ABSTRACT. Privacy is a notoriously difficult property to achieve in complicated systems and especially in electronic voting schemes. Moreover, electronic voting schemes is a class of systems that require very high assurance. The literature contains a number of ballot privacy definitions along with security proofs for common systems. Some machine-checked security proofs have also appeared. We define a new ballot privacy notion that captures a larger class of voting schemes. This notion improves on the state of the art by taking into account that verification in many schemes will happen or must happen after the tally has been published, not before as in previous definitions.

As a case study we give a machine-checked proof of privacy for Selene, which is a remote electronic voting scheme which offers an attractive mix of security properties and usability. Prior to our work, the computational privacy of Selene has never been formally verified. Finally, we also prove that MiniVoting and Belenios satisfies our definition.

ABSTRACT. We study the privacy-utility trade-off in the context of metric differential privacy. Ghosh et al. introduced the idea of universal optimality to characterise the ``best'' mechanism for a certain query that simultaneously satisfies (a fixed) $\epsilon$-differential privacy constraint whilst at the same time providing better utility compared to any other $\epsilon$-differentially private mechanism for the same query. They showed that the Geometric mechanism is universally optimal for the class of counting queries. On the other hand, Brenner and Nissim showed that outside the space of counting queries, and for the Bayes risk loss function, no such universally optimal mechanisms exist. Except for universal optimality of the Laplace mechanism, there have been no generalisations of these universally optimal results to other classes of differentially-private mechanisms.

In this paper we use metric differential privacy and quantitative information flow as the fundamental principle for studying universal optimality. Metric differential privacy is a generalisation of both standard (i.e., central) differential privacy and local differential privacy, and it is increasingly being used in various application domains, for instance in location privacy and in privacy preserving machine learning. As do Ghosh et al. and Brenner and Nissim, we measure utility in terms of loss functions, and we interpret the notion of a privacy mechanism as an information-theoretic channel satisfying constraints defined by $\epsilon$-differential privacy and a metric meaningful to the underlying state space. Using this framework we are able to clarify Nissim and Brenner's negative results by (a) that in fact all privacy types contain optimal mechanisms relative to certain kinds of non-trivial loss functions, and (b) extending and generalising their negative results beyond Bayes risk specifically to a wide class of non-trivial loss functions.

Our exploration suggests that universally optimal mechanisms are indeed rare within privacy types. We therefore propose weaker universal benchmarks of utility called privacy type capacities. We show that such capacities always exist and can be computed using a convex optimisation algorithm. Finally, we illustrate these ideas on a selection of examples with several different underlying metrics.

ABSTRACT. To address known privacy problems with the EMV standard, EMVCo have proposed a Blinded Diffie-Hellman key establishment protocol, which is intended to be part of a future 2nd Gen EMV protocol. We point out that active attackers were not previously accounted for in the privacy requirements of this proposal protocol, and demonstrate that an active attacker can compromise unlinkability within a distance of 100cm. Here, we adopt a strong definition of unlinkability that does account for active attackers and propose an enhancement of the protocol proposed by EMVCo. We prove that our protocol does satisfy strong unlinkability, while preserving authentication.

ABSTRACT. Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and reinforcement learning models. However, these methods rely on the assumed structure and probabilities of certain system transitions. These assumptions may be incorrect, and may even be violated by an adversary who gains control of some system components.

In this paper, we develop a formal framework for adversarial robustness in systems modeled as discrete time Markov chains (DTMCs). We base our framework on existing methods for verifying probabilistic temporal logic properties and extend it to include deterministic, memoryless policies acting in Markov decision processes (MDPs). Our framework includes a flexible approach for specifying structure-preserving and non structure-preserving adversarial models. We outline a class of threat models under which adversaries can perturb system transitions, constrained by an $\varepsilon$ ball around the original transition probabilities.

