## CryptoDB

### Nicholas Spooner

#### Publications

Year
Venue
Title
2022
EUROCRYPT
Succinct non-interactive arguments of knowledge (SNARKs) are cryptographic proofs with strong efficiency properties. Applications of SNARKs often involve proving computations that include the SNARK verifier, a technique called recursive composition. Unfortunately, SNARKs with desirable features such as a transparent (public-coin) setup are known only in the random oracle model (ROM). In applications this oracle must be heuristically instantiated and used in a non-black-box way. In this paper we identify a natural oracle model, the low-degree random oracle model, in which there exist transparent SNARKs for all NP computations *relative to this oracle*. Informally, letting $O$ be a low-degree encoding of a random oracle, and assuming the existence of (standard-model) collision-resistant hash functions, there exist SNARKs relative to $O$ for all languages in $NP^{O}$. Such a SNARK can directly prove a computation about its own verifier. To analyze this model, we introduce a more general framework, the *linear code random oracle model* (LCROM). We show how to obtain SNARKs in the LCROM for computations that query the oracle, given an *accumulation scheme* for oracle queries. Then we construct such an accumulation scheme for the special case of a low degree random oracle.
2021
CRYPTO
Proof-carrying data (PCD) is a powerful cryptographic primitive that enables mutually distrustful parties to perform distributed computations that run indefinitely. Known approaches to construct PCD are based on succinct non-interactive arguments of knowledge (SNARKs) that have a succinct verifier or a succinct accumulation scheme. In this paper we show how to obtain PCD without relying on SNARKs. We construct a PCD scheme given any non-interactive argument of knowledge (e.g., with linear-size arguments) that has a *split accumulation scheme*, which is a weak form of accumulation that we introduce. Moreover, we construct a transparent non-interactive argument of knowledge for R1CS whose split accumulation is verifiable via a (small) *constant number of group and field operations*. Our construction is proved secure in the random oracle model based on the hardness of discrete logarithms, and it leads, via the random oracle heuristic and our result above, to concrete efficiency improvements for PCD. Along the way, we construct a split accumulation scheme for Hadamard products under Pedersen commitments and for a simple polynomial commitment scheme based on Pedersen commitments. Our results are supported by a modular and efficient implementation.
2020
EUROCRYPT
We present a new methodology to efficiently realize recursive composition of succinct non-interactive arguments of knowledge (SNARKs). Prior to this work, the only known methodology relied on pairing-based SNARKs instantiated on cycles of pairing-friendly elliptic curves, an expensive algebraic object. Our methodology does not rely on any special algebraic objects and, moreover, achieves new desirable properties: it is post-quantum and it is transparent (the setup is public coin). We exploit the fact that recursive composition is simpler for SNARKs with preprocessing, and the core of our work is obtaining a preprocessing zkSNARK for rank-1 constraint satisfiability (R1CS) that is post-quantum and transparent. We obtain this latter by establishing a connection between holography and preprocessing in the random oracle model, and then constructing a holographic proof for R1CS. We experimentally validate our methodology, demonstrating feasibility in practice.
2020
TCC
Recursive proof composition has been shown to lead to powerful primitives such as incrementally-verifiable computation (IVC) and proof-carrying data (PCD). All existing approaches to recursive composition take a succinct non-interactive argument of knowledge (SNARK) and use it to prove a statement about its own verifier. This technique requires that the verifier run in time sublinear in the size of the statement it is checking, a strong requirement that restricts the class of SNARKs from which PCD can be built. This in turn restricts the efficiency and security properties of the resulting scheme. Bowe, Grigg, and Hopwood (ePrint 2019/1021) outlined a novel approach to recursive composition, and applied it to a particular SNARK construction which does *not* have a sublinear-time verifier. However, they omit details about this approach and do not prove that it satisfies any security property. Nonetheless, schemes based on their ideas have already been implemented in software. In this work we present a collection of results that establish the theoretical foundations for a generalization of the above approach. We define an *accumulation scheme* for a non-interactive argument, and show that this suffices to construct PCD, even if the argument itself does not have a sublinear-time verifier. Moreover we give constructions of accumulation schemes for SNARKs, which yield PCD schemes with novel efficiency and security features.
2019
EUROCRYPT
We design, implement, and evaluate a zero knowledge succinct non-interactive argument (SNARG) for Rank-1 Constraint Satisfaction (R1CS), a widely-deployed NP language undergoing standardization. Our SNARG has a transparent setup, is plausibly post-quantum secure, and uses lightweight cryptography. A proof attesting to the satisfiability of n constraints has size $O(\log ^2 n)$O(log2n); it can be produced with $O(n \log n)$O(nlogn) field operations and verified with O(n). At 128 bits of security, proofs are less than ${250}\,\mathrm{kB}$250kB even for several million constraints, more than $10{\times }$10× shorter than prior SNARGs with similar features.A key ingredient of our construction is a new Interactive Oracle Proof (IOP) for solving a univariate analogue of the classical sumcheck problem [LFKN92], originally studied for multivariate polynomials. Our protocol verifies the sum of entries of a Reed–Solomon codeword over any subgroup of a field.We also provide $\texttt {libiop}$libiop, a library for writing IOP-based arguments, in which a toolchain of transformations enables programmers to write new arguments by writing simple IOP sub-components. We have used this library to specify our construction and prior ones, and plan to open-source it.
2019
TCC
Succinct non-interactive arguments (SNARGs) are highly efficient certificates of membership in non-deterministic languages. Constructions of SNARGs in the random oracle model are widely believed to be post-quantum secure, provided the oracle is instantiated with a suitable post-quantum hash function. No formal evidence, however, supports this belief.In this work we provide the first such evidence by proving that the SNARG construction of Micali is unconditionally secure in the quantum random oracle model. We also prove that, analogously to the classical case, the SNARG inherits the zero knowledge and proof of knowledge properties of the PCP underlying the Micali construction. We thus obtain the first zero knowledge SNARG of knowledge (zkSNARK) that is secure in the quantum random oracle model.Our main tool is a new lifting lemma that shows how, for a rich class of oracle games, we can generically deduce security against quantum attackers by bounding a natural classical property of these games. This means that in order to prove our theorem we only need to establish classical properties about the Micali construction. This approach not only lets us prove post-quantum security but also enables us to prove explicit bounds that are tight up to small factors.We additionally use our techniques to prove that SNARGs based on interactive oracle proofs (IOPs) with round-by-round soundness are unconditionally secure in the quantum random oracle model. This result establishes the post-quantum security of many SNARGs of practical interest.
2019
TCC
We study the problem of delegating computations via interactive proofs that can be probabilistically checked. Known as interactive oracle proofs (IOPs), these proofs extend probabilistically checkable proofs (PCPs) to multi-round protocols, and have received much attention due to their application to constructing cryptographic proofs (such as succinct non-interactive arguments). The relevant complexity measures for IOPs in this context are prover and verifier time, and query complexity.We construct highly efficient IOPs for a rich class of nondeterministic algebraic computations, which includes succinct versions of arithmetic circuit satisfiability and rank-one constraint system (R1CS) satisfiability. For a time-T computation, we obtain prover arithmetic complexity $O(T \log T)$ and verifier complexity polylog(T). These IOPs are the first to simultaneously achieve the state of the art in prover complexity, due to [14], and in verifier complexity, due to [7]. We also improve upon the query complexity of both schemes.The efficiency of our prover is a result of our highly optimized proof length; in particular, ours is the first construction that simultaneously achieves linear-size proofs and polylogarithmic-time verification, regardless of query complexity.
2017
TCC
2016
TCC

TCC 2020