requirement: one can merge sketches without losing precision. We propose an attacker model and a corresponding privacy definition, strictly weaker than differential privacy: we assume that the attacker has no prior knowledge of the data. We then show that if a cardinality estimator satisfies this definition, then it cannot have a reasonable level of accuracy. We prove similar results for weaker versions of our definition, a nd a nalyze t he p rivacy o f existing algorithms, showing that their average privacy loss is significant, e ven f or m ultisets w ith l arge cardinalities. We conclude that strong aggregation requirements are incompatible with any reasonable definition o f privacy, and that cardinality estimators should be considered as sensitive as raw data. We also propose risk mitigation strategies for their real-world applications.

This work presents a machine-checked formalisation of the Java memory model and connects it to an operational semantics for Java and Java bytecode. For the whole model, I prove the data race freedom guarantee and type safety. The model extends previous formalisations by dynamic memory allocation, thread spawns and joins, infinite executions, the wait-notify mechanism, and thread interruption, all of which interact in subtle ways with the memory model. The formalisation resulted in numerous clarifications of and fixes to the existing JMM specification.