We define three main DTMC adversarial robustness problems: adversarial robustness verification, maximal $\delta$ synthesis, and worst case attack synthesis. We present two optimization-based solutions to these three problems, leveraging traditional and parametric probabilistic model checking techniques. We then evaluate our solutions on two stochastic protocols and a collection of Grid World case studies, which model an agent acting in an environment described as an MDP. We find that the parametric solution results in fast computation for small parameter spaces. In the case of less restrictive (stronger) adversaries, the number of parameters increases, and directly computing property satisfaction probabilities is more scalable. We demonstrate the usefulness of our definitions and solutions by comparing system outcomes over various properties, threat models, and case studies.

ABSTRACT. We study the complexity of the problem of verifying differential privacy for while-like programs working over boolean values and making probabilistic choices. Programs in this class can be interpreted into finite-state discrete-time Markov Chains (DTMC). We show that the problem of deciding whether a program is differentially private for specific values of the privacy parameters is PSPACE-complete. To show that this problem is in PSPACE, we adapt classical results about computing hitting probabilities for DTMC. To show PSPACE-hardness we use a reduction from the problem of checking whether a program almost surely terminates or not. We also show that the problem of approximating the privacy parameters that a program provides is PSPACE-hard. Moreover, we investigate the complexity of similar problems also for several relaxations of differential privacy: Rényi differential privacy, concentrated differential privacy, and truncated concentrated differential privacy. For these notions, we consider gap-versions of the problem of deciding whether a program is private or not and we show that all of them are PSPACE-complete.

ABSTRACT. Compared to ordinary concurrent and distributed systems, cryptographic protocols are distinguished by the need to reason about interference by adversaries. We suggest a new layered approach to tame that complexity, via an executable protocol language whose semantics does not reveal an adversary directly, instead enforcing a set of intuitive hygiene rules. By virtue of those rules, protocols written in this language provably behave identically with or without interference by active Dolev-Yao-style adversaries. As a result, formal reasoning about protocols can be simplified enough that even naı̈ve model checking can establish correctness of a multiparty protocol, through analysis of a state space with no adversary.

We present the design and implementation of SPICY, short for Secure Protocols Implemented CorrectlY, including the semantics of its input languages; the essential safety proofs, formalized in the Coq theorem prover; and the automation techniques. We provide a preliminary evaluation of the tool’s performance and capabilities via a handful of case studies.

ABSTRACT. Due to its amazing speed and multiplicative properties the Legendre PRF recently finds widespread applications e.g. in Ethereum 2.0, multiparty computation and in the quantum-secure signature proposal LegRoast. However, its security is not yet extensively studied.

The Legendre PRF computes for a key $k$ on input $x$ the Legendre symbol $L_k(x) = \left( \frac {x+k} {p} \right)$ in some finite field $\F_p$. As standard notion, PRF security is analysed by giving an attacker oracle access to $L_k(\cdot)$. Khovratovich's collision-based algorithm recovers $k$ using $L_k(\cdot)$ in time $\sqrt{p}$ with constant memory. It is a major open problem whether this birthday-bound complexity can be beaten.

We show a somewhat surprising wide-ranging analogy between the discrete logarithm problem and Legendre symbol computations. This analogy allows us to adapt various algorithmic ideas from the discrete logarithm setting.

More precisely, we present a small memory multiple-key attack on $m$ Legendre keys $k_1, \ldots, k_m$ in time $\sqrt{mp}$, i.e. with amortized cost $\sqrt{p/m}$ per key. This multiple-key attack might be of interest in the Ethereum context, since recovering many keys simultaneously maximizes an attacker's profit.

Moreover, we show that the Legendre PRF admits precomputation attacks, where the precomputation depends on the public $p$ only -- and not on a key $k$. Namely, an attacker may compute e.g. in precomputation time $p^{\frac 2 3}$ a hint of size $p^{\frac 1 3}$. On receiving access to $L_k(\cdot)$ in an online phase, the attacker then uses the hint to recover the desired key $k$ in time only $p^{\frac 1 3}$. Thus, the attacker's online complexity again beats the birthday-bound.

In addition, our precomputation attack can also be combined with our multiple-key attack. We explicitly give various tradeoffs between precomputation and online phase. E.g. for attacking $m$ keys one may spend time $mp^{\frac 2 3}$ in the precomputation phase for constructing a hint of size $m^2 p^{\frac 1 3}$. In an online phase, one then finds {\em all $m$ keys in total time} only $p^{\frac 1 3}$.

