International Association
for Cryptologic Research

The dream of software obfuscation is to take programs, as they are, and then generically compile them into obfuscated versions that hide their secret inner workings. In this work we investigate notions of obfuscations weaker than virtual black-box (VBB) but which still allow obfuscating cryptographic primitives preserving their original functionalities as much as possible. In particular we propose two new notions of obfuscations, which we call oracle-differing-input obfuscation (odiO) and oracle-indistinguishability obfuscation (oiO). In a nutshell, odiO is a natural strengthening of differing-input obfuscation (diO) and allows obfuscating programs for which it is hard to find a differing-input when given only oracle access to the programs. An oiO obfuscator allows to obfuscate programs that are hard to distinguish when treated as oracles. We then show applications of these notions, as well as positive and negative results around them. A few highlights include: – Our new notions are weaker than VBB and stronger than diO. – As it is the case for VBB, we show that there exist programs that cannot be obfuscated with odiO or oiO. – Our new notions allow to generically compile several flavours of secret-key primitives (e.g., SKE, MAC, designated verifier NIZK) into their public-key equivalent (e.g., PKE, signatures, publicly verifiable NIZK) while preserving one of the algorithms of the original scheme (function-preserving), or the structure of their outputs (format-preserving).

We advance the state-of-the art for zero-knowledge commit-and-prove SNARKs (CP-SNARKs). CP-SNARKs are an important class of SNARKs which, using commitments as ``glue'', allow to efficiently combine proof systems---e.g., general-purpose SNARKs (an efficient way to prove statements about circuits) and $\Sigma$-protocols (an efficient way to prove statements about group operations). Thus, CP-SNARKs allow to efficiently provide zero-knowledge proofs for composite statements such as $h=H(g^{x})$ for some hash-function $H$. Our main contribution is providing the first construction of CP-SNARKs where the proof size is succinct in the number of commitments. We achieve our result by providing a general technique to compile Algebraic Holographic Proofs (AHP) (an underlying abstraction used in many modern SNARKs) with special ``decomposition'' properties into an efficient CP-SNARK. We then show that some of the most efficient AHP constructions---Marlin, PLONK, and Sonic---satisfy our compilation requirements. Our resulting SNARKs achieve universal and updatable reference strings, which are highly desirable features as they greatly reduce the trust needed in the SNARK setup phase.

Vector commitments (VC) are a cryptographic primitive that allow one to commit to a vector and then “open” some of its positions efficiently. Vector commitments are increasingly recognized as a central tool to scale highly decentralized networks of large size and whose content is dynamic. In this work, we examine the demands on the properties that an ideal vector commitment should satisfy in the light of the emerging plethora of practical applications and propose new constructions that improve the state-of-the-art in several dimensions and offer new tradeoffs. We also propose a unifying framework that captures several constructions and show how to generically achieve some properties from more basic ones.

A number of recent works have constructed cryptographic protocols with flavors of adaptive security by having a randomly-chosen anonymous committee run at each round. Since most of these protocols are stateful, transferring secret states from past committees to future, but still unknown, committees is a crucial challenge. Previous works have tackled this problem with approaches tailor-made for their specific setting, which mostly rely on using a blockchain to orchestrate auxiliary committees that aid in the state hand-over process. In this work, we look at this challenge as an important problem on its own and initiate the study of Encryption to the Future (EtF) as a cryptographic primitive. First, we define a notion of an EtF scheme where time is determined with respect to an underlying blockchain and a lottery selects parties to receive a secret message at some point in the future. While this notion seems overly restrictive, we establish two important facts: 1. if used to encrypt towards parties selected in the “far future”, EtF implies witness encryption for NP over a blockchain; 2. if used to encrypt only towards parties selected in the “near future”, EtF is not only sufficient for transferring state among committees as required by previous works, but also captures previous tailor-made solutions. To corroborate these results, we provide a novel construction of EtF based on witness encryption over commitments (cWE), which we instantiate from a number of standard assumptions via a construction based on generic cryptographic primitives. Finally, we show how to use “near future” EtF to obtain “far future” EtF with a protocol based on an auxiliary committee whose communication complexity is independent of the length of plaintext messages being sent to the future.

We study how to construct zkSNARKs whose SRS is universal and updatable, i.e., valid for all relations within a size-bound and to which a dynamic set of participants can indefinitely add secret randomness. Our focus is: efficient universal updatable zkSNARKs with linear-size SRS and their commit-and-prove variants. We both introduce new formal frameworks and techniques, as well as systematize existing ones. We achieve a collection of zkSNARKs with different tradeoffs. One of our schemes achieves the smallest proof size and proving time compared to the state of art for proofs for arithmetic circuits. The language supported by this scheme is a variant of R1CS that we introduce, called R1CS-lite. Another of our constructions directly supports standard R1CS and achieves the fastest proving time for this type of constraints. These results stem from different contributions: (1) a new algebraically-flavored variant of IOPs that we call Polynomial Holographic IOPs (PHPs); (2) a new compiler that combines our PHPs with commit-and-prove zk-SNARKs (CP-SNARKs) for committed polynomials; (3) pairing-based realizations of these CP-SNARKs for polynomials; (4) constructions of PHPs for R1CS and R1CS-lite. Finally, we extend the compiler in item (2) to yield commit-and-prove universal zkSNARKs.

Vector commitments with subvector openings (SVC) [Lai-Malavolta, Boneh-Bunz-Fisch; CRYPTO'19] allow one to open a committed vector at a set of positions with an opening of size independent of both the vector's length and the number of opened positions. We continue the study of SVC with two goals in mind: improving their efficiency and making them more suitable to decentralized settings. We address both problems by proposing a new notion for VC that we call \emph{incremental aggregation} and that allows one to merge openings in a succinct way an \emph{unbounded} number of times. We show two applications of this property. The first one is immediate and is a method to generate openings in a distributed way. The second application is an algorithm for faster generation of openings via preprocessing. We then proceed to realize SVC with incremental aggregation. We provide two constructions in groups of unknown order that, similarly to that of Boneh et al. (which supports aggregating only once), have constant-size public parameters, commitments and openings. As an additional feature, for the first construction we propose efficient arguments of knowledge of subvector openings which immediately yields a keyless proof of storage with compact proofs. Finally, we address a problem closely related to that of SVC: storing a file efficiently in completely decentralized networks. We introduce and construct \emph{verifiable decentralized storage} (VDS), a cryptographic primitive that allows to check the integrity of a file stored by a network of nodes in a distributed and decentralized way. Our VDS constructions rely on our new vector commitment techniques.

This paper initiates a study of Fine Grained Secure Computation: i.e. the construction of secure computation primitives against “moderately complex” adversaries. We present definitions and constructions for compact Fully Homomorphic Encryption and Verifiable Computation secure against (non-uniform) $$\mathsf {NC}^1$$ adversaries. Our results do not require the existence of one-way functions and hold under a widely believed separation assumption, namely $$\mathsf {NC}^{1}\subsetneq \oplus \mathsf {L}/ {\mathsf {poly}}$$ . We also present two application scenarios for our model: (i) hardware chips that prove their own correctness, and (ii) protocols against rational adversaries potentially relevant to the Verifier’s Dilemma in smart-contracts transactions such as Ethereum.