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Verifying imperative programs is hard. A key difficulty is that the specification of what an imperative program does is often intertwined with details about pointers and imperative state. Although there are a number of powerful separation logics that allow the details of imperative state to be captured and managed, these details are complicated and reasoning about them requires significant time and expertise. In this paper, we take a different approach: a memory-safe type system that, as part of type-checking, extracts functional specifications from imperative programs. This disentangles imperative state, which is handled by the type system, from functional specifications, which can be verified without reference to pointers. A key difficulty is that sometimes memory safety depends crucially on the functional specification of a program; e.g., an array index is only memory-safe if the index is in bounds. To handle this case, our specification extraction inserts dynamic checks into the specification. Verification then requires the additional proof that none of these checks fail. However, these checks are in a purely functional language, and so this proof also requires no reasoning about pointers.

We construct public-key function-private predicate encryption for the “small superset functionality,” recently introduced by Beullens and Wee (PKC 2019). This functionality captures several important classes of predicates: Point functions. For point function predicates, our construction is equivalent to public-key function-private anonymous identity-based encryption. Conjunctions. If the predicate computes a conjunction, our construction is a public-key function-private hidden vector encryption scheme. This addresses an open problem posed by Boneh, Raghunathan, and Segev (ASIACRYPT 2013). d-CNFs and read-once conjunctions of d-disjunctions for constant-size d.

Program obfuscation is a powerful security primitive with many applications. White-box cryptography studies a particular subset of program obfuscation targeting keyed pseudorandom functions (PRFs), a core component of systems such as mobile payment and digital rights management. Although the white-box obfuscators currently used in practice do not come with security proofs and are thus routinely broken, recent years have seen an explosion of cryptographic techniques for obfuscation, with the goal of avoiding this build-and-break cycle. In this work, we explore in detail cryptographic program obfuscation and the related primitive of multi-input functional encryption (MIFE). In particular, we extend the 5Gen framework (CCS 2016) to support circuit-based MIFE and program obfuscation, implementing both existing and new constructions. We then evaluate and compare the efficiency of these constructions in the context of PRF obfuscation. As part of this work we (1) introduce a novel instantiation of MIFE that works directly on functions represented as arithmetic circuits, (2) use a known transformation from MIFE to obfuscation to give us an obfuscator that performs better than all prior constructions, and (3) develop a compiler for generating circuits optimized for our schemes. Finally, we provide detailed experiments, demonstrating, among other things, the ability to obfuscate a PRF with a 64-bit key and 12 bits of input (containing 62k gates) in under 4 hours, with evaluation taking around 1 hour. This is by far the most complex function obfuscated to date.

Secure multilinear maps (mmaps) have been shown to have remarkable applications in cryptography, such as multi-input functional encryption (MIFE) and program obfuscation. To date, there has been little evaluation of the performance of these applications. In this paper we initiate a systematic study of mmap-based constructions. We build a general framework, called 5Gen, to experiment with these applications. At the top layer we develop a compiler that takes in a high-level program and produces an optimized matrix branching program needed for the applications we consider. Next, we optimize and experiment with several MIFE and obfuscation constructions and evaluate their performance. The 5Gen framework is modular and can easily accommodate new mmap constructions as well as new MIFE and obfuscation constructions, as well as being an open-source tool that can be used by other research groups to experiment with a variety of mmap-based constructions.

A wide variety of objectively practical cryptographic schemes can be constructed using only symmetric-key operations and linear operations. To formally study this restricted class of cryptographic algorithms, we present a new model called Linicrypt. A Linicrypt program has access to a random oracle whose inputs and outputs are field elements, and otherwise manipulates data only via fixed linear combinations. Our main technical result is that it is possible to decide in polynomial time whether two given Linicrypt programs induce computationally indistinguishable distributions against arbitrary PPT adversaries, in the random oracle model. We show also that indistinguishability of Linicrypt programs can be expressed as an existential formula, making the model amenable to automated program synthesis. In other words, it is possible to use a SAT/SMT solver to automatically generate Linicrypt programs satisfying a given security constraint. Interestingly, the properties of Linicrypt imply that this synthesis approach is both sound and complete. We demonstrate this approach by synthesizing Linicrypt constructions of garbled circuits.