Precomputation attacks might again be interesting in the Ethereum 2.0 context, where keys are frequently changed such that a heavy key-independent precomputation pays off.

ABSTRACT. We give characterizations of IND$-CPA security for a large, natural class of encryption schemes. Specifically, we consider encryption algorithms that invoke a block cipher and otherwise perform linear operations (e.g., XOR and multiplication by fixed field elements) on intermediate values. This class of algorithms corresponds to the Linicrypt model of Carmer & Rosulek (Crypto 2016). Our characterization for this class of encryption schemes is sound but not complete.

We then focus on a smaller subclass of block cipher modes, which iterate over the blocks of the plaintext, repeatedly applying the same Linicrypt program. For these Linicrypt block cipher modes, we are able to give a sound and complete characterization of IND$-CPA security. Our characterization is linear-algebraic in nature and is easy to check for a candidate mode. Interestingly, we prove that a Linicrypt block cipher mode is secure if and only if it is secure against adversaries who choose all-zeroes plaintexts.

ABSTRACT. We address logic locking, a mechanism for securing digital Integrated Circuits (ICs) from piracy by untrustworthy foundries. We discuss previous work and the state-of-the-art, and observe that, despite more than a decade of research that has gone into the topic (resulting in both powerful attacks and subsequent defenses), there is no consensus on what it means for a particular locking mechanism to be secure. This paper attempts to remedy this situation. Specifically, it formulates a definition of security for a logic locking mechanism based on indistinguishability and relates the definition to security from actual attackers in a precise and unambiguous manner. We then describe a mechanism that satisfies the definition, thereby achieving (provable) security from all prior attacks. The mechanism assumes the existence of both a puncturable pseudorandom function family and an indistinguishability obfuscator, two cryptographic primitives that exist under well-founded assumptions. The mechanism builds upon the Stripped-Functionality Logic Locking (SFLL) framework, a state-of-the-art family of locking mechanisms whose potential for ever achieving security is currently in question. Along the way, partly as motivation, we present additional results, such as a reason founded in average-case complexity for why benchmark circuits locked with a prior scheme are susceptible to the well-known SAT attack against such schemes, and why provably thwarting the SAT attack is insufficient as a meaningful notion of security for logic locking.

ABSTRACT. Temporal logics for hyperproperties like HyperLTL use trace quantifiers to express properties that relate multiple system runs. In practice, the verification of such specifications is mostly limited to formulas without quantifier alternation, where verification can be reduced to checking a trace property over the self-composition of the system. Quantifier alternations like $\forall \pi. \exists \pi'. \phi$, can either be solved by complementation or with an interpretation as a two-person game between a $\forall$-player, who incrementally constructs the trace $\pi$, and an $\exists$-player, who constructs $\pi'$ in such a way that $\pi$ and $\pi'$ together satisfy $\phi$. The game-based approach is significantly cheaper but incomplete because the $\exists$-player does not know the future moves of the $\forall$-player. In this paper, we establish that the game-based approach can be made complete by adding ($\omega$-regular) temporal prophecies. Our proof is constructive, yielding an effective algorithm for the generation of a complete set of prophecies.

ABSTRACT. In system design, high-level system models typically need to be mapped to an execution platform (e.g., hardware, environment, compiler, etc). The platform may naturally strengthen some constraints or weaken some others, but it is expected that the low-level implementation on the platform should preserve all the functional and extra-functional properties of the model, including the ones for information-flow security. It is, however, well known that simple notions of refinement do not preserve information-flow security properties.

In this paper, we propose a novel automated mapping synthesis approach that preserves hyperproperties expressed in the temporal logic HyperLTL. The significance of our technique is that it can handle formulas with quantifier alternations, which is typically the source of difficulty in refinement for informationflow security policies. We reduce the mapping synthesis problem to HyperLTL model checking and leverage recent efforts in bounded model checking for hyperproperties. We demonstrate how mapping synthesis can be used in various applications, including enforcing non-interference and automating secrecy-preserving refinement mapping. We also evaluate our approach using the battleship game and password validation use cases.