732 research outputs found
Relational Symbolic Execution
Symbolic execution is a classical program analysis technique used to show
that programs satisfy or violate given specifications. In this work we
generalize symbolic execution to support program analysis for relational
specifications in the form of relational properties - these are properties
about two runs of two programs on related inputs, or about two executions of a
single program on related inputs. Relational properties are useful to formalize
notions in security and privacy, and to reason about program optimizations. We
design a relational symbolic execution engine, named RelSym which supports
interactive refutation, as well as proving of relational properties for
programs written in a language with arrays and for-like loops
Advanced Probabilistic Couplings for Differential Privacy
Differential privacy is a promising formal approach to data privacy, which
provides a quantitative bound on the privacy cost of an algorithm that operates
on sensitive information. Several tools have been developed for the formal
verification of differentially private algorithms, including program logics and
type systems. However, these tools do not capture fundamental techniques that
have emerged in recent years, and cannot be used for reasoning about
cutting-edge differentially private algorithms. Existing techniques fail to
handle three broad classes of algorithms: 1) algorithms where privacy depends
accuracy guarantees, 2) algorithms that are analyzed with the advanced
composition theorem, which shows slower growth in the privacy cost, 3)
algorithms that interactively accept adaptive inputs.
We address these limitations with a new formalism extending apRHL, a
relational program logic that has been used for proving differential privacy of
non-interactive algorithms, and incorporating aHL, a (non-relational) program
logic for accuracy properties. We illustrate our approach through a single
running example, which exemplifies the three classes of algorithms and explores
new variants of the Sparse Vector technique, a well-studied algorithm from the
privacy literature. We implement our logic in EasyCrypt, and formally verify
privacy. We also introduce a novel coupling technique called \emph{optimal
subset coupling} that may be of independent interest
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Computer-aided verification in mechanism design
In mechanism design, the gold standard solution concepts are dominant
strategy incentive compatibility and Bayesian incentive compatibility. These
solution concepts relieve the (possibly unsophisticated) bidders from the need
to engage in complicated strategizing. While incentive properties are simple to
state, their proofs are specific to the mechanism and can be quite complex.
This raises two concerns. From a practical perspective, checking a complex
proof can be a tedious process, often requiring experts knowledgeable in
mechanism design. Furthermore, from a modeling perspective, if unsophisticated
agents are unconvinced of incentive properties, they may strategize in
unpredictable ways.
To address both concerns, we explore techniques from computer-aided
verification to construct formal proofs of incentive properties. Because formal
proofs can be automatically checked, agents do not need to manually check the
properties, or even understand the proof. To demonstrate, we present the
verification of a sophisticated mechanism: the generic reduction from Bayesian
incentive compatible mechanism design to algorithm design given by Hartline,
Kleinberg, and Malekian. This mechanism presents new challenges for formal
verification, including essential use of randomness from both the execution of
the mechanism and from the prior type distributions. As an immediate
consequence, our work also formalizes Bayesian incentive compatibility for the
entire family of mechanisms derived via this reduction. Finally, as an
intermediate step in our formalization, we provide the first formal
verification of incentive compatibility for the celebrated
Vickrey-Clarke-Groves mechanism
Computer-aided proofs for multiparty computation with active security
Secure multi-party computation (MPC) is a general cryptographic technique
that allows distrusting parties to compute a function of their individual
inputs, while only revealing the output of the function. It has found
applications in areas such as auctioning, email filtering, and secure
teleconference. Given its importance, it is crucial that the protocols are
specified and implemented correctly. In the programming language community it
has become good practice to use computer proof assistants to verify correctness
proofs. In the field of cryptography, EasyCrypt is the state of the art proof
assistant. It provides an embedded language for probabilistic programming,
together with a specialized logic, embedded into an ambient general purpose
higher-order logic. It allows us to conveniently express cryptographic
properties. EasyCrypt has been used successfully on many applications,
including public-key encryption, signatures, garbled circuits and differential
privacy. Here we show for the first time that it can also be used to prove
security of MPC against a malicious adversary. We formalize additive and
replicated secret sharing schemes and apply them to Maurer's MPC protocol for
secure addition and multiplication. Our method extends to general polynomial
functions. We follow the insights from EasyCrypt that security proofs can be
often be reduced to proofs about program equivalence, a topic that is well
understood in the verification of programming languages. In particular, we show
that in the passive case the non-interference-based definition is equivalent to
a standard game-based security definition. For the active case we provide a new
NI definition, which we call input independence
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